An effective improved differential evolution algorithm to solve constrained optimization problems

Yu, Xiaobing; Lu, Yiqun; Wang, Xüming; Luo, Xiang; Cai, Mei

doi:10.1007/s00500-017-2936-5

Cited by 22 publications

(12 citation statements)

References 72 publications

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“…DE is a population-based algorithm [ 27 ]. There are three operators in DE: The mutation, the crossover, and the selection.…”

Section: Methodsmentioning

confidence: 99%

Evaluation of an Agricultural Meteorological Disaster Based on Multiple Criterion Decision Making and Evolutionary Algorithm

2018

IJERPH

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The evaluation of a meteorological disaster can be regarded as a multiple-criteria decision making problem because it involves many indexes. Firstly, a comprehensive indexing system for an agricultural meteorological disaster is proposed, which includes the disaster rate, the inundated rate, and the complete loss rate. Following this, the relative weights of the three criteria are acquired using a novel proposed evolutionary algorithm. The proposed algorithm consists of a differential evolution algorithm and an evolution strategy. Finally, a novel evaluation model, based on the proposed algorithm and the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), is presented to estimate the agricultural meteorological disaster of 2008 in China. The geographic information system (GIS) technique is employed to depict the disaster. The experimental results demonstrated that the agricultural meteorological disaster of 2008 was very serious, especially in Hunan and Hubei provinces. Some useful suggestions are provided to relieve agriculture meteorological disasters.

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“…DE is a population-based algorithm [ 27 ]. There are three operators in DE: The mutation, the crossover, and the selection.…”

Section: Methodsmentioning

confidence: 99%

Evaluation of an Agricultural Meteorological Disaster Based on Multiple Criterion Decision Making and Evolutionary Algorithm

2018

IJERPH

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“…An information-sharing scheme is also proposed to exchange the information between these sub-populations. In [52], an improved variant of DE is proposed to solve COPs, where one of two distinct mutation operator is selected randomly to improve the solution quality in the population. Moreover, to deal with equality constraints, a new scheme is proposed to transform equality constraints into inequality constraints.…”

Section: Differential Evolutionmentioning

confidence: 99%

Power Flow Analysis of Islanded Microgrids: A Differential Evolution Approach

et al. 2021

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Power flow (PF) analysis of microgrids (MGs) has been gaining a lot of attention due to the evolution of islanded MGs. To calculate islanded MGs' PF solution, a globally convergent technique is proposed using Differential Evolution (DE)-a popular optimization algorithm for global non-convex optimization. This paper formulates the PF problem as a constrained optimization problem (COP) considering all the operating conditions of the Droop Controlled Islanded MGs (DCIMGs). To solve the proposed COP, DE-NGM, (Epsilon based Differential Evolution with Newton-Gauss-based mutation) is proposed. The proposed algorithm, DE-NGM, is a novel variant of DE since it comprises a novel mutation operator, Newton-Gauss-based mutation (NGM). NGM includes all the important features of DE's mutation strategies as well as reduces the constraint violation by utilizing the information of constraint-space. Numerical experiments validate that the global convergence ability of proposed algorithms in solving COPs than existing state-of-the-art algorithms. Furthermore, the proposed algorithm as a PF tool has better robustness than existing tools on ill-and well-conditioned systems with heavy loads, different limit violations, and inappropriate final solutions (far from the flat start). The performed comparative analysis confirms good agreement of accuracy and efficacy with the existing method for islanded MG's PF.

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“…Table 7 gives the mean and standard deviation of objective values with respect to CETDE and nine competing algorithms. Among all nine competitors, the first four are DEbased methods (i.e., DPDE [31], rank-iMDDE [36], eDE [44], and FRC-CEA [28]), the next four are non-DE-based methods (i.e., AIS [45], CMPSOWV [46], I-ABC [47] and ITLBO [48]), and the last one is a PSO-and DE-based hybrid method (i.e., DPD [49]). Since the best feasible optimal values are known, we compare the mean function values with the best known optima.…”

Section: B General Performance Of Cetde On Ieee Cec2006 Problemsmentioning

confidence: 99%

“…G02 G03 G04 DPDE [31] -15.0000 ± 0.00E+00 * -0.8024 ± 1.18E-03 -1.0005 ± 0.00E+00 * -30665.5387 ± 0.00E+00 * rank-iMDDE [36] -15.0000 ± 7.78E-10 * -0.8036 ± 7.20E-08 * -1.0005 ± 6.01E-07 * -30665.5390 ± 2.56E-08 * eDE [44] -15.0000 ± 0.00E+00 * -0.8020 ± 1. [31] 5126.4967 ± 0.00E+00 * -6961.8139 ± 0.00E+00 * 24.3062 ± 6.25E-09 * -0.0958 ± 0.00E+00 * rank-iMDDE [36] 5126.…”

