Evolutionary Approach for Constrained Optimization

Constrained optimization is a challenging area of research in the science and engineering disciplines. Locating the optimal solutions for such problems is often difficult as their characteristics and mathematical properties do not follow any standard patterns or forms. Over the last few decades, evolutionary algorithms (EAs) have been widely used for solving optimization problems. Although there are many EAs for solving Constrained Optimization Problems (COPs), no single algorithm performs consistently over a wide range of problems. Therefore, ideas for multi-operator- and multi-methodology-based algorithms have recently been introduced but their actual strengths for solving COPs have not been fully explored. The choice of operators and/or algorithms and their appropriate mix, and a strategy for their use in designing an effective EA have not been well studied. In this thesis, a general framework for solving COPs that allows the use of different operators and/or algorithms under a single algorithmic structure is proposed and a good number of algorithms are designed, implemented, analyzed and tested. In this research, firstly, multi-operator EAs are studied. They can be implemented in many different ways, such as with and without population divisions, adaptations and local searches, and offer different ways of choosing and mixing operators. To test the robustness of this concept, two different EAs, known as the genetic algorithm (GA) and differential evolution (DE), are considered. Different variants of a multi-operator GA and multioperator DE are implemented with and without self-adaptation, population changes and local searches. The purpose of introducing self-adaptation is for the appropriate mix of operators to be automatically chosen with the progress of evolution. To do this, a new self-adaptive mechanism is derived and its number and choice of operators are discussed and justified. Initially, one type of operator, a crossover for GA and a mutation for DE, is considered. Later, these algorithms are extended to include multiple crossover and mutation operators and designed to use a self-adaptive mechanism to change the number of individuals assigned to each. The DE-based algorithm is further extended to include different constraint-handling techniques (CHTs). In its implementation, each chromosome contains information on the use of a single crossover, a single mutation and a single CHT. To accelerate the performances of these algorithms, a local search technique is also applied. The framework proposed for an EA with multiple operators is further extended to include multiple EAs under a single algorithmic framework. Therefore, a new algorithm, in which the population is divided into sub-populations, where each subpopulation runs a defined multi-operator EA, is introduced. The number of EAs used are discussed and analyzed. To demonstrate consistent performances of all the proposed algorithms, they solve the problems from two different specialized sets of benchmark problems and a detailed parametric analysis of them is provided. For comparisons of the competing algorithms, a new comparison matrix is introduced. The results from this thesis can be summarized as follows: (1) the multi-operator based GA is able to obtain much better solutions than those of each independent GA with a single operator; (2) the use of the self-adaptive mechanism leads to much better solutions and savings in time; (3) the multi-operator based GA is competitive with the state-of-the-art algorithms; (4) the self-adaptive multioperator based DE is not only better than the single operator-based DE but also takes 25% less computational time than a standard DE; (5) the self-adaptive multi-operator based DE with a local search technique performs much better and takes 48% less computational than the algorithm without a local search; (6) the self-adaptive DE with a mix of crossover and mutation operators plus a local search is better than those without a local search and is also superior to the state-of-the-art algorithms; (7) DE with multiple crossover and mutation operators plus CHTs is able to obtain better solutions than DE with a single operator and different state-of-the-art algorithms; (8) the multi-methodology EA with three different algorithms performs best, is superior to DE with a multiple mutation operators the state-of-the-art algorithms and consumes 26% less computational time than the self-adaptive multi-operator DE; and (9) considering all the algorithms implemented and tested in this thesis, the memetic self-adaptive multi-operator DE is the best