1. The method for solving the distributed constraint optimization problem based on ant colony inheritance is characterized by comprising the following steps of:

s100, representing the distributed constraint optimization problem by using a quadruple < A, X, D and F > in which:

A＝{a₁,...,a_nis a collection of agents;

X＝{x₁,...,x_mis a set of variables, m ≦ n;

D＝{D₁,...,D_mis a set of value ranges, each x_iHas a value range of D_iEach Agent slave value range D_iThe middle value being a variable x_iThe value is assigned to the value to be assigned, denotes x_iThe tth value of (a);

F＝{f₁,...,f_pis a set of constraint cost functions, constraintsIs from arbitrary k variablesA mapping of the combination of assignments of (a) to a non-negative cost;

if an agent only controls one variable and all constraint relations are binary relations, the solution of DCOP is represented as:

representing DCOP as a constraint graph, wherein each node represents an agent, and a connecting line between every two nodes represents that a constraint relation exists between the two nodes in the constraint graph;

s200: initializing parameters of an ant colony algorithm and a genetic algorithm, converting a constraint graph into a pseudo tree generated with breadth first, wherein one node corresponds to one agent, a connecting line between the nodes represents constraint, the value message transmission direction of the pseudo tree is transmitted to a lower node by an upper node, the nodes on the same layer are transmitted according to the priority or the node naming letter sequence, and the message transmission direction is the priority of the agent and the advancing direction of ants;

preset x_iGetAnd x_i’Get(ii) a constrained pheromone concentration where i ≠ 1,2, … n, i ≠ 1,2, … n, i ≠ i' T ═ 1,2, … T;

s300: traversing n agents once by adopting the ant colony algorithm, if a is currently available_iHaving received value messages from all of its higher priority neighbors, then a_iFor each antAt the x_iSelecting a value in the corresponding value range according to the value selection probability, and calculating a according to the current value_iThe sum of the costs of all the high-priority neighbors and the cost of the current ant is accumulated with the cost calculated before;

s400: generating a random probability q, if q is smaller than an expansion probability p, switching to S500 if the expansion solution space is satisfied, and otherwise, switching to S900;

s500: if the ant colony algorithm has K ants in total, each ant in S300 takes the values of n agents to obtain a set, and then the set is regarded as a chromosome, and S300 obtains K chromosomes aiming at the K ants, and the K chromosomes are taken as parent chromosomes of the genetic algorithm;

s600: calculating the adaptive value of each chromosome in S500, calculating the ratio of the adaptive value of each chromosome in the sum of the adaptive values of all chromosomes, directly copying and storing the chromosome with the largest adaptive value in the K chromosomes into a first generation offspring chromosome set, then calculating the selection probability of each chromosome, wherein the selection probability of each chromosome is equal to the ratio of the adaptive value of the chromosome to the sum of the adaptive values of all chromosomes, and selecting a new parent chromosome set K-1 chromosome by adopting roulette according to the selection probability;

selecting roulette: the cumulative selection probability, p [ k ], for each chromosome is calculated]Called the cumulative probability of chromosome k, i.e., the sum of the selection probabilities of the first k-1 chromosomes; generating K-1 random numbersLet k equal to 1, in the new parent chromosome set, according to the order of the chromosomes, when the cumulative probability of one chromosome is greater than or equal toCopying and storing the chromosome into a first generation child chromosome set, making k equal to k +1, continuing to select in a new parent chromosome set according to the ordering of the chromosomes, and when the cumulative probability of one chromosome is more than or equal to the cumulative probability of one chromosomeCopying and storing the chromosome into a first generation offspring chromosome set, and repeating the steps in sequence until K is equal to K-1, and selecting K-1 first generation offspring chromosomes;

s700: chromosome crossing and mutation:

chromosome crossing:

setting the cross probability, generating a cross random probability, q, for the kth first generation offspring chromosome_xDenotes the cross random probability of the x-th first generation offspring chromosome, x ═ 1,3_xIf the cross probability is less than the cross probability, crossing the cross positions corresponding to the x-th first generation offspring chromosome and the x-1 th first generation offspring chromosome, wherein the cross positions are generated randomly;

the first generation filial generation chromosomes needing chromosome crossing are copied and stored into a new first generation filial generation chromosome set after the chromosome crossing is completed, the first generation filial generation chromosomes which do not need chromosome crossing are copied and stored into the new first generation filial generation chromosome set, and the chromosomes in the first generation filial generation chromosome set are called as new first generation filial generation chromosomes;

chromosomal variation:

setting variation probability, generating a random variation probability for n positions on the new first generation offspring chromosome,represents the random variation probability of the x position of the k new first generation offspring chromosome whenWhen the variation probability is smaller than the variation probability, the value of the x-th position of the kth new first generation offspring chromosome is varied, and the variation method is to randomly select one value from the value domain to reassign the position;

the new first generation offspring chromosomes which need to carry out chromosome variation are copied and stored into a second generation offspring chromosome set after the chromosome variation is finished, the new first generation offspring chromosomes which do not need to carry out chromosome variation are copied and stored into the second generation offspring chromosome set, and chromosomes in the second generation offspring chromosome set are called as second generation offspring chromosomes;

s800: judging whether the genetic algorithm is finished in iteration, if the maximum iteration number of the running of the genetic algorithm is reached and the termination condition is met, outputting the second generation child chromosomes in the current second generation child chromosome set and transferring to S900, and otherwise, updating the parent chromosomes by adopting the second generation child chromosomes and transferring to S600;

s900: updating pheromone concentration and local information context estimated values on the path;

when the cost of each chromosome in the second generation offspring chromosome set is less than the expansion probability p, updating the pheromone concentration by using the cost of each chromosome in the second generation offspring chromosome set, otherwise, updating the pheromone concentration by using the cost of each chromosome in the K ant set, and updating the pheromone concentration constrained between each agent and the neighbor by using K chromosomes;

updating the prediction value of the local information context for each agent, and updating the value d_i∈D_iWhen variable x_i＝d_iCalculating the average value of the constraint cost generated between the current agent and the low-priority neighbor node thereof, and averaging the current non-updated pre-estimated value and the average value again to obtain an updated pre-estimated value;

s1000: and judging whether the iteration of the ant colony algorithm is finished, if the maximum iteration number of the ant colony algorithm operation is reached, indicating that the termination condition is met, outputting the cost corresponding to the chromosome with the minimum current cost and the values of the n variables, and if not, returning to the step S300.

