Efficient Constraint Handling based on the Adaptive Penalty Method with Balancing the Objective Function Value and the Constraint Violation

Kawachi, Takeshi; Kushida, Jun-ichi; Hara, Akira; Takahama, Tetsuyuki

doi:10.1109/iwcia47330.2019.8955094

Cited by 3 publications

(5 citation statements)

References 9 publications

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“…The distinctive feature of the proposed variants compared to the original ones is that necessary comparisons between individuals depend not only on the objective function value, but also on the level of constraint violation and the number of violated constraint functions. The proposed variants were successfully implemented in the metaheuristic PBA (Kallioras et al 2018), within HP-OCP, and their performance was evaluated and compared to that of the well-known adaptive penalty (Kawachi et al 2019), original feasibility rules (Deb 2000), improved ε-constrained (Fan et al 2018) and original stochastic ranking (Runarsson and Yao 2000) variants, based upon 20 single-objective benchmark mathematical and engineering COPs. The results clearly demonstrate the performance superiority of the proposed novel variants in comparison with the existing ones in most COPs, in respect of both objective function values and CoV values.…”

Section: Discussionmentioning

confidence: 99%

“…(3) Kawachi et al (2019) proposed an adaptive procedure for calculating the penalty factor during the evolution process, which effectively deals with issues of over-or under-penalization that potentially led to divergence of the search process from the optimum. More specifically, a fitness function is formulated:…”

Section: Penalty Methodsmentioning

confidence: 99%

“…In Li et al (2019a) The same year, Kawachi et al (2019) introduced a DE algorithm named LSHADE equipped with an APM CHT, which is not based solely on the objective function value or the constraint violation in the search region, but also considers their balance, and applied it to the optimization of benchmark functions provided by the Congress on Evolutionary Computation (CEC) 2017. Using the right balance between constraint violation and objective function values, the proposed method outperformed a conventional APM CHT, as well as other CHTs, in most cases considered.…”

Section: Penalty-based Constraint Handling Techniquesmentioning

confidence: 99%

“…The performance of these novel variants is evaluated later in Sect. 5, based upon 20 mathematical and engineering COPs, and compared to four existing variants of CHTs (i)-(iv), specifically: (i) adaptive penalty by Kawachi et al (2019) (ii) feasibility rules by Deb (2000); (iii) improved ε-constrained by Fan et al (2018); and (iv) stochastic ranking by Runarsson and Yao (2000), which are also described herein.…”

Section: Constraint Handling Technique Formulationmentioning

confidence: 99%

“…In this section, the performance of the 8 novel feasibility rules and ε-constrained CHT variants proposed in Sect. 3 is evaluated and compared against 4 well-known CHT variants from the literature: (i) adaptive penalty by Kawachi et al (2019) (ii) feasibility rules by Deb (2000); (iii) improved ε-constrained by Fan et al (2018); and (iv) stochastic ranking by Runarsson and Yao (2000). Consideration is given to 20 COPs previously investigated by other authors, encompassing: (i) 14 mathematical COPs, including a 2D problem investigated by Deb (2000) and 13 problems investigated by Runarsson and Yao (2000) (labelled G1-G13); and (ii) 6 engineering COPs, including a welded beam, pressure vessel and tension-compression string design investigated by Tsipianitis and Tsompanakis (2020), as well as 2D and 3D truss design examples investigated by Farshi and Alinia-ziazi (2010).…”

Section: Numerical Examplesmentioning

confidence: 99%

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Constraint handling techniques for metaheuristics: a state-of-the-art review and new variants

et al. 2023

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Metaheuristic optimization algorithms (MOAs) are computational randomized search processes which draw inspiration from physical and biological phenomena, with an application spectrum that extends to numerous fields, ranging from engineering design to economics. MOAs were originally developed for solving unconstrained NP-complete problems, and hence their application to constrained optimization problems (COPs) requires the implementation of specialized techniques that facilitate the treatment of performance and bound constraints. While considerable research efforts have been oriented towards the development and subsequent enhancement of novel constraint handling techniques (CHTs) for MOAs, a systematic review of such techniques has not been conducted hitherto. This work presents a state-of-the-art review on CHTs used with MOAs and proposes eight novel variants based on the feasibility rules and ε-constrained techniques. The distinctive feature of the new variants is that they consider the level and number of constraint violations, besides the objective function value, for selection of individuals within a population. The novel variant performance is evaluated and compared with that of four well-known CHTs from the literature using the metaheuristic pity beetle algorithm, based upon 20 single-objective benchmark COPs. The computational results highlight the accuracy, effectiveness, and versatility of the novel variants, as well as their performance superiority in comparison with existing techniques, stemming from their distinctive formulation. The complete code can be downloaded from GitHub (https://github.com/nikoslagaros/MOAs-and-CHTs).

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