A Firefly Algorithm for Mixed-Variable Optimization Based on Hybrid Distance Modeling

TL;DR

This paper introduces FAmv, an adaptation of the Firefly Algorithm that effectively handles mixed-variable optimization problems by integrating continuous and discrete components through a novel distance-based attractiveness mechanism.

Contribution

The paper presents a new hybrid distance modeling approach within the Firefly Algorithm to optimize heterogeneous variable types in mixed-variable problems.

Findings

FAmv achieves superior performance on the CEC2013 benchmark.

The method demonstrates robustness on engineering design problems.

Incorporating mixed-distance modeling improves search effectiveness.

Abstract

Several real-world optimization problems involve mixed-variable search spaces, where continuous, ordinal, and categorical decision variables coexist. However, most population-based metaheuristic algorithms are designed for either continuous or discrete optimization problems and do not naturally handle heterogeneous variable types. In this paper, we propose an adaptation of the Firefly Algorithm for mixed-variable optimization problems (FAmv). The proposed method relies on a modified distance-based attractiveness mechanism that integrates continuous and discrete components within a unified formulation. This mixed-distance approach enables a more appropriate modeling of heterogeneous search spaces while maintaining a balance between exploration and exploitation. The proposed method is evaluated on the CEC2013 mixed-variable benchmark, which includes unimodal, multimodal, and composition functions. The results show that FAmv achieves competitive, and often superior, performance compared with state-of-the-art mixed-variable optimization algorithms. In addition, experiments on engineering design problems further highlight the robustness and practical applicability of the proposed approach. These results indicate that incorporating appropriate distance formulations into the Firefly Algorithm provides an effective strategy for solving complex mixed-variable optimization problems.