Optimizing the Multidimensional Knapsack Problem Using Guided Genetic Algorithm and an AI-augmented Binary Water Optimization Algorithm

Abstract

This thesis optimizes the Multidimensional Knapsack Problem (MKP), one of the most prominent and challenging combinatorial optimization problems since it is intricate and contains multiple constraints. MKP is present in real-world issues such as resource allocation, task scheduling, and investment. The overall aim of this study is to evaluate the performance of two metaheuristics for MKP problem solving: the Guided Genetic Algorithm (GGA) and binary Water Optimization Algorithm (WOA). For enhancing the performance of WOA, we used a hybrid approach based on artificial intelligence techniques. A dynamic parameter prediction such as the number of flipped bits and the evaporation retention ratio is performed based on a Multi-Layer Perceptron (MLP) neural network. Graph Neural Networks (GNNs) are also adopted in order to utilize the structural relationships among items. In addition, reinforcement learning techniques are employed for enhancing the exploration and exploitation phases during the searching procedure. Experimental results indicate that the improved version of WOA (BWOA), augmented by AI techniques, can produce high-quality solutions in shorter convergence time compared to other traditional algorithms. This confirms the effectiveness of the proposed method in solving complex constrained optimization problems like MKP.