A tri-objective differential evolution approach for multimodal optimization

Yu, Wei; Ji, Jing-Yu; Gong, Yue-Jiao; Yang, Qiang; Zhang, Mengjie

doi:10.1016/j.ins.2017.09.044

Cited by 47 publications

(14 citation statements)

References 30 publications

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“…For example, in [13], the authors proposed a modified MOEA/D algorithm with repair strategy and penalty function for constraints processing to solve the MOOPF problem. A tri-objective differential evolution (DE) approach was carried out for the TOP problem contains all global optima of the MMOP in [14]. In [15], Emilio Barocio implemented the modified flower pollination algorithm (MFPA) to calculate the PFs under different objective combinations of the MOOPF problem, using added penalty functions to handle the constraints.…”

Section: Introductionmentioning

confidence: 99%

Solving the Multi-Objective Optimal Power Flow Problem Using the Multi-Objective Firefly Algorithm with a Constraints-Prior Pareto-Domination Approach

Chen

Zhang

et al. 2018

Energies

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Known as a multi-objective, large-scale, and complicated optimization problem, the multi-objective optimal power flow (MOOPF) problem tends to be introduced with many constraints. In this paper, compared with the frequently-used penalty function-based method (PFA), a novel constraint processing approach named the constraints-prior Pareto-domination approach (CPA) is proposed for ensuring non-violation of various inequality constraints on dependent variables by introducing the Pareto-domination principle based on the sum of constraint violations. Moreover, for solving the constrained MOOPF problem, the multi-objective firefly algorithm with CPA (MOFA-CPA) is proposed and some optimization strategies, such as the crowding distance calculation and non-dominated sorting based on the presented CPA, are utilized to sustain well-distributed Pareto front (PF). Finally, in order to demonstrate the feasible and effective improvement of MOFA-CPA, a comparison study between MOFA-CPA and MOFA-PFA is performed on two test systems, including three bi-objective optimization cases and three tri-objective optimization cases. The simulation results demonstrate the capability of the MOFA-CPA for obtaining PF with good distribution and superiority of the proposed CPA for dealing with inequality constraints on dependent variables. In addition, some quality indicators are used to evaluate the convergence, distribution, and uniformity of the PFs found by the MOFA-CPA and MOFA-PFA.

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Section: Introductionmentioning

confidence: 99%

Solving the Multi-Objective Optimal Power Flow Problem Using the Multi-Objective Firefly Algorithm with a Constraints-Prior Pareto-Domination Approach

Chen

Zhang

et al. 2018

Energies

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“…The number of runs on each function, N R, is 50 for each of the eight algorithms. The population of each algorithm is set dependent on the specific problem, and is given by N = 40 DN g [72]. For the i-th run of each algorithm, the population is initialised from the same location to ensure that the performance is determined by the internal search mechanism, rather than the initial location of the population, where the initial location for each run is randomly set between the design space bounds.…”

