Proportional Reward and Temporal Discounting for Monopoly-Free Heterogeneous Metaheuristic Portfolios

Real-world optimization landscapes are typically dynamic, high-dimensional, and uncertain, and a single meta-heuristic with fixed control parameters rarely sustains strong performance across such environments, as formalized by the No Free Lunch theorem. Existing adaptive frameworks attempt to address this through online operator or algorithm selection, but they suffer from two persistent limitations: coarse feed-back mechanisms that reward the frequency rather than the magnitude of improvements, and cumulative memory bias that allows early-performing algorithms to monopolize selection long after their advantage has faded. This work proposes a problem-agnostic adaptive framework that integrates the Relative Improvement Metric (RIM), a proportional reward quantifying the magnitude of each solver’s contribution, with a Sliding Window (SW) policy that discounts older rewards temporally so that algorithmic influence remains contingent on recent effectiveness. The framework orchestrates a heterogeneous portfolio of eight metaheuristics (GA, PSO, GWO, ACO, SSA, ABC, WOA, FA) through probabilistic selection driven by SW-RIM weights, with a small base probability that prevents any solver from being permanently excluded. Empirical evaluation across 23 standard benchmarks and the CEC2020 suite shows that the proposed mechanism reduces maximum solver participation from above 70% in the baseline configuration to under 40%, improves mean fitness on the majority of functions in both groups, and achieves statistically significant gains over both a baseline portfolio and a sliding-window-only variant (Wilcoxon p < 0.001; Vargha-Delaney A12 between 0.72 and 0.85, large effect across all comparisons). The two exceptions are functions with deceptive or ill-conditioned landscapes (a narrow-valley Rosenbrock-type function and a highly multimodal Schwefel-type function), where all three configurations perform comparably, indicating that SW-RIM’s benefit is contingent on the portfolio containing at least one solver structurally suited to the current landscape rather than on the selection strategy alone. The results support SW-RIM as a lightweight, general-purpose mechanism for sustaining diversity and impact-sensitive adaptation in complex continuous optimization, without the training cost of reinforcement-learning-based selectors.

@article{Bataineh2026,
  title     = {Proportional Reward and Temporal Discounting for Monopoly-Free Heterogeneous Metaheuristic Portfolios},
  journal   = {International Journal of Advanced Computer Science and Applications},
  volume    = {17},
  number    = {8},
  year      = {2026},
  publisher = {The Science and Information Organization},
  author    = {Bilal Bataineh and Sofian Kassaymeh},
  doi       = {10.14569/IJACSA.2026.0170896},
  url       = {https://doi.org/10.14569/IJACSA.2026.0170896}
}