Learning automata and sigma imperialist competitive algorithm for optimization of single and multi-objective functions

Abstract

Evolutionary Algorithms (EA) consist of several heuristics which are able to solve optimisation tasks by imitating some aspects of natural evolution. Two widely-used EAs, namely Harmony Search (HS) and Imperialist Competitive Algorithm (ICA), are considered for improving single objective EA and Multi Objective EA (MOEA), respectively. HS is popular because of its speed and ICA has the ability for escaping local optima, which is an important criterion for a MOEA. In contrast, both algorithms have suffered some shortages. The HS algorithm could be trapped in local optima if its parameters are not tuned properly. This shortage causes low convergence rate and high computational time. In ICA, there is big obstacle that impedes ICA from becoming MOEA. ICA cannot be matched with crowded distance method which produces qualitative value for MOEAs, while ICA needs quantitative value to determine power of each solution. This research proposes a learnable EA, named learning automata harmony search (LAHS). The EA employs a learning automata (LA) based approach to ensure that HS parameters are learnable. This research also proposes a new MOEA based on ICA and Sigma method, named Sigma Imperialist Competitive Algorithm (SICA). Sigma method provides a mechanism to measure the solutions power based on their quantity value. The proposed LAHS and SICA algorithms are tested on wellknown single objective and multi objective benchmark, respectively. Both LAHS and MOICA show improvements in convergence rate and computational time in comparison to the well-known single EAs and MOEAs.