Abstract
Constrained optimization problems (COPs) are widely encountered in chemical engineering processes, and are normally defined by complex objective functions with a large number of constraints. Classical optimization methods often fail to solve such problems. In this paper, to solve COPs efficiently, a two-phase search method based on a heat transfer search (HTS) algorithm and a tandem running (TR) strategy is proposed. The main framework of the MHTS–TR method aims to alternate between a feasible search phase that only examines feasible solutions, using the HTS algorithm, and an infeasible search phase where the treatment of infeasible solutions is relaxed in a controlled manner, using the TR strategy. These two phases play different roles in the search process; the former ensures an intensified optimum in a relevant feasible region, whereas the latter is used to introduce more diversity into the former. Thus, the ensemble of these two complementary phases can provide an effective method to solve a wide variety of COPs. The proposed variant was investigated over 24 well-known constrained benchmark functions, and then compared with various well-established metaheuristic approaches. Furthermore, it was applied for solving a chemical COP. The promising results demonstrate that the MHTS–TR approach is applicable for solving real-world COPs.
Highlights
Nowadays, many real-world chemical engineering processes are defined by complex objective functions with a large number of constraints [1]
It can be observed from the results table that the MHTS–tandem running (TR), heat transfer search (HTS), and artificial bee colony (ABC) algorithms markedly outperformed the other four algorithms on the results of the quadratic function (C01)
The results obtained by the α-based branch and bound method (αBB), cultural algorithm with evolutionary programming (CAEP), and constrained ant colony system (CACS) (δ = 5 × 10−4 ) methods were superior to that of the MHTS–TR, but the MHTS–TR method did not violate any constraint
Summary
Many real-world chemical engineering processes are defined by complex objective functions with a large number of constraints [1]. The optimization problems that contain several constraints are described as constrained optimization problems (COPs) [2] These problems are generally characterized by their different types, such as linear, nonlinear, polynomial, quadratic, cubic, etc. Due to the complexity of highly constrained chemical processes, new generation optimization methods need to be found, as classical methods often fail to solve COPs efficiently. Self-adaptive penalty methods modify the penalty term value throughout the search course, such as the adaptive penalty method (APM) [10], an effective penalty-based method that automatically calibrates the infeasible surface throughout evolution. It may lose feasible solutions during the search course
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