Decomposition-Based Multiobjective Optimization for Constrained Evolutionary Optimization

Abstract

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.

Helper and Equivalent Objectives: Efficient Approach for Constrained Optimization

“…A new equivalent function and a new mechanism of dynamically weighting are used in HECO-DE. Experimental results show that the overall performance of HECO-DE is ranked first when compared with LSHADE44, other EAs in the CEC 2018 competition [7] and DeCODE [14]. This case study proves the efficiency of the helper and equivalent objective method for constrained optimisation.…”

“…Furthermore, in objective decomposition [11], [14], minimisation of linear combination w 1 f (x)+w 2 v(x) (where weights w 1 > 0, w 2 ≥ 0) points to x = −1000, far away from Ω * . (6) This example shows that using two objectives makes the problem more complicated.…”

“…The first seven EAs come from the CEC 2018 constrained optimisation competition [7]. The last one, DeCODE [14], was a decomposition-based multi-objective EAs for constrained optimisation published in 2018. In the first population, UDE employs all the three trial vector generation strategies on each target vector.…”

“…Furthermore, a new mutation operator DE/randr1*/1 is proposed. 8) DeCODE [14]: A recent decomposition-based EA made use of the weighted sum approach to decompose the transformed bi-objective problem into a number of scalar optimisation subproblems and then applied differential evolution to solve them. They designed a strategy of [7] adopted the same benchmark suit as the CEC 2017 competition [8].…”

Multiobjective differential evolution enhanced with principle component analysis for constrained optimization

“…8. DeCODE [29]: A recent decomposition-based EA made use of the weighted sum approach to decompose the transformed bi-objective problem into a number of scalar optimisation subproblems and then applied differential evolution to solve them. They designed a strategy of adjusting weights and a restart strategy to tackle COPs with complicated constraints.…”