Hybrid Firefly-Genetic Algorithm for Single and Multi-dimensional 0-1 Knapsack Problems

TL;DR

This paper introduces a hybrid Firefly-Genetic Algorithm that effectively solves both unconstrained and constrained 0-1 Knapsack Problems, improving solution accuracy and efficiency over traditional methods.

Contribution

A novel hybrid FAGA algorithm combining Firefly and Genetic Algorithms, specifically designed for complex constrained optimization problems like the 0-1 Knapsack.

Findings

Enhanced solution accuracy for knapsack problems

Improved computational efficiency over conventional algorithms

Effective handling of complex constraints

Abstract

This paper addresses the challenges faced by algorithms, such as the Firefly Algorithm (FA) and the Genetic Algorithm (GA), in constrained optimization problems. While both algorithms perform well for unconstrained problems, their effectiveness diminishes when constraints are introduced due to limitations in exploration, exploitation, and constraint handling. To overcome these challenges, a hybrid FAGA algorithm is proposed, combining the strengths of both algorithms. The hybrid algorithm is validated by solving unconstrained benchmark functions and constrained optimization problems, including design engineering problems and combinatorial problems such as the 0-1 Knapsack Problem. The proposed algorithm delivers improved solution accuracy and computational efficiency compared to conventional optimization algorithm. This paper outlines the development and structure of the hybrid algorithm and demonstrates its effectiveness in handling complex optimization problems.