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


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.