Melez elektromanyetizma benzeri-parçacık sürü optimizasyon algoritması

Abstract

Optimizasyon, bir problemin alternatif çözümleri içinden en uygununu seçme işlemidir. Optimizasyon problemlerinin çözümü için, kabul edilebilir sürede optimuma yakın çözümler verebilen birçok sezgisel optimizasyon algoritması önerilmiştir. Literatürde çok başarılı sezgisel optimizasyon algoritmaları bulunsa da; tüm problemlerin çözümü için en optimum çözümü bulan algoritmalar henüz tasarlanmamıştır. Bu yüzden yeni sezgisel optimizasyon algoritmaları önerilmekte ya da var olanların daha etkili çalışması için öneriler sunulmaktadır. Bu çalışmada, global optimizasyon için, Elektromanyetizma Benzeri (EM) algoritma ile Parçacık Sürü Optimizasyon (PSO) algoritmasının birleşiminden oluşan yeni bir melez yöntem olan EM-PSO önerilmiştir. Önerilen yöntemde, PSO algoritmasının hız denklemindeki sabit katsayılar yerine EM algoritmasındaki yük ve toplam kuvvet değerleri kullanılmış ve EM algoritmasındaki parçacıkların hareketi bu denklem ile gerçekleştirilmiştir. Önerilen yöntemin performansı beş farklı kalite testi fonksiyonu kullanılarak test edilmiştir ve sonuçlar standart EM ve PSO algoritmalarının sonuçları ile karşılaştırılmıştır. Deneysel sonuçlar, önerilen yöntemin standart EM ve PSO algoritmalarına göre daha başarılı olduğunu göstermiştir.

Keywords

• Elektromanyetizma benzeri algoritma, Parçacık sürü optimizasyon algoritması, Melez EM-PSO

Hybrid electromagnetism like–particle swarm optimization algorithm

Abstract

Optimization is the process of selecting the most appropriate solution in all alternative solutions of a problem. A lot of meta-heuristic optimization algorithms are proposed to find approximate solutions for solving optimization problems in acceptable time. Although there are many successful meta-heuristic optimization algorithms in the literature, an algorithm hasn’t been designed to find optimum solutions for solving all optimization problems yet. Therefore, new meta-heuristic algorithms are proposed or the existing algorithms are modified for better results. In this paper, a novel hybrid optimization algorithm EM-PSO which is consist of the Electromagnetism-like (EM) algorithm and the Particle Swarm Optimization (PSO) algorithm has been proposed for global optimization. The EM was firstly proposed by Birbil and Fang in 2003. The EM is inspired by attraction-repulsion mechanism of electromagnetism theory. Each member in the search space is considered as a charged particle. The general algorithm consists of four phases. These are initialization of algorithm, local search, calculation of the total force, and movement. In initialization phase, the particles are initialized with random positions between the corresponding upper bound and lower bound of the search space. After, the objective function values of the each particle are calculated. Finally, the best objective function value is stored as x best. In the local search phase, local information about each particle is gathered. In the calculation of the total force phase, the charges of the each particle are calculated according to their objective function values. Then, the total force exerted on a particle from other particles is calculated. In movement phase, each particle is moved in the direction of the total force by a random step length. If maximum number of iterations is reached then algorithm terminates. At the end of the algorithm, the best particle is selected as the solution of the optimization problem. The PSO is proposed by Kennedy and Eberhart in 1995 which is an evolutionary computation technique. The PSO was inspired from social behaviors of bird and fish swarms. Each member in the search space is considered as a particle. The population is considered as a swarm. The PSO algorithm focused on initializing and particle movement. The particles are initialized with random positions throughout the search space. Each particle should consider the current position and its best position (pbest). Moreover, each particle should know the best position of the swarm (gbest). With this information, the velocities of the each particle toward its pbest and gbest are calculated. Then each particle is moved by its velocity. If maximum number of iterations is reached then algorithm terminates. At the end of the algorithm, the best particle is selected as the solution of the optimization problem. In EM algorithm, each particle is only moved in the direction of the total force. In EM-PSO algorithm, the movement of particles in movement phase of EM has been executed with PSO. The values q and F in the EM have been used instead of the values c1, c2, rand1 and rand2 in the velocity equation that is in PSO. In this way, the movement of the each particle is influenced by its best position (pbest) and the best position of the swarm (gbest). The performance of proposed hybrid EM-PSO algorithm has been tested with five benchmark functions which are Rastrigin, Rosenbrock, De Jong, Griewang and Ackley. The obtained test results have been compared with standard EM and standard PSO algorithms’ test results. According to the all benchmark test results we have showed that the new proposed hybrid algorithm is successful than standard EM and standard PSO. In the future works, parallel and distributed versions of EM-PSO algorithm can be developed. Generalization of EM-PSO algorithm for multiobjective optimization problems can also be one of the further works

Keywords

• Electromagnetism-like algorithm, Particle swarm optimization algorithm, Hybrid EMPSO