### Multi-Objective Differential Evolution: Theory and Applications

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.