2. The method for solving the ant colony genetic-based distributed constraint optimization problem of claim 1, wherein: the calculation method of the ant probability in S300 is shown in formula (7):

in the formula p_k,i(d_i) Expressing ant probability, alpha is pheromone factor weight, beta is heuristic factor weight, theta_k,i(d′_i) Denotes a selection value d'_iConcentration of pheromone of [ (. eta. ])_k,i(d′_i) Denotes a selection value d'_iA heuristic value of_k,i(d_i) Is a pheromone factor, η_k,i(d_i) Is a heuristic factor:

pheromone factor theta_k,i(d_i) The calculation formula is shown in formula (8):

in the formula H_iFor the set of high priority nodes of the node, the constrained pheromone tau between two nodes_ij(d_i,V_k,j)、V_k,jIndicating a high priority node a_jGiving the value selected by the ant k; heuristic factor eta_k,i(d_i) The calculation formula is shown in formula (9):

in the formula cost_ij(d_i,V_k,j) Is x_i＝d_i，x_j＝V_k,jConstraint of time f_ijCost of generation, when x_i＝d_iWhen, est_i(d_i) Is to a_iThe minimum cost sum of the low-priority neighbors is calculated according to the formula (10):

wherein cost_ij(d_i,d_j) Denotes x_i＝d_i，x_j＝d_jThe cost of time constraint generation;

LB is the current node a_iWith its high priority,The minimum cost sum of the low-priority neighbors is calculated according to the formula (11):

3. the method for solving the ant colony genetic-based distributed constraint optimization problem of claim 1, wherein: in S400, the spreading probability p is calculated by using formula (12):

in the formula, maxCycle is the maximum iteration round, and currcycle is the current round.

4. The method for solving the ant colony genetic-based distributed constraint optimization problem of claim 1, wherein: the method for calculating the fitness value of each chromosome in S600 is as follows:

wherein cost_kThe size of the cost for the kth chromosome,is the sum of the costs of all chromosomes.

5. The method for solving the ant colony genetic-based distributed constraint optimization problem of claim 1, wherein: the method for calculating the cost of each second generation offspring chromosome in S900 is as follows:

for the kth second generation child chromosome, adding the cost corresponding to the constraint between each agent and the neighbor thereof to remember the cost of the kth second generation child chromosome_k。

6. The method of solving an ant colony genetic-based distributed constraint optimization problem of claim 5, wherein: the process of updating the pheromone of the constraint between each agent and its neighbor in the kth second generation child chromosome in S900 is as follows:

the updating process includes the increase and/or decrease of pheromone, and the updating method when the pheromone is increased is shown in formula (15):

updating pheromone constrained between each agent and its neighbor in the kth second generation child chromosome by adopting the method of formula (15), wherein k is 1,2, … n:

in the formula,. DELTA._kFor pheromone increment, τ_ij(V_k,i,V_k,j) Denotes a_iTaking the value of ant k as V_k,i，a_jTaking the value of ant k as V_k,jConcentration of pheromone on the corresponding path, delta_k,ijIs a_iAnd a_jSee equation (16) for the calculation formula for pheromone weighting results in between:

where λ is the number of constraints in DCOP, cost_ij(V_k,i,V_k,j) Denotes a_iTaking the value of ant k as V_k,i，a_jTaking the value of ant k as V_k,jCost value of time, cost (V)_k,*) Represents the total cost of ant k;

where mincost is the minimum cost in the second generation offspring chromosomes, cost_kThe cost of the k-th chromosome is expressed,cost_k′represents the cost of the k' th chromosome,the average value of the sum of all the second generation offspring chromosome costs;

for the update method when pheromone is reduced, see formula (17):

τ_ij(d_i,d_j)＝(1-ρ)τ_ij(d_i,d_j)+ρτ₀ (17)

in the formula tau_ij(d_i,d_j) Denotes a_iTaking the value of ant k as d_i，a_jTaking the value of ant k as d_jConcentration of pheromone on hour path, j ∈ H_i，τ₀Representing the initial pheromone concentration, tau₀Where ρ < 1 is 0 < 3, the evaporation rate and pheromone concentration range is [ τ ]_min,τ_max]。

7. The method of solving an ant colony genetic-based distributed constraint optimization problem of claim 5, wherein: the process of updating the estimate of the minimum cost sum of the low-priority neighbors of each agent in each second generation child chromosome in S900 is as follows: firstly when x_i＝d_iWhen, calculate a_iThe sum of the constraint costs incurred between its low priority neighbors is averaged, and then est is added_i(d_i) The value obtained by the last iteration and the average value obtained currently are subjected to average solution, and the obtained value is updated est_i(d_i)。

8. The application of the method for solving the problem of the distributed constraint optimization based on the ant colony inheritance is characterized in that the method for solving the problem of the distributed constraint optimization based on the ant colony inheritance in claim 7 is applied to the problem of emergency rescue in urban emergencies;

giving a problem traffic network G (C, E), wherein C represents a node in the network, E represents a connecting line between two nodes, namely a road section, and simultaneously, a passable path planning of the urban emergency is constructed into a DCOP model which is marked as the DCOP model of the urban emergency, and the model is described in detail as follows:

A＝{car₁,...,car_na vehicle represents an agent;

X＝{x₁,...,x_mis a collection of variables, one agent controls one variable x_i；

D＝{S₁,...,S_mIs a set of value ranges, each variable x_iHas a value range of S_i，S_iWhere is a set of feasible paths, one feasible path is a variable x_iOne value of (a);

F＝{f₁,...,f_pis a constraint, f_ijFor the constraint between two vehicle travel paths, that is, the coincidence degree of the paths between two feasible paths is less than 30%, since the travel paths between each two vehicles need to satisfy the constraint, the abstracted constraint graph of the DCOP model of the urban emergency is a full-connection constraint graph.

9. The method of solving an ant colony genetic-based distributed constraint optimization problem of claim 8, wherein: solving x in DCOP model of urban emergency through following objective function_iGetAnd x_i’GetThe cost of time constraint comprises the following specific steps:

1) and (3) calculating the running speed of the vehicle by adopting the Underwood model in the formula (2):

in the formula v_fIs the maximum speed on the road section h,is the speed of vehicle travel on road section h, c is the actual traffic density on road section h, c_mIs the maximum traffic density on road section h;

2) the route is time-consuming, and the formula (3) is the time-consuming cost of any normal road section_i：

In the formula s_iIs the length of road segment h;

the time-consuming cost of the accident influence range is determined by adopting a BPR (path per path) resistance function, and the formula (4) is the time-consuming cost of any path with a fault:

where normal is the set of m normal segments, break is the set of n failed segments,is the actual travel time at the link k, t_kIs the travel time of the free stream at the link k, q_kIs the traffic flow at the link k, C_kRepresenting the traffic capacity at a road section k, the influence factor is a random variable phi obeying uniform distribution when the road section k is influenced by an emergency_k(0＜φ_k< 1), the maximum traffic density at the section k is c_kThen the actual traffic capacity of the road section k is phi_kc_kThe parameters a and b are constants; s_hIndicates the length of the trouble-free section h,representing the driving speed on the trouble-free road section h;

let the length of path 1 be len₁Path 2 has a length of len₂，len₁＜len₂Of path 1 and path 2The length of the overlapped part between the paths is opart, the overlapping rate between the path 1 and the path 2 is set to be less than 30%, and then the constraint between the path 1 and the path 2 is f₁₂:opart/len₁< 30%, equation (5) is the constraint cost between the feasible paths chosen for each two vehicles:

in the formula cost_iCost for path i, cost_jAnd the time-consuming cost of the path j is the sum of the time-consuming costs of the two paths when the constraint is satisfied, otherwise, a very large value is taken.

