SWARM OPTIMIZATION ALGORITHMS FOR SOLVING MULTI-OBJECTIVE PROBLEMS IN COMPLEX SYSTEMS

Abstract

Multi-objective optimization in complex systems requires decision-makers to compare nondominated trade-offs rather than search for one universally best solution. This paper presents an evidence-bounded review and reproducible comparison framework for multi-objective particle swarm optimization, ant colony optimization and the firefly algorithm. The three families are analysed through their search mechanisms, archive management, constraint handling, convergence behaviour, diversity preservation and computational cost. Ten editable equations define the common optimization problem, Pareto dominance, method-specific updates, hypervolume and dominant complexity. A structured notation table and an IEEE/ACM-style algorithm specify how matched evaluation budgets, repeated runs and uncertainty reporting should be used. Because the source manuscript contains no raw run-level outputs, the revised paper does not claim new empirical superiority. Instead, it identifies defensible method-selection hypotheses and a transparent protocol for engineering design, logistics, resource allocation and environmental applications.