Rahimi Iman, Gandomi Amir H, Nikoo Mohammad Reza, Mousavi Mohsen, Chen Fang
Data Science Institute, University of Technology Sydney, Sydney, NSW, Australia.
University Research and Innovation Center (EKIK), Óbuda University, 1034, Budapest, Hungary.
Sci Rep. 2024 Feb 27;14(1):4816. doi: 10.1038/s41598-024-54841-z.
Many real-world optimization problems, particularly engineering ones, involve constraints that make finding a feasible solution challenging. Numerous researchers have investigated this challenge for constrained single- and multi-objective optimization problems. In particular, this work extends the boundary update (BU) method proposed by Gandomi and Deb (Comput. Methods Appl. Mech. Eng. 363:112917, 2020) for the constrained optimization problem. BU is an implicit constraint handling technique that aims to cut the infeasible search space over iterations to find the feasible region faster. In doing so, the search space is twisted, which can make the optimization problem more challenging. In response, two switching mechanisms are implemented that transform the landscape along with the variables to the original problem when the feasible region is found. To achieve this objective, two thresholds, representing distinct switching methods, are taken into account. In the first approach, the optimization process transitions to a state without utilizing the BU approach when constraint violations reach zero. In the second method, the optimization process shifts to a BU method-free optimization phase when there is no further change observed in the objective space. To validate, benchmarks and engineering problems are considered to be solved with well-known evolutionary single- and multi-objective optimization algorithms. Herein, the proposed method is benchmarked using with and without BU approaches over the whole search process. The results show that the proposed method can significantly boost the solutions in both convergence speed and finding better solutions for constrained optimization problems.
许多实际的优化问题，尤其是工程领域的问题，都涉及到一些约束条件，这使得找到可行解具有挑战性。众多研究人员针对约束单目标和多目标优化问题对这一挑战进行了研究。特别是，这项工作扩展了Gandomi和Deb（《计算机方法与应用力学工程》363:112917，2020）提出的用于约束优化问题的边界更新（BU）方法。BU是一种隐式约束处理技术，旨在通过迭代削减不可行的搜索空间，从而更快地找到可行域。在这个过程中，搜索空间会发生扭曲，这可能会使优化问题更具挑战性。作为回应，实现了两种切换机制，当找到可行域时，它们会将景观以及变量一起转换回原始问题。为了实现这一目标，考虑了两个代表不同切换方法的阈值。在第一种方法中，当约束违反达到零时，优化过程转变为不使用BU方法的状态。在第二种方法中，当目标空间中没有进一步变化时，优化过程转变为无BU方法的优化阶段。为了进行验证，使用著名的进化单目标和多目标优化算法来解决基准问题和工程问题。在此，所提出的方法在整个搜索过程中分别使用和不使用BU方法进行基准测试。结果表明，所提出的方法在收敛速度和为约束优化问题找到更好的解方面都能显著提升解决方案。
