Multi-population parallel imperialist competitive algorithm for solving systems of nonlinear equations

Majd, Amin; Abdollahi, Mahdi; Sahebi, Golnaz; Abdollahi, Davoud; Daneshtalab, Masoud; Plosila, Juha; Tenhunen, Hannu

doi:10.1109/hpcsim.2016.7568412

Cited by 7 publications

(3 citation statements)

References 23 publications

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“…In this paper, a parallel implementation of the ICA (PICA – Parallel ICA) is proposed. We extend our previous works (see the works of Majd et al()) by presenting two different parallel implementations of PICA (multi‐population and master‐slave) to improve the speed and accuracy. The results are extensively analyzed with eight benchmarks and three case studies.…”

Section: Introductionmentioning

confidence: 87%

Parallel imperialist competitive algorithms

Majd

Sahebi

Daneshtalab

et al. 2018

Concurrency and Computation

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Summary The importance of optimization and NP‐problem solving cannot be overemphasized. The usefulness and popularity of evolutionary computing methods are also well established. There are various types of evolutionary methods; they are mostly sequential but some of them have parallel implementations as well. We propose a multi‐population method to parallelize the Imperialist Competitive Algorithm. The algorithm has been implemented with the Message Passing Interface on 2 computer platforms, and we have tested our method based on shared memory and message passing architectural models. An outstanding performance is obtained, demonstrating that the proposed method is very efficient concerning both speed and accuracy. In addition, compared with a set of existing well‐known parallel algorithms, our approach obtains more accurate results within a shorter time period.

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Section: Introductionmentioning

confidence: 87%

Parallel imperialist competitive algorithms

Majd

Sahebi

Daneshtalab

et al. 2018

Concurrency and Computation

Self Cite

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“…Abdollahi et al [24] used the standard imperialist competitive algorithm (ICA), Oliveira et al [25] proposed a variant of simulated annealing algorithm with fuzzy rules adaptations, Wu et al [26] used a new variant of the Social emotional optimization for solving nonlinear systems of equations. Other applications of metaheuristics for nonlinear systems include invasive weed optimization algorithm [27], polarization technique [28], cuckoo optimization algorithm [29], genetic algorithm [30][31][32], artificial bee colony algorithm [33] and multi-population parallel ICA [34] their successful applications, there also exist two main challenges for metaheuristics that are (i) maintaining balance between exploration and exploitation (ii) avoiding large computational cost. Abdollahi et al [35] highlighted that in most of the previous applications [1,[21][22][23][24][25][26]29,30,33,36,37] of metaheuristics to nonlinear systems large population sizes were used which resulted in high computation costs and slow convergence.…”

Section: Introductionmentioning

confidence: 99%

A Multi-Simplex Imperialist Competitive Paradigm for Solving Nonlinear Physical Systems

Ali¹,

Iqbal²,

Alkhalaf³

2022

Intelligent Automation &Amp; Soft Computing

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This paper proposes a novel gradient free multi-simplex topology fabric aided imperialist competitive algorithm (ICA) for solving nonlinear systems of algebraic equations by transforming them to equivalent global optimization problems. The high dependence of traditional gradient based solvers of such systems on initial guesses and the Jacobeans resulting in false convergence is the main motivation behind the present work. The present work provides a mechanism for enhancing exploitation powers of imperialist search phase of the algorithm and hence improves the convergence speed. The variants emerging from the proposed approach are applied to diverse nonlinear systems arising in different scientific areas and the results so obtained are analyzed in details. Based on the analysis of empirical results on complex benchmark models, it is observed that the proposed enhancement of ICA has not only boosted the problem solving power of the imperialist system when applied multidimensional nonlinear physical systems but also emerged as an efficient gradient/initial guess free alternative solver with high accuracy for nonlinear systems.

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“…Some heuristic optimization algorithms have also been used for the solutions of the nonlinear equation systems. Genetic algorithms [2], parallel imperialist competitive algorithm [6], weed optimization algorithm [7], particle swarm optimization [8], immune genetic algorithm [9], leader glowworm swarm optimization [10] and hybrid social emotional optimization algorithm [11] have been used for the solution of the nonlinear equation systems.…”

Section: Introductionmentioning

confidence: 99%

A New Solution Approach for Non-Linear Equation Systems with Grey Wolf Optimizer

Erdoğmuş

2018

Sakarya University Journal of Computer and Information Sciences

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The aim of this study is to bring a new perspective for the solutions of non-linear equation systems. So this study handles the non-linear equation systems as a constrained optimization problem, while generally is handled unconstrained optimization problem or multi objective optimization problem. The object is to minimize the sum of the squares of nonlinear equations under the nonlinear equality constraints. A recently developed heuristic optimization algorithm called Grey Wolf Optimizer (GWO) is proposed for the solution of nonlinear equation systems. Two results were obtained. Firstly, it has been seen that GWO can be an alternative solution technique for the solution of nonlinear equation systems. Secondly, modelling the systems of nonlinear equations as constrained optimization gives better results.

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Multi-population parallel imperialist competitive algorithm for solving systems of nonlinear equations

Cited by 7 publications

References 23 publications

Parallel imperialist competitive algorithms

Parallel imperialist competitive algorithms

A Multi-Simplex Imperialist Competitive Paradigm for Solving Nonlinear Physical Systems

A New Solution Approach for Non-Linear Equation Systems with Grey Wolf Optimizer

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