Addressing The Knapsack Challenge Through Cultural Algorithm Optimization

TL;DR

This paper presents a novel Cultural Algorithm variant designed to efficiently solve the 0-1 knapsack problem by dynamically adjusting evolutionary parameters, demonstrating superior performance in complex, high-dimensional instances.

Contribution

Introduces a new Cultural Algorithm with a belief space and adaptive functions for crossover and mutation, improving global optimum detection in knapsack problems.

Findings

Consistently finds the global optimum in high-dimensional knapsack problems

Outperforms existing algorithms in efficiency and accuracy

Effective in complex constraint scenarios

Abstract

The "0-1 knapsack problem" stands as a classical combinatorial optimization conundrum, necessitating the selection of a subset of items from a given set. Each item possesses inherent values and weights, and the primary objective is to formulate a selection strategy that maximizes the total value while adhering to a predefined capacity constraint. In this research paper, we introduce a novel variant of Cultural Algorithms tailored specifically for solving 0-1 knapsack problems, a well-known combinatorial optimization challenge. Our proposed algorithm incorporates a belief space to refine the population and introduces two vital functions for dynamically adjusting the crossover and mutation rates during the evolutionary process. Through extensive experimentation, we provide compelling evidence of the algorithm's remarkable efficiency in consistently locating the global optimum, even in knapsack problems characterized by high dimensions and intricate constraints.