Background

DCOP(Distributed Constraint Optimiztion schemes, DCOP) is the basic framework of a Multi-agent System (MAS) in which agents need to collaborate together in decisions to optimize a global goal. The DCOP model has been successfully applied to various practical problems such as sensor networks, resource allocation, etc. There are many existing algorithms for solving DCOP, and the algorithms can be divided into two categories according to the difference of solving targets: a complete algorithm and a non-complete algorithm. The complete algorithm obtains the optimal solution by traversing all solution spaces of the problem, and a typical complete algorithm based on search comprises SynchBB^[7]、ADOPT^[8]、BnB-ADOPT^[9]Etc., complete algorithm DPOP based on reasoning^[10]Dynamic programming techniques are employed to solve for DCOP. However, DCOP is an NP-hard problem, but for large scale problems, the time and space costs of a complete algorithm are too large, so that by using an incomplete algorithm, the time efficiency can be greatly improved and the occupied space can be reduced at the expense of some accuracy of the solution. Among the non-complete algorithms, the algorithm based on the local search strategy is a research hotspot, and such algorithms include DSA, MGM2, etc., however, when these algorithms are optimized, the quality of the solution cannot be guaranteed. To improve the solution quality of the local search algorithm, the frameworks such as ALS, LSGA, etc. are proposed for solving the DCOP.

Recently, many swarm intelligence optimization ideas have also gradually been used to solve DCOP, such as ant colony optimization ideas. Compared with the traditional algorithm, after the group intelligent optimization thought is added, the algorithm can be optimized to a solution with better quality. Ziyu Chen et al propose An Ant colony Optimization concept-based DCOP solution Algorithm ACO _ DCOP (An Ant-based Algorithm to solution Distributed Optimization schemes, ACO _ DCOP), which utilizes Ant pheromones to mark paths of a desired solution and searches for areas in a solution space where a better solution is expected. However, due to the pheromone decay mechanism of the ant colony algorithm, the algorithm may fall into local optima.

Disclosure of Invention

Aiming at the problems in the prior art, the technical problems to be solved by the invention are as follows: how to effectively avoid falling into local optimization when solving the DCOP.

In order to solve the technical problems, the invention adopts the following technical scheme: the method for solving the distributed constraint optimization problem based on ant colony inheritance comprises the following steps:

s100, representing the distributed constraint optimization problem by using a quadruple < A, X, D and F > in which:

A＝{a₁,...,a_nis a collection of agents;

X＝{x₁,...,x_mis a set of variables, m ≦ n;

D＝{D₁,...,D_mis a set of value ranges, each x_iHas a value range of D_iEach Agent slave value range D_iThe middle value being a variable x_iThe value is assigned to the value to be assigned, denotes x_iThe tth value of (a);

F＝{f₁,...,f_pis a set of constraint cost functions, constraintsIs from arbitrary k variablesA mapping of the combination of assignments of (a) to a non-negative cost;

if an agent only controls one variable and all constraint relations are binary relations, the solution of DCOP is represented as:

representing DCOP as a constraint graph, wherein each node represents an agent, and a connecting line between every two nodes represents that a constraint relation exists between the two nodes in the constraint graph;

s200: initializing parameters of an ant colony algorithm and a genetic algorithm, converting a constraint graph into a pseudo tree generated with breadth first, wherein one node corresponds to one agent, a connecting line between the nodes represents constraint, the value message transmission direction of the pseudo tree is transmitted to a lower node by an upper node, the nodes on the same layer are transmitted according to the priority or the node naming letter sequence, and the message transmission direction is the priority of the agent and the advancing direction of ants;

preset x_iGetAnd x_i’GetCost of time constraint and pheromone concentration, where i ═ 1,2, … n, i '═ 1,2, … n, i ≠ i' T ═ 1,2, … T;

s300: traversing n agents once by adopting the ant colony algorithm, if a is currently available_iHaving received value messages from all of its higher priority neighbors, then a_iFor each ant in x_iSelecting a value in the corresponding value range according to the value selection probability, and calculating a according to the current value_iThe sum of the costs of all the high-priority neighbors and the cost of the current ant is accumulated with the cost calculated before;

s400: generating a random probability q, if q is smaller than an expansion probability p, switching to S500 if the expansion solution space is satisfied, and otherwise, switching to S900;

s500: if the ant colony algorithm has K ants in total, each ant in S300 takes the values of n agents to obtain a set, and then the set is regarded as a chromosome, and S300 obtains K chromosomes aiming at the K ants, and the K chromosomes are taken as parent chromosomes of the genetic algorithm;

s600: calculating the adaptive value of each chromosome in S500, calculating the ratio of the adaptive value of each chromosome in the sum of the adaptive values of all chromosomes, directly copying and storing the chromosome with the largest adaptive value in the K chromosomes into a first generation offspring chromosome set, then calculating the selection probability of each chromosome, wherein the selection probability of each chromosome is equal to the ratio of the adaptive value of the chromosome to the sum of the adaptive values of all chromosomes, and selecting a new parent chromosome set K-1 chromosome by adopting roulette according to the selection probability;

selecting roulette: the cumulative selection probability, p [ k ], for each chromosome is calculated]Called the cumulative probability of chromosome k, i.e., the sum of the selection probabilities of the first k-1 chromosomes; generating K-1 random numbersLet k equal to 1, in the new parent chromosome set, according to the order of the chromosomes, when the cumulative probability of one chromosome is greater than or equal toCopying and storing the chromosome into a first generation child chromosome set, making k equal to k +1, continuing to select in a new parent chromosome set according to the ordering of the chromosomes, and when the cumulative probability of one chromosome is more than or equal to the cumulative probability of one chromosomeCopying and storing the chromosome into a first generation offspring chromosome set, and repeating the steps in sequence until K is equal to K-1, and selecting K-1 first generation offspring chromosomes;

s700: chromosome crossing and mutation:

chromosome crossing:

setting the cross probability, generating a cross random probability, q, for the kth first generation offspring chromosome_xDenotes the cross random probability of the x-th first generation offspring chromosome, x ═ 1,3_xIf the cross probability is less than the cross probability, crossing the cross positions corresponding to the x-th first generation offspring chromosome and the x-1 th first generation offspring chromosome, wherein the cross positions are generated randomly;

the first generation filial generation chromosomes needing chromosome crossing are copied and stored into a new first generation filial generation chromosome set after the chromosome crossing is completed, the first generation filial generation chromosomes which do not need chromosome crossing are copied and stored into the new first generation filial generation chromosome set, and the chromosomes in the first generation filial generation chromosome set are called as new first generation filial generation chromosomes;

chromosomal variation:

