Research On Fuzzy Multiple Objective Optimization Based On Decision Maker's Satisfying Degree

The repaid development of modern industry and economy make the optimization technique be greatly used in many kinds of fields. With higher requirements of the optimization objective are put forward, the simultaneous optimization of multiple objectives is the key factor for the final decision in the systems. Under the complex decision making environments, multiple objectives are always conflicting and noncommensurable, which often result in inexistence of optimal solution. Therefore multiple objective optimization problem (MOOP) can't be efficiently solved using the optimization methods for single objective problem. In addition, there are all kinds of preference in MOOP. Then how to find the final one from the Pareto optimal solutions becomes important in solving MOOP. Moreover the uncertainties also cause many difficulties to directly use the conventional optimization approaches and optimization theories, and bring challenges for MOOP. In this thesis, based on decision maker (DM)'s satisfying degree, the MOOPs with different types of preferences are studied using fuzzy optimization methods.The main contents are as follows:For the MOOP with linguistic preference, the order of the desirable satisfying degrees is used to express the vague importance requirement among the objectives showed by linguistic information based on the principle that the more important objective has higher desirable satisfying degree. As for the different types of fuzzy goals and optimization requirements, the two-step fuzzy optimization algorithm and enhanced additive model fuzzy optimization algorithm are designed. The former formulates the two-step optimization models by relaxing the maximum overall satisfying degree. It gurantees the original characteristics of the problem and realizes the tradeoff between the optimization and importance difference. The latter gives the single objective formulations with parameter based on goal programming. It is suitable for all kinds of fuzzy relations. The balance between the sum of the desirable satisfying degrees and importance difference is actualized through regulating the parameter. After the optimality and parameter analysises, the numerical examples are illustrated to verify their effectiveness, flexibility and sensitivity.Focusing on the MOOP with preemptive priority, using the order of the satisfying degrees instead of that of the desirable ones, the importance requirement is transformed into priority. Correspondingly, the two-step algorithm and enhanced additive model algorithm for vague importance are modified. For the former, with the same first step model, the priority model is formulated via the order of the satisfying degrees. The opitimization and priority requirement is acquired by means of the relaxation of the maximum overall satisfying degree. For the latter, the order of the satisfying degrees is transformed into the comparison between deviational variables. The tradeoff between the sum of the satisfying degrees and priority difference is realized by regulating the parameter. The effectiveness and sensitivity of the two approaches are verified by the simulation of numerical examples, distributed parameter system and production decision making problem.Considering the MOOP with progressive preference, the interactive fuzzy optimization method based on alternative tolerance is proposed according to DM's satisfying degree. The different membership function structures resulted from the alternative tolerance reflect the changing of the preference during the optimization procedure. For the optimization problem with fuzzy goals, the auxiliary model is incorporated in order to ensure the feasibility of the proposed optimization algorithm. The two-phase model or revised two-phase model guarantees the Pareto optimality or weak Pareto optimality of the solution. In addition, the MOOP with fuzzy parameters in the objectives and constraints is studied. The optimization problem based on parameter is formulated using the cut set of fuzzy number. According to the principle of alternative tolerance, the optimization procedure including the inner and outer interactions is realized. The regulation of parameter and the alternation of tolerance denote the changing of the progressive preference of DM. The satisfyingα-Pareto optimal solution or weakα-Pareto optimal solution can be obtained by solving the two-phase models with parameter. The examples show the effectiveness of the methods.For the MOOP with posteriori preference, DM's satisfying degree is expressed by posteriori satisfying degree. Firstly, the uniformly distributed approximate Pareto optimal set of the MOOP is acquired by the multiple objective genetic algorithm: Nsga-II. Then the MOOP with fuzzy goals is reformulated according to DM. The corresponding satisfying degrees of all the objectives for each solution are got. Finally, the eliminating optimization method reduces the obtained set to the M-Pareto optimal subset. Furthermore, the traditional fuzzy c mean (FCM) clustering classifies the subset including many M-Pareto optimal solutions to acquire the representative subset such that DM can easily select his preferred result. The simulations of the numerical example and scheduling optimization problem demonstrate the feasibility of the three-step optimization strategy.