Multi-Objective Differential Evolution: Theory and Applications


Most decision support systems involve rnulti-objective optimization problems (MOOP). Previous research has usually treated these MOOPs by heuristically combining the multiple objectives into a single one. However, it is extremely difficult to incorporate a decision maker's (DM) preference structure and have an appropriate way for this combination. This has been a hurdle for the DM to obtain an optimal tradeoff solution. The fundamental theme of this research work is to develop the foundation of an efficient rnulti-objective optimization strategy from a theoretical perspective and demonstrate its applications as the core search engine of decision support systems for real-world problems. In this thesis, a new evolutionary rnulti-objective optimization strategy--Multi- Objective Differential Evolution (MODE) is proposed. The MODE is developed for both continuous (C-MODE) and discrete (D-MODE) domains. A set of performance metrics called Pareto Front Approximation Error (PFAE) is introduced to evaluate the non-dominated solutions obtained by optimization approaches. A theoretical foundation to explain the behaviors of MODE is developed through proofs of convergence of the MODE algorithms. The analysis of the D-MODE is treated based on a Markov model while the C-MODE is modeled in the global random search framework. The convergence of the population to the Pareto front with probability one is developed. A set of guidelines on the parameter setting of the C-MODE is derived based on both mathematical modeling and simulation analysis of its operators. A class of decision problems arising in integrated design, supplier, and manufacturing (DSM) planning involved in modular product development is formally modeled as a multi-objective optimization assignment problem. The MODE is applied to solving such MOOPs to generate the Pareto optimal solutions for further decision making. An object oriented framework of a multi-objective decision support system is proposed for such DSM planning with MODE as the core search engine. This can serve as a prototype for other applications. The routing problems in wireless networks is formally modeled as a MOOP that optimizes both power consumption and communication latency. The MODE concept is implemented with its internal data structure tailored to the network specifics.