setting variation probability, generating a random variation probability for n positions on the new first generation offspring chromosome,represents the random variation probability of the x position of the k new first generation offspring chromosome whenWhen the variation probability is smaller than the variation probability, the value of the x-th position of the kth new first generation offspring chromosome is varied, and the variation method is to randomly select one value from the value domain to reassign the position;

the new first generation offspring chromosomes which need to carry out chromosome variation are copied and stored into a second generation offspring chromosome set after the chromosome variation is finished, the new first generation offspring chromosomes which do not need to carry out chromosome variation are copied and stored into the second generation offspring chromosome set, and chromosomes in the second generation offspring chromosome set are called as second generation offspring chromosomes;

s800: judging whether the genetic algorithm is finished in iteration, if the maximum iteration number of the running of the genetic algorithm is reached and the termination condition is met, outputting the second generation child chromosomes in the current second generation child chromosome set and transferring to S900, and otherwise, updating the parent chromosomes by adopting the second generation child chromosomes and transferring to S600;

s900: updating pheromone concentration and local information context estimated values on the path;

when the cost of each chromosome in the second generation offspring chromosome set is less than the expansion probability p, updating the pheromone concentration by using the cost of each chromosome in the second generation offspring chromosome set, otherwise, updating the pheromone concentration by using the cost of each chromosome in the K ant set, and updating the pheromone concentration constrained between each agent and the neighbor by using K chromosomes;

updating the prediction value of the local information context for each agent, and updating the value d_i∈D_iWhen variable x_i＝d_iCalculating the constraint cost generated between the current agent and the neighbor node with low priorityAveraging the current non-updated estimated value and the calculated average value again to obtain an updated estimated value;

s1000: and judging whether the iteration of the ant colony algorithm is finished, if the maximum iteration number of the ant colony algorithm operation is reached, indicating that the termination condition is met, outputting the cost corresponding to the chromosome with the minimum current cost and the values of the n variables, and if not, returning to the step S300.

As an improvement, the calculation method of the ant probability in S300 is described in formula (7):

in the formula p_k,i(d_i) Expressing ant probability, alpha is pheromone factor weight, beta is heuristic factor weight, theta_k,i(d′_i) Denotes a selection value d'_iConcentration of pheromone of [ (. eta. ])_k,i(d′_i) Denotes a selection value d'_iA heuristic value of_k,i(d_i) Is a pheromone factor, η_k,i(d_i) Is a heuristic factor:

pheromone factor theta_k,i(d_i) The calculation formula is shown in formula (8):

in the formula H_iFor the set of high priority nodes of the node, the constrained pheromone tau between two nodes_ij(d_i,V_k,j)、V_k,jIndicating a high priority node a_jGiving the value selected by the ant k; heuristic factor eta_k,i(d_i) The calculation formula is shown in formula (9):

in the formula cost_ij(d_i,V_k,j) Is x_i＝d_i，x_j＝V_k,jConstraint of time f_ijCost of generation, when x_i＝d_iWhen, est_i(d_i) Is to a_iThe minimum cost sum of the low-priority neighbors is calculated according to the formula (10):

wherein cost_ij(d_i,d_j) Denotes x_i＝d_i，x_j＝d_jThe cost of time constraint generation;

LB is the current node a_iThe calculation formula is given by formula (11) together with the minimum cost of its high-priority and low-priority neighbors:

as an improvement, the spreading probability p in S400 is calculated by using formula (12):

in the formula, maxCycle is the maximum iteration round, and currcycle is the current round.

As an improvement, the method for calculating the fitness value of each chromosome in S600 is as follows:

wherein cost_kThe size of the cost for the kth chromosome,is the sum of the costs of all chromosomes.

As an improvement, the method of calculating the cost of each second generation offspring chromosome in S900 is as follows:

for the kth second generation child chromosome, adding the cost corresponding to the constraint between each agent and the neighbor thereof to remember the cost of the kth second generation child chromosome_k。

As an improvement, the process of updating the pheromone of the constraint between each agent and its neighbor in the kth second generation child chromosome in S900 is as follows:

the updating process includes the increase and/or decrease of pheromone, and the updating method when the pheromone is increased is shown in formula (15):

updating pheromone constrained between each agent and its neighbor in the kth second generation child chromosome by adopting the method of formula (15), wherein k is 1,2, … n:

in the formula,. DELTA._kFor pheromone increment, τ_ij(V_k,i,V_k,j) Denotes a_iTaking the value of ant k as V_k,i，a_jTaking the value of ant k as V_k,jConcentration of pheromone on the corresponding path, delta_k,ijIs a_iAnd a_jSee equation (16) for the calculation formula for pheromone weighting results in between:

where λ is the number of constraints in DCOP, cost_ij(V_k,i,V_k,j) Denotes a_iTaking the value of ant k as V_k,i，a_jTaking the value of ant k as V_k,jCost value of time, cost (V)_k,*) Represents the total cost of ant k;

where min cost is the minimum cost in the second generation offspring chromosomes, cost_kDenotes the kth barCost of chromosomes, cost_k′Represents the cost of the k' th chromosome,the average value of the sum of all the second generation offspring chromosome costs;

for the update method when pheromone is reduced, see formula (17):

τ_ij(d_i,d_j)＝(1-ρ)τ_ij(d_i,d_j)+ρτ₀ (17)

in the formula tau_ij(d_i,d_j) Denotes a_iTaking the value of ant k as d_i，a_jTaking the value of ant k as d_jConcentration of pheromone on hour path, j ∈ H_i，τ₀Representing the initial pheromone concentration, tau₀Where ρ < 1 is 0 < 3, the evaporation rate and pheromone concentration range is [ τ ]_min,τ_max]。

As an improvement, the process of updating the estimate of the minimum cost sum of the low-priority neighbors of each agent in each second generation child chromosome in S900 is as follows: firstly when x_i＝d_iWhen, calculate a_iThe sum of the constraint costs incurred between its low priority neighbors is averaged, and then est is added_i(d_i) The value obtained by the last iteration and the average value obtained currently are subjected to average solution, and the obtained value is updated est_i(d_i)。

The distributed constraint optimization problem solving method based on the ant colony inheritance is applied to emergency rescue problems of urban emergencies by adopting the distributed constraint optimization problem solving method based on the ant colony inheritance;

giving a problem traffic network G (C, E), wherein C represents a node in the network, E represents a connecting line between two nodes, namely a road section, and simultaneously, the urban emergency passable path planning is constructed into a DCOP model, and the model is described in detail as follows:

A＝{car₁,…,car_na vehicle represents an agent;

X＝{x₁,...,x_mis a collection of variables, one agent controls one variable x_i；

D＝{S₁,...,S_mIs a set of value ranges, each variable x_iHas a value range of S_i，S_iWhere is a set of feasible paths, one feasible path is a variable x_iOne value of (a);

F＝{f₁,...,f_pis a constraint, f_ijFor the constraint between the two vehicle traveling paths, that is, the coincidence degree of the paths between the two feasible paths is less than 30%, since the traveling path between each two vehicles needs to satisfy the constraint, the abstracted constraint graph of the DCOP model is a full-connection constraint graph.

