An Energy Valley Optimizer Approach for Solving the Modified Quadratic Bounded Knapsack Problem with Multiple Constraints

Abstract

The Modified Quadratic Bounded Knapsack Problem with Multiple Constraints (MQBKMC) represents a challenging combinatorial optimization problem with considerable importance in practical domains such as inventory management and logistics. This study investigates the performance and parameter sensitivity of the Energy Valley Optimizer (EVO) algorithm in solving MQBKMC. Specifically, we examine the effects of varying critical algorithm parameters, including the maximum number of function evaluations (MaxFes) and the number of particles (nParticle), on the quality of obtained solutions. Experimental results reveal that increasing MaxFes consistently leads to improved solution quality, underscoring the significance of extended exploration in facilitating algorithm convergence. In contrast, increasing the number of particles does not necessarily yield performance gains and instead significantly elevates computational demands. These findings provide practical insights into the optimal parameterization of EVO, particularly beneficial for applications that require efficient handling of high-dimensional, multi-constrained optimization problems. Overall, the EVO algorithm demonstrates promising efficacy and robustness for effectively addressing MQBKMC.