### Entropy Approach to Meta-Modeling, Multi-Objective Genetic Algorithm and Quality Assessment of Solution Sets for Design Optimization

Abstract

A new entropy-based approach to meta-modeling and
multi-objective optimization of engineering design
problems is presented. The approach consists of four
main components, as follows: (1) Meta-Modeling:
Engineering design optimization problems often involve
computationally costly simulation models. Multi-objective
optimization of such models usually involves many function
evaluations that prohibit a direct application of most
available techniques. In this dissertation, a new sequential
meta-modeling technique--referred to as Sequential MAXimum
Entropy Design, or SMAXED--is presented that aims at
finding a good meta-model with minimum computational burden.
(2) Multi-Objective Genetic Algorithm (MOGA): We introduce
a new multi-objective genetic algorithm that aims at obtaining
the most diverse (i.e., highest entropy) solution set. The new
MOGA--referred to as Thermodynamical MOGA or T-MOGA--is based
on simulating Maxwellian system (of monoatomic gas molecules
in a container). (3) Minimality of Quality Indexes: Once a
Pareto solution set to a multi-objective optimization problem
is obtained via a multi-objective optimization algorithm, it
is usually of great interest to know how "good" the observed
solution set represents the Pareto frontier. This can be done
either visually, or objectively via quality indexes. In this
part of research, a new theoretical framework is presented
for selection of a handful of these indexes such that all
desired aspects of quality are addressed with minimum or no
redundancy. (4) Entropy Index: Finally, to assure the quality
of solution sets in terms of diversity, a new quality index is
presented. The new index--referred to as entropy index--is
based on the notion of entropy. In situations where a direct
application of most optimization techniques is computationally
intractable, the proposed SMAXED approach can be employed to
construct a global approximation to the simulation model,
followed by T-MOGA to obtain a diverse solution set. Using a
carefully selected set of quality indexes assures an objective
performance assessment and comparison of the proposed methodology.