Novel Strategies for Single and Multi-Objective Imperialistic Competitive Algorithm

Abstract

ABSTRACT: In this thesis, two different algorithms for solving global optimization problems were developed. The first is imperialistic competitive algorithm with updated assimilation (ICAMA), which is used for solving single-objective optimization problems. ICAMA is a new strategic improvement on the imperialist competitive algorithm (ICA) that is originally proposed based on inspirations from imperialistic competition. Another algorithm is a multi-objective imperialistic competitive algorithm (MOICA), which is for global multi-objective optimization problems. ICA is based on the idea of imperialism. Two fundamental components of ICA are empires and colonies. Initially, the algorithm builds several randomly initialized empires where each empire includes one emperor and several colonies. Competitions take place between the empires and these competitions result in the development of more powerful empires and the collapse of the weaker ones. In ICAMA a new method is introduced for the movement of colonies towards their imperialist, which is called assimilation. The proposed method uses Euclidean distance along with Pearson correlation coefficient as an operator for assimilating colonies with respect to their imperialists. In order to test the effectiveness and competitiveness of ICAMA against other state of the art algorithms it was applied to three sets of benchmark problems – the set of 23 classical benchmark problems, CEC2005 and CEC2015 benchmarks. MOICA is a modified multi-objective version of ICA. MOICA incorporates the competition between empires and their colonies for the solution of multi-objective problems. Therefore, it employs a proposed approach of several non-dominated solution sets, whereby each set is called a local non-dominated solution set (LNDS). All imperialists in an empire are considered non-dominated solutions, whereas all colonies are considered dominated solutions. Aside from local non-dominated solution sets, there is one global non-dominated solution set (GNDS), which is created from LNDS sets of all empires. MOICA is applied to a number of benchmark problems such as the set of ZDT problems and CEC2009 multi-objective optimization benchmark problems set. Simulations and experimental results on the benchmark problems showed that ICAMA produces competitive results for many test problems compared to other state-of-the-art algorithms used in this study. Moreover, MOICA is more efficient with comparison to many of the competitor algorithms used in this study, since it produces better results for most of the test problems. Keywords: Multi-objective metaheuristics, imperialistic competitive algorithm, multiple non-dominated sets, global optimization.