An Adaptive Metaheuristic Framework for Changing Environments

TL;DR

This paper tackles dynamic optimization where the objective $f(x,t)$ and constraints $g(x,t) \le 0$, $h(x,t)=0$ evolve over time, challenging static metaheuristics. It introduces the Adaptive Metaheuristic Framework (AMF), which combines a dynamic problem representation, real-time sensing, and an adaptation module to continuously adjust search strategies. AMF embeds the Differential Evolution (DE) algorithm as a core optimizer, augmented with strategies such as partial re-initialization and high-mutation-rate local search to rapidly respond to changes. Through simulations of a dynamic optimization task, AMF detects environmental shifts, quickly adapts the solution $x$ to preserve high-quality results, and generally outperforms traditional metaheuristics. Overall, the work offers a generalizable, real-time adaptive optimization framework with implications for robotics, control, and large-scale dynamic systems.

Abstract

The rapidly changing landscapes of modern optimization problems require algorithms that can be adapted in real-time. This paper introduces an Adaptive Metaheuristic Framework (AMF) designed for dynamic environments. It is capable of intelligently adapting to changes in the problem parameters. The AMF combines a dynamic representation of problems, a real-time sensing system, and adaptive techniques to navigate continuously changing optimization environments. Through a simulated dynamic optimization problem, the AMF's capability is demonstrated to detect environmental changes and proactively adjust its search strategy. This framework utilizes a differential evolution algorithm that is improved with an adaptation module that adjusts solutions in response to detected changes. The capability of the AMF to adjust is tested through a series of iterations, demonstrating its resilience and robustness in sustaining solution quality despite the problem's development. The effectiveness of AMF is demonstrated through a series of simulations on a dynamic optimization problem. Robustness and agility characterize the algorithm's performance, as evidenced by the presented fitness evolution and solution path visualizations. The findings show that AMF is a practical solution to dynamic optimization and a major step forward in the creation of algorithms that can handle the unpredictability of real-world problems.

Figures (9)

• Figure 1: AMF framework workflow
• Figure 2: Comparison of Fitness function evaluation over time with iteration increase
• Figure 3: Evaluation of how the fitness function of the problem change over time
• Figure 4: Optimal Solution Changes over time
• Figure 5: Fitness History of the Adaptive Algorithm