The Study On Hub Center Location Problem By Equilibrium Optimization Methods

Hub location problems consist in how to locate a set of hubs and determining the paths for sending commodities. In real hub location problems, the demands of commodities are usually uncertain, a decision-maker may encounter complex deci-sion environments where randomness and fuzziness coexist, so we should employ equilibrium optimization method to study hub location problems.At first, according to the definition and proposition of equilibrium chance, this dissertation discusses convex programming problem with equilibrium constraint un-der different chance constraint forms. Then, this dissertation develops a new two-stage uncapacitated hub location (UHL) problem with recourse, in which uncertain parameters are characterized by random fuzzy variables with known distributions. When demands are the only uncertain parameters, the proposed two-stage hub lo-cation model is equivalent to a static optimization problem subject to equilibrium constraint. In the case that the randomness of uncertain demands follows normal distributions, this dissertation reduces the equilibrium constraint to its equivalent credibility constraint. In the case that the fuzziness of uncertain demands follows tri-angular distributions, we discuss the convexity of equilibrium objective function, and derive the deterministic programming model of original UHL problem. In general case, this dissertation adopts the technique of fuzzy simulation (FS) to approximate continuous fuzzy parameters. To solve the proposed hub location problem, we de-sign a hybrid heuristic algorithm that integrates genetic algorithm (GA), variable neighborhood search (VNS) and FS. Finally, some numerical experiments are per-formed to illustrate the new modeling idea, and the effectiveness of designed solution method.The major new results included the following several aspects:(i) According to the definition and proposition of equilibrium chance, we dis-cussed convex programming problem with equilibrium constraint under two condi-tion between "separate chance constraints" and "joint chance constraints".(ii) Under twofold uncertain circumstances, we developed a new compatible two-stage UHL problem, in which uncertain parameters are characterized by randomfuzzy vector. Under mild assumption, we turned the equilibrium constraint to itsequivalent credibility constraint, and discussed the convexity of objective function.(iii) We designed a hybrid heuristic algorithm by integrating VNS, GA and FSto enhance the efectiveness of solution.(iv) For the proposed model, we performed some numerical experiments toillustrate our new modeling ideas and the efectiveness of designed solution method.