Section: Parameter Tuningmentioning

confidence: 99%

Constrained niching using differential evolution

Poole

Allen

2019

Swarm and Evolutionary Computation

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The work presented here involves development and detailed investigations of niching methods for multimodal optimization of constrained functions. There is a lack of investigations in the literature on constrained multimodal optimization, hence a number of constrained niching algorithms have been developed here that leverage existing differential evolution-based niching methods with a feasibility rules-domination selection procedure. Furthermore, a suite of 18 benchmark functions has been developed and are presented in this paper; nine newly developed functions are incorporated with nine existing functions from the literature. Optimization results on these analytical functions using the constrained niching algorithms are presented, with analysis provided on the ability to locate multiple global optima, the convergence speed and constraint handling nature of the methods. The differential evolution strategy is also investigated, with SHADE and L-SHADE strategies considered. Finally, a dimensionality study also compares against the only other known constrained niching algorithm. Results indicate that all of the algorithms developed and tested generally perform well for low dimensional, low modality problems, but that local neighbourhood-based methods show the best results across the suite of functions tested. When high-dimensional problems are considered, using the L-SHADE strategy yields excellent results. An accompanying supplementary data file is provided with the manuscript.has also been successfully applied to DE [51]. The ensemble approach takes any number of constraint handling techniques and adaptively applies them to exploit the individual performance of each technique. Mezura-Montes et al.[52] investigated the effect of different mutation strategies in DE on constrained optimization. They highlighted the fact that much work in solving CNOPs using DE uses the feasibility rules of Deb [14], and as such, used this to handle the constraints.Commonly, population diversity is a requirement of EAs, such that design space exploration is achieved, with diversity decreasing through the optimization to exploit the global optimum within the space. On the other hand, while diversity is important for unimodal optimization, this is not necessarily the main driver of niching techniques. Niching requires a more careful balance of diversity to be able to locate and maintain strong and stable niches, and therefore exploit all the optima in the design space. Comprehensive reviews on niching techniques have been provided by Das et al.[53] and more recently by Li et al. [25] (the reader is particularly guided to the review of Li et al. for discussions of niching using SIAs as well as EAs), and a short review is presented here with particular attention paid to niching using EAs.One of the earliest bodies of work on maintaining population diversity, and therefore implicitly also multimodal optimization, was by de Jong [17], who introduced the classical idea of crowding. Crowding compares the fitness of close individuals and attemp...

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“…Moreover, an adaptive peak detection strategy is employed to find peaks where optimal solutions may exist. Yu et al [19] proposed a tri-objective differential evolution approach algorithm, where three optimization objectives are constructed to ensure good population diversity. In addition, a solution comparison rule and a ranking strategy are employed to enhance the accuracy of solutions.…”

Section: Related Workmentioning

confidence: 99%

“…However, the performance of the two improved versions of CMA-ES is highly sensitive to niching parameters. So far, some works have been done to convert a multimodal optimization problem (MMOP) to a multi-objective optimization problem (MOP) [15][16][17][18][19]. The advantage of transforming an MMOP into an MOP is that it is unnecessary to use the problem-dependent niching parameters.…”

Section: Introductionmentioning

confidence: 99%

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Matrix Adaptation Evolution Strategy with Multi-Objective Optimization for Multimodal Optimization

2019

Algorithms

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The standard covariance matrix adaptation evolution strategy (CMA-ES) is highly effective at locating a single global optimum. However, it shows unsatisfactory performance for solving multimodal optimization problems (MMOPs). In this paper, an improved algorithm based on the MA-ES, which is called the matrix adaptation evolution strategy with multi-objective optimization algorithm, is proposed to solve multimodal optimization problems (MA-ESN-MO). Taking advantage of the multi-objective optimization in maintaining population diversity, MA-ESN-MO transforms an MMOP into a bi-objective optimization problem. The archive is employed to save better solutions for improving the convergence of the algorithm. Moreover, the peaks found by the algorithm can be maintained until the end of the run. Multiple subpopulations are used to explore and exploit in parallel to find multiple optimal solutions for the given problem. Experimental results on CEC2013 test problems show that the covariance matrix adaptation with Niching and the multi-objective optimization algorithm (CMA-NMO), CMA Niching with the Mahalanobis Metric and the multi-objective optimization algorithm (CMA-NMM-MO), and matrix adaptation evolution strategy Niching with the multi-objective optimization algorithm (MA-ESN-MO) have overall better performance compared with the covariance matrix adaptation evolution strategy (CMA-ES), matrix adaptation evolution strategy (MA-ES), CMA Niching (CMA-N), CMA-ES Niching with Mahalanobis Metric (CMA-NMM), and MA-ES-Niching (MA-ESN).

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A tri-objective differential evolution approach for multimodal optimization

Cited by 47 publications

References 30 publications

Solving the Multi-Objective Optimal Power Flow Problem Using the Multi-Objective Firefly Algorithm with a Constraints-Prior Pareto-Domination Approach

Solving the Multi-Objective Optimal Power Flow Problem Using the Multi-Objective Firefly Algorithm with a Constraints-Prior Pareto-Domination Approach

Constrained niching using differential evolution

Matrix Adaptation Evolution Strategy with Multi-Objective Optimization for Multimodal Optimization

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