An Intelligent Programmed Genetic Algorithm with advanced deterministic diversity creating operator using objective surf
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RESEARCH PAPER
An Intelligent Programmed Genetic Algorithm with advanced deterministic diversity creating operator using objective surface visualization Devnath Shah1 · Saibal Chatterjee2 Received: 9 April 2019 / Revised: 28 October 2019 / Accepted: 8 March 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract This paper presents a new fast Intelligent Programmed Genetic Algorithm (IPGA) based evolutionary optimization algorithm which requires lesser number of objective function evaluation for reaching optima. The proposed algorithm, apart from using probabilistic genetic operator, i.e. crossover and mutation, also uses a deterministic diversity creating operator for generating new solution in the current population. This is done by first projecting objective surface from higher dimension to lower dimension for visualization purpose and then deterministically generates new solution using some predefined rules in the region with higher objective function value. As the newly generated solution is in lower-dimensional space, these solutions are again projected back to higher dimensional space and then the objective function is evaluated at that point. The proposed IPGA is tested on three different categories of standard test functions viz. Unimodal function (2 Test Function), Unrotated Multimodal function (6 Test Function) and Rotated Multimodal function (5 Test Function). Simulation results were compared with that obtained using Binary Coded GA, Real Coded GA, recently proposed GA with Differential Evolution crossover operator (GA–DEx) and another success-history-based adaptive GA with aging mechanism (GA–aDExSPS) in terms of mean and standard deviation of the objective function, average number of objective function evaluation required to reach optima and algorithmic complexity. Simulation results clearly demonstrate better performance of the proposed IPGA when compared with other variants of GAs. Keywords Evolutionary algorithm · Diversity · Multimodal · Visualized interactive GA · Intelligent programmed GA
1 Introduction Optimization is one of the most active area of research. Complexity of today’s real world optimization problem is very high and it requires a sophisticated optimization algorithm with optimal exploration and exploitation capability in reasonable time. A generalized unconstrained variable bounds single objective optimization problem with D-dimensions can be defined as follow [1–4]: * Devnath Shah [email protected] Saibal Chatterjee [email protected] 1
Department of Electrical Engineering, NERIST, Nirjuli, Arunachal Pradesh 791109, India
Department of Electrical and Electronics Engineering, NIT Mizoram Aizawl, Aizawl, Mizoram, India
2
Min f (x) [ ] x = x1 x2 … xD
(1)
Here the aim is to search for a vector x* such that f (x*) is minimum with x* ∈ [xmin, xmax]. The complexity of real world optimization problem is increasingly very high, efficient evolutionary algorithm like Genetic Algorithm (GA) [5], Simulated Annealing (SA) [6], Particle Swarm Optimization (
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