Hybridizing interval method with a heuristic for solving real-world constrained engineering optimization problems

Abstract

Practical issues in real-world engineering problems limit the use of traditional optimization methods in finding solutions to design optimization problems. Although several advanced optimization approaches have been developed recently, a unified way to solve almost every problem effectively is yet to arise. To address this, we present a new method for optimizing several structure engineering design problems using our unique hybrid optimization approach inspired by the integration of branch and bound-like concepts of interval analysis with heuristics, and it differs from other methods in the literature. We hybridize the Split-Detect-Discard-Shrink technique and the Sophisticated ABC (SDDS-SABC) algorithm. The advantage of the SDDS process is that it shrinks the entire search region through recursive breakdown and improves computational effort to focus on subregion covering potential solutions for further decomposition. SABC plays a vital role in extracting the best solutions from subregions whose values help detect the promising subregion. SDDS and SABC are sequentially repeated until global/ close to the global solution(s) is reached. The ranking and selection rules are applied to assist in an optimistic decision-making process. In the SABC algorithm, we introduce Latin Hypercube, a new initialization scheme for food sources. This enhances the computational approach towards the optimal solution. Develop a dual strategy employed bees phase to explore their neighbourhoods better. Introduce a new Dynamic penalty method free from extra parameters/ factors. Here 57 real-world complex constrained optimization benchmark problems (CEC2020) featuring problems with Industrial Chemical Processes, Synthesis and Design, Mechanical Engineering, Power System, Power Electronics, and Livestock Feed Ration Optimization are presented, where our method is applied to optimize the decision parameters. Finally, our optimal results are compared in terms of their statistical significance using Friedman and Wilcoxon rank tests with three well-known optimizer algorithms in the literature. The results show that SDDS-SABC outperforms most tested competitors and demonstrates the practicability of SDDS-SABC in solving challenging real-world problems. Moreover, the SDDS-SABC method is numerically stable and suitable for the illustrated optimization examples. The key novelty of the presented approach is the ability to perform a static and better optimal solution in most runs despite the problem being too complex.