A New Metaphor-Free Metaheuristic Approach Based on Complex Networks and Bezier Curves

Abstract

A metaheuristic method is an optimization technique that is generally inspired by natural or physical processes. The use of metaphors has created a tendency to reproduce existing algorithms with slight modifications or variations rather than encouraging the development of novel algorithmic techniques and principles. On the other hand, a complex network is a mathematical structure whose main characteristic is the ability to capture and analyze the intricate patterns and properties that emerge from the interactions between the elements that it connects. In this paper, a new metaphor-free metaheuristic algorithm based on complex networks and Bezier curves is presented. In this approach, candidate solutions are represented as nodes in a graph, whereas the connections between nodes or edges reflect the differences in their objective function values. Therefore, the graph provides a higher-level representation that captures the essential relationships and dependencies among the solutions. Once the graph is generated, the shortest path between each solution and the best solution is obtained. Then, the nodes obtained from this process are used as control points in the Bezier equation to generate the new agent position. Therefore, during the optimization process, the graph is continuously modified based on the evaluation of new candidate solutions and their objective function values, producing trajectories that allow the exploration and exploitation of the search space. The experimental results demonstrated the effectiveness of our approach by achieving competitive results compared to other well-known metaheuristic algorithms on various benchmark functions.

Keywords

• Complex networks
• metaheuristics
• Bezier curves
• optimization
• complex systems
• graphs theory