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## The multi-robot task allocation method of intelligent storage system, based on the multi-robot task allocation problem model, establish a multi-objective optimization model of time cost and energy cost; where the energy cost is expressed as the total path length of the multi-robot system, and the time cost is expressed as multi-robot The variance of the total path of each robot in the system;

Specific steps are as follows:

(1) Construct a mathematical model of the multi-objective task allocation method. For a given N pickup points, a graph G = {V, E}, where V is the set of pickup points, E is the edge set of the graph, and m is arranged. The robot traverses the pickup point set V, so that all pickup points except the starting point vn ∈ V have and only one robot passes, and the sum of the paths is the smallest, and the variance of the paths of the robots is the smallest; for the multi-object task assignment problem, There are the following optimization goals: where: S: total path length of all robots; Si: total path length of the i-th robot; Savg: average length of each robot; where Si is based on the path of the i-th robot Pi = {Ui, Ei ) The calculated total distance of the path, the value of which is the sum of the distances of the nodes of the path sequence calculated according to the adjacency matrix D (G) of graph G, where Ui is the collection point set responsible for the robot i, and Ei is the end-to-end composed of Ui The edge set, that is: where duv represents the distance from node u to node v, and its value is the element value of the u-th row and v column of the adjacency matrix D (G); the assignment method for multi-robot tasks is as follows: all robots must start from a specified starting point Departure, and return strictly after visiting all other nodes once Point vn; that is, for the point set U = V \ {vn} other than the starting point: and each set of valid solutions must contain m trivial sub-paths, that is, the formulas (2)-(4) constitute the constraints of the task allocation method ;

(2) Construction of non-dominated multi-objective genetic algorithm

(2-1) Solving by genetic algorithm requires encoding individual genes, and using breakpoint markers to encode genes, the steps are as follows:

(2-1-1) Mark the non-starting points in the set V as 1,2, ... n-1, mark the starting point as n, and add m-2 breakpoints and number them n + 1, n + 2 ... n + m-2;

(2-1-2) Combining breakpoints n + 1, n + 2 ... n + m-2 and 1,2 ... n into a gene sequence, and numbering n + 1 when calculating S ... n + m-2 points to the starting point O, so that the problem is transformed into a traveling salesman problem to solve; (2-1-3). In order to prevent n + 1 ... n + m-2 from being connected back and forth, it is guaranteed Each robot path is a trivial sub-path, and dnn = ∞ should be in the adjacency matrix D of G to ensure that the individuals connected to the interruption point of the evolution process are eliminated;

(2-2). A non-dominated sorting algorithm is used to ensure effective access to high-quality offspring. The method is as follows:

(2-2-1). Each individual in the population is given a dominated set Ni and a dominated solution set Si, where Ni represents the set of individuals dominating the individual i in the current population, and Si represents the set of individuals dominated by the individual i;

(2-2-2) In the actual ranking, the characteristics of individuals are obtained according to the fitness equation. Among them, Fi represents the feature vector of individual i, which is composed of fi1 and fi2, which respectively represent the current time cost and space cost of the individual. Traverse the population individuals, obtain the dominating set Si and the dominated set Ni of individual i, find all the individuals with Ni in the population P = 0, store them in the set T0, assign the dominance level to the individuals in T0, and from the population P Exclude the set T0 to obtain the remaining population P1, and then examine the remaining population P1. If the individual j ∈ P1 and | Nj | -1 = 0, it is stored in the set T1, and the individuals in T1 are given a dominance level until the population P is empty. That is, until individuals in the population P are assigned corresponding dominance levels, a new population P ′ having all the dominance levels is obtained;

(2-3) The parent population selected for the non-dominated sorting strategy has diversity, avoiding the inclusion of individuals with similar optimal components in the population into the parent, and introducing the population crowding degree calculation strategy of the same dominating order among which the individual's crowding degree The parameter Gi is defined as the sum of the differences between the feature vectors (f1, f2) of the two individuals j, k closest to the individual i, that is: when selecting the offspring, the individual with the smaller dominant order is preferentially selected, and under the same dominant order, Individuals with larger congestion parameters are preferred to ensure the diversity of the population;

(2-4) Aiming at the disadvantage that genetic algorithms cannot avoid falling into the local optimal value, a population restart strategy with an elite pool is introduced, that is, for each calculation, when the population reaches the convergence condition, the population is reinitialized, and Incorporate high-quality solution individuals who have reached the convergence condition into the elite pool. When the conditions for using the elite pool to evolve are reached, the elite pool is continued to iterate as a new population, thereby increasing the probability of the algorithm converging to the non-dominated solution. Reach convergence, store the current high-quality parent individuals into the elite pool, initialize the population, and return to step (1);

(2-5) Check whether the current iteration meets the elite pool iteration conditions. If the conditions are met, use the individuals stored in the elite pool as a new population, and return to the first step;

(2-6). Use the selected outstanding parent individuals to generate the next generation individuals through the crossover operator and mutation operator, and use the next generation individuals and the parent individuals as the new population, and return to step (1);

(2-7) Check whether the termination condition is reached and terminate the cycle, and select the smallest sum of the squares of the scattered points as the optimal solution; ensure that the solution has the optimal time cost and energy cost.