A novel constraint-handling technique based on dynamic weights for constrained optimization problems

Peng, Chaoda; Liu, Hai Lin; Gu, Fangqing

doi:10.1007/s00500-017-2603-x

Cited by 30 publications

(13 citation statements)

References 26 publications

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“…As another generic multiobjective optimization framework, decomposition-based multiobjective optimization has been gaining increasing attention for solving MOPs, nevertheless, it has scarcely been applied for constrained evolutionary optimization. Recently, Peng et al [48] took advantage of the Tchebycheff decomposition approach to solve COPs. In this method, N weight vectors are used to select N promising infeasible solutions, and the remaining (NP − N) candidate solutions are selected based on the feasibility rule [49].…”

Section: ) Standard Multiobjective Optimization Methods: This Kind Omentioning

confidence: 99%

“…First, DeCODE was evaluated on the 24 benchmark test functions from IEEE CEC2006. Its performance was compared with four state-of-the-art COEAs with various constrainthandling techniques: CMODE [7], NSES [9], DW [48], and FROFI [54]. Note that CMODE and NSES are methods based on Pareto dominance.…”

Section: B Experiments On the 24 Benchmark Test Functions From Ieee mentioning

confidence: 99%

“…In summary, the experimental results validate that DeCODE yields better or similar performance compared with other four competitors on the 24 test functions from IEEE CEC2006. were selected as the competitors: ITLBO [59], FROFI [54], CACDE [60], AIS-IRP [61], and DW [48]. The experimental results of ITLBO and FROFI can be available from our previous study.…”

Section: B Experiments On the 24 Benchmark Test Functions From Ieee mentioning

confidence: 99%

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Decomposition-Based Multiobjective Optimization for Constrained Evolutionary Optimization

Wang

Zhang

et al. 2021

IEEE Trans. Syst. Man Cybern, Syst.

101

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Pareto dominance-based multiobjective optimization has been successfully applied to constrained evolutionary optimization during the last two decades. However, as another famous multiobjective optimization framework, decompositionbased multiobjective optimization has not received sufficient attention from constrained evolutionary optimization. In this paper, we make use of decomposition-based multiobjective optimization to solve constrained optimization problems (COPs). In our method, first of all, a COP is transformed into a biobjective optimization problem (BOP). Afterward, the transformed BOP is decomposed into a number of scalar optimization subproblems. After generating an offspring for each subproblem by differential evolution, the weighted sum method is utilized for selection. In addition, to make decompositionbased multiobjective optimization suit the characteristics of constrained evolutionary optimization, weight vectors are elaborately adjusted. Moreover, for some extremely complicated COPs, a restart strategy is introduced to help the population jump out of a local optimum in the infeasible region. Extensive experiments on three sets of benchmark test functions, namely, 24 test functions from IEEE CEC2006, 36 test functions from IEEE CEC2010, and 56 test functions from IEEE CEC2017, have demonstrated that the proposed method shows better or at least competitive performance against other state-of-the-art methods.

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Section: ) Standard Multiobjective Optimization Methods: This Kind Omentioning

confidence: 99%

Section: B Experiments On the 24 Benchmark Test Functions From Ieee mentioning

confidence: 99%

Section: B Experiments On the 24 Benchmark Test Functions From Ieee mentioning

confidence: 99%

See 1 more Smart Citation

Decomposition-Based Multiobjective Optimization for Constrained Evolutionary Optimization

Wang

Zhang

et al. 2021

IEEE Trans. Syst. Man Cybern, Syst.

101

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show abstract

“…They designed a strategy of adjusting weights. Peng et al [13] applied the Chebyshev approach to decompose the problem (2). They designed biased dynamic weights for selecting different individuals with low objective values and low degree of constraint violations.…”

Section: Literature Reviewmentioning

confidence: 99%

Helper and Equivalent Objectives: Efficient Approach for Constrained Optimization

Shang

2022

IEEE Trans. Cybern.

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Numerous multi-objective evolutionary algorithms have been designed for constrained optimisation in last two decades. This method is to transform a constrained optimisation problem into a multi-objective optimisation problem, then solve it by an evolutionary algorithm. In this paper, we propose a new multi-objective method for constrained optimisation, which is to convert a constrained optimisation problem into a problem with helper and equivalent objectives. An equivalent objective means that its optimal solution set is the same as that to the constrained problem but a helper objective not. Then this multiobjective optimisation problem is decomposed into a group of sub-problems using the weighted sum approach. Weights are dynamically adjusted so that each subproblem eventually tends to a problem with an equivalent objective. We theoretically analyse the computation time of the helper and equivalent objective method on a hard problem called "wide gap". The "wide gap" problem means that an algorithm needs exponential time to cross between two fitness levels. We prove that using helper and equivalent objectives may shorten the time of crossing the "wide gap". We conduct a case study for validating our method. An algorithm with helper and equivalent objectives is implemented. Experimental results show that its overall performance is ranked first when compared with other eight state-of-art evolutionary algorithms. The case study proves the efficiency of the helper and equivalent objective method for constrained optimisation.

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“…The performance of C 2 oDE was compared with that of four state-of-the-art CDE (i.e., CMODE [40], FROFI [8], NDE [71], and DW [72]). From [21], we know that it is extremely difficult to find a feasible solution for g22 and there are no feasible solutions for g20.…”

Section: B Experiments On Ieee Cec2006 Test Suitementioning

confidence: 99%

Composite Differential Evolution for Constrained Evolutionary Optimization

Wang

et al. 2019

IEEE Trans. Syst. Man Cybern, Syst.

149

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Abstract-When solving constrained optimization problems by evolutionary algorithms, the search algorithm plays a crucial role. In general, we expect that the search algorithm has the capability to balance not only diversity and convergence but also constraints and objective function during the evolution. For this purpose, this paper proposes a composite differential evolution for constrained optimization, which includes three different trial vector generation strategies with distinct advantages. In order to strike a balance between diversity and convergence, one of these three trial vector generation strategies is able to increase diversity, and the other two exhibit the property of convergence. In addition, to accomplish the tradeoff between constraints and objective function, one of the two trial vector generation strategies for convergence is guided by the individual with the least degree of constraint violation in the population, and the other is guided by the individual with the best objective function value in the population. After producing offspring by the proposed composite differential evolution, the feasibility rule and the ε constrained method are combined elaborately for selection in this paper. Moreover, a restart scheme is proposed to help the population jump out of a local optimum in the infeasible region for some extremely complicated constrained optimization problems. By assembling the above techniques together, a constrained composite differential evolution is proposed. The experiments on two sets of benchmark test functions with various features, i.e., 24 test functions from IEEE CEC2006 and 18 test functions with 10 dimensions and 30 dimensions from IEEE CEC2010, have demonstrated that the proposed method shows better or at least competitive performance against other state-of-the-art methods.

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A novel constraint-handling technique based on dynamic weights for constrained optimization problems

Cited by 30 publications

References 26 publications

Decomposition-Based Multiobjective Optimization for Constrained Evolutionary Optimization

Decomposition-Based Multiobjective Optimization for Constrained Evolutionary Optimization

Helper and Equivalent Objectives: Efficient Approach for Constrained Optimization

Composite Differential Evolution for Constrained Evolutionary Optimization

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