Solving the 0-1 knapsack problem with genetic algorithms

Abstract

This paper describes a research project on using Genetic Algorithms (GAs) to solve the 0-1 Knapsack Problem (KP). The Knapsack Problem is an example of a combinatorial optimization problem, which seeks to maximize the benefit of objects in a knapsack without exceeding its capacity. The paper contains three sections: brief description of the basic idea and elements of the GAs, definition of the Knapsack Problem, and implementation of the 0-1 Knapsack Problem using GAs. The main focus of the paper is on the implementation of the algorithm for solving the problem. In the program, we implemented two selection functions, roulette-wheel and group selection. The results from both of them differed depending on whether we used elitism or not. Elitism significantly improved the performance of the roulette-wheel function. Moreover, we tested the program with different crossover ratios and single and double crossover points but the results given were not that different.