Flexible job-shop scheduling method based on limited stable matching strategy

A flexible job-shop scheduling method based on a limited stable matching strategy, comprising the following steps:

• (a) initializing related parameters:
• obtaining an initial chromosome population meeting constraint conditions through integer coding according to specific contents of a production order;
• determining a neighborhood of each subproblem;
• and calculating a fitness value;
• (b) selecting a parent chromosome from the neighborhood of each subproblem;
• generating progeny chromosomes through simulated binary crossover and polynomial mutation;
• and calculating a fitness value;
• (c) selecting progeny populations:
• (c1) combining a set of generated progeny chromosomes and a set of original parent chromosomes into a set S={s1, s2, . . . , s2N} of to-be-selected chromosomes, and mapping the set to a target space to obtain a set X={x1, x2, . . . , x2N} of to-be-selected solutions, a subproblem set P={p1, . . . , pt, . . . , pN} and a weight vector set w={ω1, . . . , ωt, . . . , ωN}, wherein N is the number of the chromosomes;
• (c2) selecting the angle of the solution relative to the subproblem as position information θ;
• (c3) constructing an adaptive transfer function, and using the position information θ to obtain limit information;
• (c4) obtaining preference values through a preference value calculation formula of the subproblem with limit information for the solutions;
• arranging the preference values in an ascending order to obtain a preference sequence of the subproblem for all solutions;
• and conducting the same operation for all the subproblems to obtain a preference matrix ψp;
• (c5) obtaining the preference values through the preference value calculation formula of the solutions for the subproblems;
• arranging the preference values in an ascending order to obtain a preference sequence of the solutions for all the subproblems;
• and conducting the same operation for all the subproblems to obtain a preference matrix ψx;
• (c6) using the information of the preference matrices ψp and ψx as input, and delaying an acceptance procedure to obtain a stable matching relationship of the subproblems and the solutions, thereby selecting progeny solutions and also selecting chromosomes corresponding to the progeny solutions;
• and
• (d) outputting a population Pareto solution set when meeting cut-off conditions;
• selecting a chromosome by a decision maker from the Pareto solution set according to practical needs;
• decoding the chromosome to form a feasible scheduling solution;
• otherwise, returning to step (b).