As an improvement, solving x in DCOP model of urban emergency through the following objective function_iGetAnd x_i' getThe cost of time constraint comprises the following specific steps:

1) and (3) calculating the running speed of the vehicle by adopting the Underwood model in the formula (2):

in the formula v_fIs the maximum speed on the road section h,is the speed of vehicle travel on road section h, c is the actual traffic density on road section h, c_mIs the maximum traffic density on road section h;

2) the route is time-consuming, and the formula (3) is the time-consuming cost of any normal road section_i：

In the formula s_iIs the length of road segment h;

the time-consuming cost of the accident influence range is determined by adopting a BPR (path per path) resistance function, and the formula (4) is the time-consuming cost of any path with a fault:

where normal is the set of m normal segments, break is the set of n failed segments,is the actual travel time at the link k, t_kIs the travel time of the free stream at the link k, q_kIs the traffic flow at the link k, C_kRepresenting the traffic capacity at a road section k, the influence factor is a random variable phi obeying uniform distribution when the road section k is influenced by an emergency_k(0＜φ_k< 1), the maximum traffic density at the section k is c_kThen the actual traffic capacity of the road section k is phi_kc_kThe parameters a and b are constants; s_hIndicates the length of the trouble-free section h,representing the driving speed on the trouble-free road section h;

let the length of path 1 be len₁Path 2 has a length of len₂，len₁＜len₂The length of the overlapping portion between the path 1 and the path 2 is opart, and the overlapping rate between the path 1 and the path 2 is set to be less than 30%, so that the constraint between the path 1 and the path 2 is f₁₂:opart/len₁< 30%, equation (5) is the constraint cost between the feasible paths chosen for each two vehicles:

in the formula cost_iTime consuming cost for path i，cost_jAnd the time-consuming cost of the path j is the sum of the time-consuming costs of the two paths when the constraint is satisfied, otherwise, a very large value is taken.

Compared with the prior art, the invention has at least the following advantages:

the invention provides an ant colony heredity-based solution method of a distributed constraint optimization problem, called AG _ DCOP for short, which can effectively avoid ACO _ DCOP from being trapped in local optimization by combining the ant colony optimization thought and the search advantage of a genetic operator, thereby expanding the search of an algorithm on a solution space and obtaining a solution with better quality.

The AG _ DCOP combines the ant colony optimization thought and the search advantage of the genetic operator, and increases the expansion probability p of dynamic change so as to trigger the genetic operator to perform expansion optimization on the ant colony traversal result. And the expansion probability p is gradually reduced along with the increase of the iteration turns, and when the generated random number q is smaller than the expansion probability p, the solution generated by the ant colony is subjected to cross variation. The larger expansion probability p further opens an understanding space at the early stage of the algorithm, which is helpful for the algorithm to search an expected solution in a larger solution space and prevent the ant colony from falling into local optimum. And at the later stage of iteration, the expansion probability p is reduced, so that the better solution found currently can be kept.

Drawings

FIG. 1 is a DCOP example diagram, FIG. 1(a) constraint diagram and FIG. 1(b) constraint matrix.

FIG. 2 is a flow chart of the method of the present invention.

Fig. 3 is a comparison of statistical results of 30 runs of each algorithm for different test problems, fig. 3(a) is a statistical result of 30 runs on a sparse random DCOP problem, fig. 3(b) is a statistical result of 30 runs on a dense random DCOP problem, fig. 3(c) is a statistical result of 30 runs on a sparse non-scale problem, fig. 3(d) is a statistical result of 30 runs on a dense non-scale problem, and fig. 3(e) is a statistical result of 30 runs on a weighted graph coloring problem.

Fig. 4 is a comparison of the optimization performance of different algorithms on random DCOPs, where fig. 4(a) shows sparse random DCOPs and fig. 4(b) shows dense random DCOPs.

Fig. 5 is a comparison of the optimization performance of different algorithms on the scale-free problem, where fig. 5(a) is a sparse scale-free problem and fig. 5(b) is a dense scale-free problem.

FIG. 6 is a comparison of the optimization performance of different algorithms on the weighted graph coloring problem.

Fig. 7 is a diagram of the DCOP constraints in example 2.

Detailed Description

The present invention is described in further detail below.

Example 1: referring to fig. 2, the method for solving the ant colony genetic-based distributed constraint optimization problem includes the following steps:

s100, representing the distributed constraint optimization problem by using a quadruple < A, X, D and F > in which:

A＝{a₁,...,a_nis a collection of agents;

X＝{x₁,...,x_mis a set of variables, m ≦ n;

D＝{D₁,...,D_mis a set of value ranges, each x_iHas a value range of D_iEach Agent slave value range D_iThe middle value being a variable x_iThe value is assigned to the value to be assigned, denotes x_iThe tth value of (a);

F＝{f₁,...,f_pis a set of constraint cost functions, constraintsIs from arbitrary k variablesA mapping of the combination of assignments of (a) to a non-negative cost;

if an agent only controls one variable and all constraint relations are binary relations, the solution of DCOP is represented as:

and representing the DCOP as a constraint graph, wherein each node represents an agent, and a connecting line between every two nodes represents that a constraint relation exists between the two nodes. Fig. 1 shows an example of DCOP, which is a constraint graph in fig. 1(a) and a constraint matrix in fig. 1 (b).

S200: initializing parameters of an ant colony algorithm and a genetic algorithm, converting a constraint graph into a pseudo tree generated with breadth first, wherein one node corresponds to one agent, a connecting line between the nodes represents constraint, the value message transmission direction of the pseudo tree is transmitted to a lower node by an upper node, the nodes on the same layer are transmitted according to the priority or the node naming letter sequence, and the message transmission direction is the priority of the agent and the advancing direction of ants; the priority determination method in this step is that the upper layer is higher than the lower layer, and if the definition propagates from left to right in the same layer, the priority of the points on the left side is higher than that of the nodes on the right side. The method for converting the constraint graph into the pseudo tree generated with breadth first in the step is the existing method, and is not repeated at this time.

Preset x_iGetAnd x_i’Get(ii) a constrained pheromone concentration where i ≠ 1,2, … n, i ≠ 1,2, … n, i ≠ i' T ═ 1,2, … T; i.e. x at the same time_iThe t th getAnd x_i’T' th takingAnd (4) the pheromone concentration corresponding to the connection line between the two nodes.

With respect to x_iGetAnd x_i’GetThe cost of the time constraint may be preset when the DCOP model is solved, or may be solved by setting an objective function, and in embodiment 2, the cost is solved by the objective function.

