A fuzzy imperialistic competitive algorithm for optimizing convex functions

Abstract

Purpose – The purpose of this paper is to describe imperialist competitive algorithm (ICA), a novel socio-politically inspired optimization strategy for proposing a fuzzy variant of this algorithm. ICA is a meta-heuristic algorithm for dealing with different optimization tasks. The basis of the algorithm is inspired by imperialistic competition. It attempts to present the social policy of imperialisms (referred to empires) to control more countries (referred to colonies) and use their sources. If one empire loses its power, among the others making a competition to take possession of it. Design/methodology/approach – In fuzzy imperialist competitive algorithm (FICA), the colonies have a degree of belonging to their imperialists and the top imperialist, as in fuzzy logic, rather than belonging completely to just one empire therefore the colonies move toward the superior empire and their relevant empires. Simultaneously for balancing the exploration and exploitation abilities of the ICA. The algorithms are used for optimization have shortcoming to deal with accuracy rate and local optimum trap and they need complex tuning procedures. FICA is proposed a way for optimizing convex function with high accuracy and avoiding to trap in local optima rather than using original ICA algorithm by implementing fuzzy logic on it. Findings – Therefore several solution procedures, including ICA, FICA, genetic algorithm, particle swarm optimization, tabu search and simulated annealing optimization algorithm are considered. Finally numerical experiments are carried out to evaluate the effectiveness of models as well as solution procedures. Test results present the suitability of the proposed fuzzy ICA for convex functions with little fluctuations. Originality/value – The proposed evolutionary algorithm, FICA, can be used in diverse areas of optimization problems where convex functions properties are appeared including, industrial planning, resource allocation, scheduling, decision making, pattern recognition and machine learning (optimization techniques; fuzzy logic; convex functions).

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“…ICA is one of the recent EAs proposed to solve optimization problems. ICA was first proposed by Atashpaz Gargari and Lucas (2007), and up to now, it has been used to solve continuous optimization problems (Esmaeilzadeh et al, 2014). The problem which is considerable is that "what can affect the optimization process?"…”

“…Fuzzy logic is a probabilistic logic; it is an approximation rather than fixed and exact. Compared to traditional binary sets (where variables may take on true or false values), fuzzy logic variables may have a truth value that ranges in degree between 0 and 1 (Esmaeilzadeh et al, 2014). Fuzzy logic has been extended to handle the concept of partial truth, where the truth value may range between completely true and completely false (Novk et al, 1999).…”

“…FICA is one of the recently modified ICA that is presented by (Esmaeilzadeh et al, 2014). In FICA, the colonies have a degree of belonging to their imperialists and the top imperialist, as in fuzzy logic, rather than belonging completely to just one empire; therefore, the colonies move toward the superior empire and their relevant empires simultaneously.…”