Modified FOX Optimizer for Solving optimization problems

2025-02-27

AI Summary

FOX optimizer suffers from premature convergence due to its reliance solely on the current global best position for agent updates, rapidly eroding population diversity. To address this, we propose mFOX—an enhanced variant integrating three key innovations: (1) opposition-based learning (OBL) to improve initial population quality; (2) a relative-position-based update mechanism replacing absolute-position dependency; and (3) adaptive control parameters enabling dynamic exploration–exploitation trade-off without additional computational overhead. Comprehensive evaluations on 23 classical, 10 CEC2019, and 12 CEC2022 benchmark functions demonstrate mFOX’s superiority, achieving win rates of 74%, 60%, and 58% against 12 state-of-the-art optimizers, respectively. Furthermore, mFOX successfully solves four real-world engineering optimization problems, confirming its robustness and practical applicability.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Optimization
• Constraint Satisfaction and Optimization: Constraint Optimization

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments

Abstract

The FOX optimizer, inspired by red fox hunting behavior, is a powerful algorithm for solving real-world and engineering problems. However, despite balancing exploration and exploitation, it can prematurely converge to local optima, as agent positions are updated solely based on the current best-known position, causing all agents to converge on one location. This study proposes the modified FOX optimizer (mFOX) to enhance exploration and balance exploration and exploitation in three steps. First, the Oppositional-Based Learning (OBL) strategy is used to improve the initial population. Second, control parameters are refined to achieve a better balance between exploration and exploitation. Third, a new update equation is introduced, allowing agents to adjust their positions relative to one another rather than relying solely on the best-known position. This approach improves exploration efficiency without adding complexity. The mFOX algorithm's performance is evaluated against 12 well-known algorithms on 23 classical benchmark functions, 10 CEC2019 functions, and 12 CEC2022 functions. It outperforms competitors in 74% of the classical benchmarks, 60% of the CEC2019 benchmarks, and 58% of the CEC2022 benchmarks. Additionally, mFOX effectively addresses four engineering problems. These results demonstrate mFOX's strong competitiveness in solving complex optimization tasks, including unimodal, constrained, and high-dimensional problems.

Problem

• Enhances exploration in optimization algorithms
• Balances exploration and exploitation effectively
• Improves performance on engineering problems

Innovation

• Oppositional-Based Learning strategy
• Refined control parameters
• New position update equation