S300: performing one-time traversal on the n agents by adopting the ant colony algorithm, and in each iteration, when a is_iUpon receiving the value message of its high priority node, it first merges the received solution sets, a_iFor each ant in x_iSelecting a value in the corresponding value range according to the value selection probability, and calculating a according to the current value_iAnd accumulating the sum of the current ant cost and all the high-priority neighbor values with the previous value to obtain the current ant cost. If a is present_iHaving received value messages from all its higher priority neighbors, each ant selects a value for each agent in the value domain corresponding to that agent according to the ant probability; the neighbors in this step are referred to as a's in the pseudo tree with the current one_iAll agents directly connected. Specifically, the calculation method of the ant probability in S300 is shown in formula (7): the ant probability depends on pheromone factors and heuristic factors:

in the formula p_k,i(d_i) Expressing ant probability, alpha is pheromone factor weight, beta is heuristic factor weight, theta_k,i(d′_i) Denotes a selection value d'_iConcentration of pheromone of [ (. eta. ])_k,i(d′_i) Denotes a selection value d'_iA heuristic value of (1). Theta_k,i(d_i) Is a pheromone factor, η_k,i(d_i) Is a heuristic factor.

Pheromone factor theta_k,i(d_i) The calculation formula is shown in formula (8):

in the formula H_iFor the set of high priority nodes of the node, the constrained pheromone tau between two nodes_ij(d_i,V_k,j)、V_k,jCorresponding cost correlation, V_k,jIndicating a high priority node a_jFor the value selected by ant k, the pheromone factor can make ant remember the path that ant has gone through, and the heuristic factor can help ant explore new path.

Heuristic factor eta_k,i(d_i) The calculation formula is shown in formula (9):

in the formula cost_ij(d_i,V_k,j) Is x_i＝d_i，x_j＝V_k,jConstraint of time f_ijCost of generation, when x_i＝d_iWhen, est_i(d_i) Is to a_iThe minimum cost sum of the low-priority neighbors is calculated according to the formula (10):

wherein cost_ij(d_i,d_j) Denotes x_i＝d_i，x_j＝d_jThe cost of time constraint generation;

LB is the current node a_iThe calculation formula is given by formula (11) together with the minimum cost of its high-priority and low-priority neighbors:

s400: judging whether the expansion solution space condition is met: and generating a random probability q, if q is less than the expansion probability p, switching to S500 when the expansion solution space is satisfied, triggering a genetic operator mechanism, expanding the solution space, and otherwise, switching to S900.

Specifically, the extended probability p is calculated by using the formula (12):

in the formula, maxCycle is the maximum iteration round, and currcycle is the current round.

S500: obtaining an initial chromosome set of a genetic algorithm: if the ant colony algorithm has K ants in total, each ant in S300 takes the values of n agents to obtain a set, and then the set is regarded as a chromosome, and S300 obtains K chromosomes aiming at the K ants, and the K chromosomes are taken as parent chromosomes of the genetic algorithm; each ant in the basic ant colony algorithm has a number, i.e., a number of 1,2,3 …, so that the number of the chromosome corresponding to each ant is the same as the number of the ant.

S600: selecting chromosomes: calculating an adaptive value of each chromosome in S500, wherein the larger the adaptive value is, the smaller the cost corresponding to the solution is, and the better the quality of the solution is; calculating the proportion of the fitness value of each chromosome in the sum of the fitness values of all chromosomes,directly copying and storing the chromosome with the maximum fitness value in the K chromosomes into a first generation offspring chromosome set, then calculating the selection probability of each chromosome, and setting the selection probability of each chromosome to be equal to the ratio of the fitness value of the chromosome to the sum of the fitness values of all chromosomes; . And selecting k-1 chromosomes in the new parent chromosome set by roulette according to the selection probability.

Selecting roulette: the cumulative selection probability for each chromosome is calculated, and p [ k ] is called the cumulative probability of chromosome k, i.e., the sum of the selection probabilities of the top k-1 chromosomes.

Directly copying and storing the chromosome with the maximum fitness value in the K chromosomes into a first generation child chromosome set, and removing the parent chromosome to obtain a new parent chromosome set.

Generating K-1 random numbersLet k equal to 1, in the new parent chromosome set, according to the order of the chromosomes, when the cumulative probability of one chromosome is greater than or equal toCopying and storing the chromosome into a first generation child chromosome set, making k equal to k +1, continuing to select in a new parent chromosome set according to the ordering of the chromosomes, and when the cumulative probability of one chromosome is more than or equal to the cumulative probability of one chromosomeThe chromosome is copied and stored in the first generation offspring chromosome set, and the steps are repeated until K is equal to K-1, and K-1 first generation offspring chromosomes are selected.

Specifically, the method for calculating the fitness value of each chromosome in S600 is as follows:

wherein cost_kThe size of the cost for the kth chromosome,is the sum of the costs of all chromosomes.

S700: chromosome crossing and mutation:

chromosome crossing:

setting the cross probability as an empirical value, and generating a cross random probability, q, for the kth first generation offspring chromosome_xDenotes the cross random probability of the x-th first generation offspring chromosome, x ═ 1,2_xAnd when the cross probability is smaller than the cross probability, crossing the corresponding cross positions of the x-th first generation child chromosome and the x-1-th first generation child chromosome, wherein the cross positions are generated randomly.

And the first generation child chromosomes which do not need chromosome crossing are copied and stored into the new first generation child chromosome set, and the chromosomes in the first generation child chromosome set are called as new first generation child chromosomes.

Adopting single-point cross operation on chromosomes, randomly generating cross positions for two parent chromosomes meeting the cross probability according to the cross probability, exchanging partial genes behind the cross positions to obtain two new child chromosomes, carrying out mutation operation on the new self-carried chromosomes, and changing the gene values meeting the mutation probability.

Chromosomal variation:

setting mutation probability, wherein the cross probability is an empirical value, generating random mutation probability for n positions (namely n agents) on the chromosome of the new first generation offspring respectively,represents the random variation probability of the x position of the k new first generation offspring chromosome whenAnd when the variation probability is smaller than the variation probability, the value of the agent on the x-th position of the kth new first generation offspring chromosome is varied, and the variation method is to randomly select one value from the value range corresponding to the agent to be varied to reassign the agent.

And the new first generation child chromosomes which do not need to carry out the chromosome variation are copied and stored into the second generation child chromosome set, and the chromosomes in the second generation child chromosome set are called as second generation child chromosomes.

S800: judging whether the genetic algorithm is finished in iteration, if the maximum iteration number of the running of the genetic algorithm is reached and the termination condition is met, outputting the second generation child chromosomes in the current second generation child chromosome set and transferring to S900, and otherwise, updating the parent chromosomes by adopting the second generation child chromosomes and transferring to S600;

s900: updating the pheromone concentration and the local information on the path according to the following estimated values, calculating pheromone increment and an updated global optimal solution by the agent with the lowest priority, informing all agents of the two messages, and calculating the cost of each second generation child chromosome by the following method:

and when the cost of each chromosome in the second generation offspring chromosome set is less than the expansion probability p, updating the pheromone concentration by using the cost of each chromosome in the second generation offspring chromosome set, otherwise, updating the pheromone concentration by using the cost of each chromosome in the K ant set, and updating the pheromone concentration constrained between each agent and the neighbor thereof by using the K chromosomes.

