Continuous optimization with evoluationary and swarm intelligence algorithms

Abstract

Continuous optimization generally refers to the task of finding values for a set of continuous variables that optimizes a given objective function. The problem of continuous optimization appears frequently in every field of science and engineering, and there exist several paradigms of algorithms that deal with the continuous optimization problem. However, in comparison to other analytical, single state and local search based algorithms, the evolutionary and swarm intelligence algorithms show more resilience against local optima and premature convergence, especially when dealing with complex, high dimensional, multimodal problems. This is because both the evolutionary and swarm intelligence algorithms maintain a whole population of candidate solutions that provide diversity and explorative search capacity against locally optimal points. However, some experimental studies also reveal that sometimes the population of candidate solutions may lose its diversity too soon and the entire population may prematurely converge around the locally optimal points. The aim of this thesis is the study and development of novel evolutionary and swarm intelligence algorithms for continuous optimization problems that try to balance between global explorations and local exploitations and to maintain sufficient amount of population diversity to avoid premature convergence. Along the course of this thesis, we have developed two novel evolutionary algorithms and three improved swarm intelligence algorithms, which include the Recurring Two Stage Evolutionary Programming (RTEP), the Diversity Guided Evolutionary Programming (DGEP), the ABC with Self-adaptive Mutation (ABC-SAM), ABC with Improved Explorations (ABC-IX) and ABC with Adaptive Explorations and Exploitations (ABC-AX2). They employ techniques like dynamic adaptation and self-adaptation (e.g., ABC-SAM and ABC-AX2), hybridization with other meta-heuristic techniques for more explorations (e.g., ABC-IX), recurring alternations between complementary explorations and exploitations (e.g., RTEP) and automatic control of mutation step size using population diversity information (e.g., DGEP). We have also carried out intensive experimental studies on each of these algorithms to better understand how they work, how their components, control parameters and the proposed techniques affect their performance, final solution quality, convergence speed, population diversity and explorative search capacity. Each of our newly introduced algorithms is tested and evaluated on as many as 55 benchmark problems on continuous optimization from two different benchmark suites. Experimental studies show that the performance of the proposed algorithms is significantly better than many other relevant state-of-the-art evolutionary and swarm intelligence algorithms, which empirically establishes the effectiveness of our proposed techniques for the continuous optimization problems.