Hybrid Salp Swarm-Genetic Algorithm Optimization for the Multidimensional Knapsack Problem: A Conceptual Review and Framework Synthesis

Abstract

The Multidimensional Knapsack Problem (MKP) is a classical NP-hard combinatorial optimization problem used in wide variety of applications such as in logistics, cloud computing, manufacturing, telecommunications, scheduling and resource allocation. Metaheuristic algorithms are widely used because as the size of the problem and complexity of the optimization problem grows, the traditional exact methods are not able to compute them. In this regard, the Genetic Algorithm (GA) and Salp Swarm Algorithm (SSA) have received high interest due to their complementary search capabilities. The global exploration via the adaptive leader–follower mechanism in SSA, and the strong local exploitation by evolutionary operators in GA, complement each other well. In recent years, these algorithms are being incorporated into hybrid frameworks to accelerate the convergence process, preserve the diversity of the population and increase the quality of the solutions in large-scale optimization problems. But most of the current research is implementation oriented, and there are very few conceptual syntheses of concepts for the theoretical foundations, evolution, hybridization strategies and emerging developments of SSA–GA optimization for MKP. This paper discusses the complete overview of the conceptual review of Hybrid Salp Swarm–Genetic Algorithm optimization in Multidimensional Knapsack Problem. It outlines the development of the MKP, metaheuristic optimization, evolutionary computation, swarm intelligence and hybrid optimization and discusses the complementary nature of exploring/exploiting, constraint-handling and adaptive optimization mechanisms. The review also outlines the recent research trends, conceptual gaps, and suggests a common framework to inform the design of the scalable, adaptive, and computationally efficient hybrid optimization models. By consolidating current knowledge and outlining future research directions, this review provides a valuable reference for researchers and practitioners working in combinatorial optimization and intelligent resource allocation.