Updating the prediction value of the local information context for each agent, and updating the value d_i∈D_iWhen variable x_i＝d_iAnd calculating the average value of the constraint cost generated between the current agent and the low-priority neighbor node thereof, and averaging the current non-updated estimated value and the calculated average value again to obtain an updated estimated value.

Specifically, the method comprises the following steps: for the kth second generation child chromosome, adding the cost corresponding to the constraint between each agent and the neighbor thereof, and recording the cost of the kth second generation child chromosome_k。

Updating pheromones constrained between each agent and the neighbors of the k second generation child chromosome, wherein k is 1,2 and … n, and the specific updating process is as follows:

the updating process includes the increase and/or decrease of pheromone, and the updating method when the pheromone is increased is shown in formula (15):

updating pheromone constrained between each agent and its neighbor in the kth second generation child chromosome by adopting the method of formula (15), wherein k is 1,2, … n:

in the formula,. DELTA._kFor pheromone increments，τ_ij(V_k,i,V_k,j) Denotes a_iTaking the value of ant k as V_k,i，a_jTaking the value of ant k as V_k,jConcentration of pheromone on the corresponding path, delta_k,ijIs a_iAnd a_jSee equation (16) for the calculation formula for pheromone weighting results in between:

where λ is the number of constraints in DCOP, cost_ij(V_k,i,V_k,j) Denotes a_iTaking the value of ant k as V_k,i，a_jTaking the value of ant k as V_k,jA cost value of time. cost (V)_k,*) Representing the total cost of ant k.

Where mincost is the minimum cost in the second generation offspring chromosomes, cost_kRepresents the cost, of the k-th chromosome_k′Represents the cost of the k' th chromosome,the average value of the sum of all the second generation offspring chromosome costs;

for the update method when pheromone is reduced, see formula (17):

τ_ij(d_i,d_j)＝(1-ρ)τ_ij(d_i,d_j)+ρτ₀ (17)

in the formula tau_ij(d_i,d_j) Denotes a_iTaking the value of ant k as d_i，a_jTaking the value of ant k as d_jConcentration of pheromone on hour path, j ∈ H_i。τ₀Representing the initial pheromone concentration, tau₀3. Rho is more than 0 and less than 1, the evaporation rate is, and the pheromone concentration range is [ tau ]_min,τ_max]。

Updating estimates of the minimum cost sum for each agent's low priority neighbors in each second generation child chromosome as follows: firstly when x_i＝d_iWhen, calculate a_iThe sum of the constraint costs incurred between its low priority neighbors is averaged, and then est is added_i(d_i) The value obtained by the last iteration and the average value obtained currently are subjected to average solution, and the obtained value is updated est_i(d_i)。

S1000: and judging whether the iteration of the ant colony algorithm is finished, if the maximum iteration number of the ant colony algorithm operation is reached, indicating that the termination condition is met, outputting the cost of the second generation child chromosome with the minimum current cost and the values of n agents, and if not, returning to the step S300.

Example 2: the method for solving the distributed constraint optimization problem based on the ant colony inheritance is applied to emergency rescue problems of urban emergencies, and the method for solving the distributed constraint optimization problem based on the ant colony inheritance defined in the embodiment 1 is applied to emergency rescue problems of urban emergencies;

considering that the traffic flows in opposite directions of the same road section are not consistent, a problem traffic network G (C, E) is given, C represents a node in the network, E represents a connecting line between two nodes, namely the road section, the passable path planning of the urban emergency is constructed into a DCOP model, and the model is solved by using the provided AG _ DCOP algorithm so as to find out a plurality of optimal path sets meeting the constraint as the optimal path and the alternative path for emergency rescue. The model is described in detail as follows:

A＝{car₁,...,car_na vehicle represents an agent;

X＝{x₁,...,x_mis a collection of variables, one agent controls one variable x_iThus agent can be equated to a variable;

D＝{S₁,...,S_mis a set of value ranges, each variable x_iHas a value range of S_i，S_iWhere is a set of feasible paths, one feasible path is a variable x_iOne value of (a);

F＝{f₁,...,f_pis a constraint, f_ijFor two vehiclesThe constraint between the paths, that is, the coincidence ratio of the paths between two feasible paths is less than 30%, since the travel path between each two vehicles needs to satisfy the constraint, the abstracted constraint graph of the DCOP model is a full-connection constraint graph, which is shown in fig. 7.

For the planning of the route from the departure point to the rescue point, it is most important that the rescue vehicle arrives at the rescue scene in the shortest possible time, however, an emergency may have a certain influence on some road sections, such as traffic jam on the road sections, which may delay the rescue. Therefore, the time consumption of the path under the emergency is considered and analyzed, and for a single path, the time consumption cost comprises the time consumption of driving on a normal road section and the additional time consumption caused by the emergency on the road section. For the distributed constraint optimization problem, the time-consuming cost is the sum of the time-consuming costs of several feasible paths that satisfy the constraint with each other.

1) Road segment driving speed. Vehicle travel speed is a major factor affecting the time taken for a route. On the road, the vehicle running speed is mainly limited by the traffic flow, so in consideration of the factors, the invention adopts the Underwood model in the formula (2) to calculate the vehicle running speed:

in the formula v_fIs the maximum speed on the road section h,is the speed of vehicle travel on road section h, c is the actual traffic density on road section h, c_mIs the maximum traffic density on the road segment h. The Underwood model is prior art.

2) The path is time consuming. When the time consumption of a single path is calculated, a single complete path needs to be found out at first, and all paths from a starting point to an end point are obtained by adopting an adjacency list. The time-consuming cost of the equation (3) for any normal road section is the ratio of the length of the road section to the driving speed of the road section, s_iIs the length of the road segment h.

And on the feasible fault road section, calculating the running time of the normal part of the road section and the time of the accident influence road section according to the influence range of the accident road section. The time-consuming cost of the accident influence range is determined by adopting a BPR (path per path) resistance function, and the formula (4) is the time-consuming cost of any path with a fault:

in the formula, normal is a set of m normal road sections, and the sum of time consumption and cost of the normal road sections is obtained. break is a collection of n failed road segments,is the actual travel time at the link k, t_kIs the travel time of the free stream at link k. q. q.s_kIs the traffic flow at the link k, C_kRepresenting the capacity of the road section k, assuming that the influencing factor is a random variable phi subject to uniform distribution when the road section k is influenced by an emergency_k(0＜φ_k< 1). The maximum traffic density at the section k is c_kThen the actual traffic capacity of the road section k is phi_kc_k. The parameters a, b are generally 0.15 for a, 4 for b, s_hIndicates the length of the trouble-free section h,representing the speed of travel on the trouble-free road section h.