Section: G01mentioning

confidence: 99%

“…[31] 5126.4967 ± 0.00E+00 * -6961.8139 ± 0.00E+00 * 24.3062 ± 6.25E-09 * -0.0958 ± 0.00E+00 * rank-iMDDE [36] 5126. [31] 680.6301 ± 3.65E-14 * 7049.2480 ± 8.36E-08 * 0.7499 ± 0.00E+00 * -1.0000 ± 0.00E+00 * rank-iMDDE [36] 680.6300 ± 1.56E-06 * 7049.2490 ± 8.24E-04 0.7499 ± 1.61E-07 * -1.0000 ± 0.00E+00 * eDE [44] 680.6301 ± 1.10E-25 * 7049.2480 ± 4.89E-19 * 0.7499 ± 1.28E-32 * -1.0000 ± 0.00E+00 * FRC-CEA [28] 680.6300 ± 2.49E-13 * 7049.2480 ± 1.40E-04 * 0.7499 ± 0.00E+00 * -1.0000 ± 0.00E+00 * AIS [45] 680.6300 ± 0.00E+00 * 7049.5700 ± 4.50E-04 0.7499 ± 1.40E-08 * -1.0000 ± 0.00E+00 * CMPSOWV [46] 680.6300 ± 2.76E-12 * 7085.1718 ± 7.13E+02 0.7499 ± 1.03E-12 * -1.0000 ± 0.00E+00 * I-ABC [47] 680.6330 ± 1.53E-03 7124.0420 ± 5.94E+01 0.7499 ± 2.44E-06 * -1.0000 ± 0.00E+00 * ITLBO [48] 680.6300 ± 3.36E-13 * 7049.2490 ± 4.29E-05 0.7499 ± 1.13E-16 * -1.0000 ± 0.00E+00 * DPD [49] 680.6301 ± 0.00E+00 * 7049.2480 ± 0.00E+00 * 0.7499 ± 0.00E+00 * -1.0000 ± 0.00E+00 * CETDE 680.6301 ± 1.88E-09 * 7049.2480 ± 6.24E-08 * 0.7499 ± 1.54E-09 * -1.0000 ± 0.00E+00 * G13 G14 G15 G16 DPDE [31] 0.0539 ± 1.16E-17 * -47.7649 ± 2.56E-09 * 961.7150 ± 0.00E+00 * -1.9052 ± 0.00E+00 * rank-iMDDE [36] 0. [28] -398.2812 ± 6.27E+00 -5.5080 ± 0.00E+00 * 19 AIS [45] -399.8743 ± 2.00E+00 -5.5080 ± 0.00E+00 * 15 CMPSOWV [46] -360.2836 ± 1.43E+01 -5.5080 ± 0.00E+00 * 16 I-ABC [47] 169.0210 ± 3.67E+02 -5.5080 ± 1.78E-15 * 7 ITLBO [48] -256.4000 ± 1.42E+02 -5.5080 ± 9.06E-16 * 15 DPD [49] -398.1809 ± 2.97E+00 -5.5080 ± 0.00E+00 * 20 CETDE -399.4736 ± 2.88E+00 -5.5080 ± 5.69E-11 * 19 This work is licensed under a Creative Commons Attribution 4.0 License.…”

Section: G01mentioning

confidence: 99%

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Constrained Optimization Based on Ensemble Differential Evolution and Two-Level-Based Epsilon Method

Zhang

2020

IEEE Access

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Constrained optimization problems (COPs) are common in many fields, and the search algorithm and constraint handling technique play important roles in the constrained evolution algorithms. In this paper, we propose a new optimization algorithm named CETDE based on ensemble differential evolution (DE) and a two-level epsilon-constrained method. In the ensemble DE variant, some promising parameters and mutation strategies constitute the candidate pool, and each element in the pool coexists throughout the search process and competes to generate new solutions. The two-level epsilon method is proposed by incorporating a generation and a population comparison level to retain more promising solutions without degrading the solution quality. Moreover, a diversity promotion scheme is developed to improve the population distribution when the search becomes trapped in a small region. The superior performance of CETDE is validated by comparison with some state-of-the-art COEAs over two sets of artificial benchmarks and five real-world problems. The competitive results show that CETDE is an effective method for solving COPs.

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An effective improved differential evolution algorithm to solve constrained optimization problems

Cited by 22 publications

References 72 publications

Evaluation of an Agricultural Meteorological Disaster Based on Multiple Criterion Decision Making and Evolutionary Algorithm

Evaluation of an Agricultural Meteorological Disaster Based on Multiple Criterion Decision Making and Evolutionary Algorithm

Power Flow Analysis of Islanded Microgrids: A Differential Evolution Approach

Constrained Optimization Based on Ensemble Differential Evolution and Two-Level-Based Epsilon Method

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