A Decomposition based Multi-Objective Heat Transfer Search algorithm for structure optimization

Abstract

Multi-objective (MO) problems are complex and challenging to solve due to multiple conflicting objectives and incommensurate constraints. Heat Transfer Search is a recently introduced thermodynamic laws-based algorithm for solving many single objective problems. But it faces criticism due to its shortcomings including local optima trap, computational complexity, and reliability issues while solving MO problems. Decompositions is a simple yet efficient framework that aids in resolving fitness assignments and diversity maintenance issues of MO problems. It is also popular for reducing computational complexity and improving solution quality. Therefore, this work proposes and investigates a novel, simple, and robust Decomposition-based Multi-Objective Heat Transfer Search (MOHTS/D) for solving real-world structural problems. To achieve the Pareto optimal solutions and to confirm their coverage behaviour, the evenly generated weight vectors sorting and Euclidean distance strategies were employed in the proposed posteriori method. The performance of MOHTS/D is investigated through eight constrained widely accepted benchmarks. The results contrast with the MOHTS, MO evolutionary algorithm based on decomposition, MO passing vehicle search, MO slime mould, MO symbiotic organisms search, and MO multi-verse optimization. The efficacy of MOHTS/D is evaluated based on hyper-volume, coverage, inverted generational distance, pure diversity, spacing, spread, coverage Pareto front, diversity maintenance, generational distance, and runtime metrics. The results reveal that MOHTS/D is a robust optimization approach compared to others for optimizing real-life structural problems. MOHTS/D was able to find the optimal solution with minor computational complexity, and the obtained solutions demonstrate a better convergence, coverage, diversity, and spread behaviour over Pareto fronts