Assume path 1 has a length of len₁Path 2 has a length of len₂，len₁＜len₂The length of the overlapped part between the path 1 and the path 2 is opart, and the overlapping rate of the two paths is set to be less than 30 percent. The constraint between the two paths is f₁₂:opart/len₁Is less than 30 percent. Equation (5) is the constraint cost between the feasible paths chosen for each two vehicles:

in the formula cost_iCost for path i, cost_jAnd the time-consuming cost of the path j is the sum of the time-consuming costs of the two paths when the constraint is satisfied, otherwise, a very large value is taken. In the case of satisfying the constraint, 5 feasible paths are obtained as alternatives, and the time cost spent on the feasible paths is the least, so equation (6) is the solution set of the DCOP model.

Results and analysis of the experiments

In order to test the optimizing capability and stability of the method, AG _ DCOP compiling of the method is completed on the existing software platform. Multithread communication is used to simulate a distributed environment, each thread represents an agent, and communication between threads represents intercommunication between agents. Several types of generic test problems are automatically generated using the ContentWriter problem generator. The invention adopts random DCOP problem (density problem and sparse problem), weighted graph coloring problem and scale-free network problem (density problem and sparse problem) to test. The setup parameters for the problem are as follows:

1) random DCOP

The number of the agents is set to be 70, the value domain size of the variable is 10, and the value range of the constraint cost is 1,100]. Density p for sparseness problem₁0.1 for denseness problem, the density is p₁＝0.6。

2) Weighted graph coloring problem

The number of the agents is set to be 120, the size of a variable value domain is 3, and the value range of the constraint cost is 1,100]. Problem density p₁＝0.05。

3) Problem of scale-free network

The number of the agents is set to be 70, the value domain size of the variable is 10, and the value range of the constraint cost is 1,100]. In the sparseness problem, the thickness is m₁＝10,m₂In the case of 3 dense, the dense density is m₁＝10,m₂＝7。

In order to prove the optimizing capability and stability of the method, experiments compare several types of DCOP solving algorithms with better optimizing capability, namely ACO _ DCOP, ALS _ DSA (0.8), MGM and LSGA _ MGM 2. In order to ensure the fairness of the experimental comparison, the parameter setting of the comparison algorithm adopts the recommended value of the original text of the algorithm, the invention has different values of the alpha, beta and rho parameters suitable for each problem due to different types of test problems, and the parameters in the text are determined according to the experiment as follows: the sparse dimensionless problem α is 1, β is 3, ρ is 0.0015, and the other problems α is 2, β is 3, and ρ is 0.0025.

The termination condition of the method is set as iteration 1000 times, the ant number is recommended according to ACO _ DCOP, the ant number is set to be K to 13 for sparse random DCOP and sparse non-scale network problem, and the ant number is set to be K to 20 for dense random DCOP, dense non-scale network problem and weighted graph coloring problem. Because the method has random results, each group of problems is subjected to 30 independent experiments, and the statistical results of 30 times are taken for experimental comparison.

As can be seen from fig. 3(a) to 3(e), on the 5 types of general test problems, the results obtained by the 5 algorithms are statistically distributed substantially uniformly, the performance of the MGM algorithm is the worst, the solution obtained by the MGM algorithm has a large cost, and the quality difference of the solution is large. The solution quality obtained by the LSGA _ MGM2 is improved compared with the MGM, but the solution quality obtained by the LSGA _ MGM2 is unstable compared with the MGM, in contrast, the ALS _ DSA has better stability, but the ACO _ DCOP and the AG _ DCOP can obtain better solutions, wherein the AG _ DCOP obtains the best solution quality in the 5 algorithms, and the difference between the solutions is smaller, which means that the AG _ DCOP has better optimization performance and stability.

To test the AG _ DCOP optimization performance, the convergence effect of the method of the present invention is verified by taking the average value of 30 iterations of the method of the present invention, as shown in fig. 4 to 6.

Fig. 4(a) and 4(b) show the comparison of the optimization results of the method of the present invention on sparse random DCOPs and dense random DCOPs, respectively. Experiments show that the MGM algorithm quickly converges to a poor solution on sparse random DCOPs. The LSGA _ MGM2 and ALS _ DSA algorithms have improved performance over the MGM algorithm, but after 200 iterations, the two algorithms fall into local optima. The performance of the ACO _ DCOP is obviously improved compared with the performance of the three algorithms, but according to experimental results, after about 100 iterations, the ACO _ DCOP is already in local optimum, and the solution quality is not improved significantly in the iterations of the following iterations. Finally, for AG _ DCOP, since the previous stage is in the extended solution space, although the convergence rate of AG _ DCOP is not as fast as ACO _ DCOP, the solution quality is better than the above algorithm. After 1000 iterations, the quality of the solution of the AG _ DCOP is improved by 2% to 18.3% compared to the solutions of other algorithms. On dense random DCOPs, due to the more constraint and higher complexity of the dense problem, AG _ DCOP needs longer time to search a solution space in the early period and converges slower, but can converge to a solution with higher quality in the later period of the algorithm. The AG _ DCOP performance is slightly worse than that of ALS _ DSA algorithm, and is better than that of other comparison algorithms, and the solution quality is improved by 1.2-2.0%.

Fig. 5(a) and 5(b) show the comparison of the optimization results of the method of the present invention on the sparse scale-free problem and the dense scale-free problem, respectively. Experiments show that compared with three algorithms including LSGA _ MGM2, ALS _ DSA and MGM, the ACO _ DCOP algorithm has obviously better performance on the aspect of sparse scale-free problem, but as the iteration turns increase, the ACO _ DCOP algorithm has obviously better performance

After approximately 100 rounds of fast convergence, the quality of the solution does not change at the end of the iteration. The results in fig. 5(a) show that the AG _ DCOP solution is better in quality than the above algorithm and still has a continuing downward trend. The solution quality obtained by AG _ DCOP is improved by 3.0-35.4% compared with the solution quality of other algorithms. On dense non-scale problems, the MGM algorithm converges faster, but the resulting solution quality is the worst. The LSGA _ MGM2 algorithm improves the quality of the understanding, but a stall also occurs after 300 iterations. The ALS _ DSA algorithm can obtain better results and faster convergence speed than the two algorithms, but the obtained solution quality is not as good as that of ACO _ DCOP, but the algorithm is also stalled quickly. The AG _ DCOP maintains a better solution optimizing state when a solution space is expanded, and has higher solution quality than all the algorithms. After the iteration is finished, the quality of the solution obtained by the AG _ DCOP is improved by 1.1-8.5% compared with the quality of the solutions of other algorithms.

FIG. 6 shows a comparison of the optimization results of the method of the present invention on the weighted graph coloring problem. Experiments show that in the aspect of the problem, the performance difference of the method is large, the algorithm performance of the MGM is the worst, the LSGA _ MGM2 and the ALS _ DSA have almost the same optimizing capability, and the ACO _ DCOP also greatly improves the understanding quality and shows remarkable performance compared with the two algorithms. But the AG _ DCOP algorithm shows better performance, and the quality of the solution is improved by 21.7-76.8%.

Finally, the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting, although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions may be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all of them should be covered in the claims of the present invention.