Solving Mono- and Multi-Objective Problems Using Hybrid Evolutionary Algorithms and Nelder-Mead Method

Solving Mono- and Multi-Objective Problems Using Hybrid Evolutionary Algorithms and Nelder-Mead Method

Noureddine Boukhari, Fatima Debbat, Nicolas Monmarché, Mohamed Slimane
Copyright: © 2021 |Pages: 19
DOI: 10.4018/IJAMC.2021100106
OnDemand:
(Individual Articles)
Available
$37.50
No Current Special Offers
TOTAL SAVINGS: $37.50

Abstract

Evolution strategies (ES) are a family of strong stochastic methods for global optimization and have proved their capability in avoiding local optima more than other optimization methods. Many researchers have investigated different versions of the original evolution strategy with good results in a variety of optimization problems. However, the convergence rate of the algorithm to the global optimum stays asymptotic. In order to accelerate the convergence rate, a hybrid approach is proposed using the nonlinear simplex method (Nelder-Mead) and an adaptive scheme to control the local search application, and the authors demonstrate that such combination yields significantly better convergence. The new proposed method has been tested on 15 complex benchmark functions and applied to the bi-objective portfolio optimization problem and compared with other state-of-the-art techniques. Experimental results show that the performance is improved by this hybridization in terms of solution eminence and strong convergence.
Article Preview
Top

Introduction

Metaheuristic algorithms can find global optimal solutions for the problems where there are many local solutions due to their random nature. These reasons have led to extensive use of such algorithms in solving various optimization problems and have been successfully applied to mono and multi-objective complicated problems of scientific and engineering computing. In the last decade, researchers have carried out extensive studies on metaheuristic algorithms such as particle swarm optimization (PSO) (Erdogmus, 2018) harmony search (HS) (Abdel-Raouf & Metwally, 2013), artificial bee colony (ABC) (Karaboga, Gorkemli, Ozturk & Karaboga, 2012), cuckoo search (CS) firefly algorithm (FA) (Fister, Yang, Fister, & Fister, 2013), imperialist competitive algorithm (ICA) (Liu, Su, & Chiu, 2013), teaching-learning-based optimization (TLBO) (Rao, 2015), differential evolution algorithm (DE) (Das & Suganthan, 2011), Social Spider Optimization (SSO) (Cuevas, Cienfuegos, Zaldívar, & Pérez-Cisneros, 2013) and biogeography-based optimizer (BBO) (Ma & Simon, 2017). Besides, many metaheuristic algorithms have been improved to solve real-world optimization problems such as evolutionary algorithms for mobile multi-hop Ad Hoc network optimization problems (Reina, et al., 2016), a decomposition-based multi-objective firefly algorithm developed for RFID network planning (Zhao et al., 2017) and an enhanced bees algorithm for resource constrained optimization problems (Nemmich, Debbat & Slimane, 2019). Based on the “no free lunch” theorem (NFL) (Koehler, 2007), there is no optimization algorithm that works well on all optimization problems. An optimization algorithm may achieve very good results on a set of optimization problems, while it is not suitable for others.

Metaheuristics have a strong ability of exploration and a cheap running cost, however, due to the complexity and non-linearity of real word problems, they suffer from slow convergence and low precision. Recently, there has been an emergence of hybrid algorithms, combining global heuristic methods together with traditional local exploitation algorithms. They are also called Memetic, in which one or more local search phases are included in algorithms’ every evolutionary cycle and are considered more effective than traditional evolutionary algorithms for some problem domains (Neri, Cotta, & Moscato, 2013) such as a hybrid differential evolution for electric motor design (Essaid, Idoumghar, Lepagnot, Brévilliers, & Fodorean, 2018), a hybrid genetic algorithm is combined with tabu local search method for solving machine layout problem (Jaramillo & Mckendall, 2018) and memetic PSO with simulated annealing for solving missing value imputation (Sivaraj & Devipriya, 2019).

Complete Article List

Search this Journal:
Reset
Volume 15: 1 Issue (2024)
Volume 14: 1 Issue (2023)
Volume 13: 4 Issues (2022): 2 Released, 2 Forthcoming
Volume 12: 4 Issues (2021)
Volume 11: 4 Issues (2020)
Volume 10: 4 Issues (2019)
Volume 9: 4 Issues (2018)
Volume 8: 4 Issues (2017)
Volume 7: 4 Issues (2016)
Volume 6: 4 Issues (2015)
Volume 5: 4 Issues (2014)
Volume 4: 4 Issues (2013)
Volume 3: 4 Issues (2012)
Volume 2: 4 Issues (2011)
Volume 1: 4 Issues (2010)
View Complete Journal Contents Listing