Multi-objective differential evolution: theory and applications

  • Authors:
  • Arthur C. Sanderson;Robert J. Graves;Feng Xue

  • Affiliations:
  • Rensselaer Polytechnic Institute;Rensselaer Polytechnic Institute;Rensselaer Polytechnic Institute

  • Venue:
  • Multi-objective differential evolution: theory and applications
  • Year:
  • 2004

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Abstract

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.