Wissem Ahmed Zaid, Alain Hertz, Defeng Liucs.AI cs.LG math.CO
Designing high-performance tactical wireless networks under realistic operational constraints gives rise to challenging combinatorial optimization problems, where the evaluation of candidate solutions relies on detailed physical and traffic-aware models. Although classical metaheuristics such as Tabu Search offer effective mechanisms for exploring large search spaces, their computational cost remains high because numerous candidate moves must be evaluated at every iteration. In this paper, we propose a data-driven framework that improves the efficiency of Tabu Search by learning to guide its move selection process. Rather than altering the neighborhood structure, our approach exploits the information contained in the search trajectories generated during the optimization process. At each iteration, we record both improving and non-improving edge-based transformations together with a set of descriptive features capturing the structural, geometric, and performance characteristics of the network. This information is used to train a Graph Neural Network (GNN) that predicts the impact of candidate moves on the objective function. The trained model is then integrated into the Tabu Search algorithm to rank candidate transformations according to their predicted quality, thereby reducing the number of costly objective evaluations while maintaining an effective exploration of the search space. Experimental results on synthetic benchmark instances demonstrate that the proposed learning-assisted Tabu Search notably reduces computation time while consistently producing higher-quality solutions than the standard algorithm. These findings highlight the potential of combining machine learning with metaheuristics by leveraging the implicit knowledge embedded in search trajectories, paving the way for more efficient solution methods for large-scale network design problems.
Machine learning for combinatorial optimization typically relies on neural constructors trained via reinforcement learning on large offline datasets for a fixed problem class-incurring high pretraining costs and generalizing poorly outside the training distribution. We propose an alternative: a metaheuristic framework that reformulates the randomized constructive phase of GRASP as an online imitation learning task, trained from scratch on each problem instance. A local search procedure acts as an expert oracle, while a decoder-only Transformer serves as the constructive policy. Unlike classical GRASP, which relies on static, myopic heuristic rules based on localized scalar costs, our approach is fully data-driven: the construction policy emerges from high-quality solutions discovered during the search itself, with no problem-specific feature engineering required. We instantiate this as LM-GRASP, a hybrid metaheuristic following an iterative learn-infer-improve cycle, training the policy online via behavioral cloning on a dynamic archive of elite trajectories-no external data or offline pretraining needed. The pipeline interfaces with the domain solely through the objective evaluator used by local search. Evaluated on the Taillard PFSP benchmark (ta51-ta60), the most discriminating block due to half its optima being unknown, LM-GRASP outperforms GPU-GRASP by 28.4 makespan units on average-comparable to the gain from GPU acceleration over sequential execution (27.2 units), though with overlapping standard deviations. This suggests instance-specific, online-trained language models are a promising, practical alternative to hand-engineered constructors, especially for landscapes resistant to classical greedy construction.
Parameter settings in evolutionary algorithms and metaheuristics are important because such parameter values can influence the performance of algorithms under evaluation. For a given algorithm, there are many different numerical experiments to show that the algorithm can work well in practice; however, in most cases there is no theoretical analysis of parameter settings. In this work, we show that theoretical analysis using the theory of dynamical systems and evolution of population variance can give some good results in terms of parameter ranges for the bat algorithm. We also show that results from numerical experiments are consistent with theoretical bounds. Such analyses can provide good insights from different perspectives about the algorithmic characteristics such as variance evolution, transition between exploration and exploitation as well as convergence behaviour.
This paper introduces RACL, a Reasoning-Agent Control Layer for metaheuristics. RACL places a reasoning agent above an existing optimizer. The agent does not replace the optimizer and does not modify business constraints. Instead, it controls the optimizer's internal search behavior by observing operational memory, reasoning over past behavior, formulating bounded hypotheses, testing interventions, evaluating outcomes, applying guardrails, consolidating useful policies and explaining its decisions. The experiment uses vehicle routing as a testbed, but the contribution is not a new routing solver, a particular ALNS configuration or a specific set of routing rules. The contribution is the RACL method: a way for a reasoning agent to discover, validate, consolidate and explain algorithmic control rules for a metaheuristic. In the current experimental setting, RACL improves or ties the Operational Memory Policy in 21 of 21 feasible cases and improves or ties a non-reasoning Stagnation-Triggered Policy in 18 of 21 feasible cases, with an average RACL vs STP cost delta of -0.641%. In the Sevilla-9/10 runtime sample, RACL improves average cost by -8.337% versus Fixed and -1.605% versus STP without showing material computational overhead. During the proof-of-concept, Codex was used as an in-the-loop reasoning agent observing executions, interpreting logs and proposing live bounded interventions. The policy proxy was later used only to make quantitative evaluation reproducible.
Finding D-optimal designs for generalized linear models (GLMs) is challenging due to the dependence of the Fisher information matrix on unknown parameters and the lack of closed-form solutions, particularly when input factors include both discrete and continuous variables. Although classical algorithms and recent metaheuristic approaches have offered partial solutions, there remains a need for robust and computationally efficient methods. In this paper, we propose a penalized Particle Swarm Optimization (PSO) approach, named $p$-PSO. Here we introduce a new, general-purpose penalty formulation for constrained optimization and demonstrate its effectiveness in optimal design problems. The formulation is algorithm-agnostic and applicable to a broad class of black-box optimization methods. Results show that the method is highly efficient, with its primary contribution being a penalty formulation that enables the direct use of an off-the-shelf PSO algorithm and extends naturally to more general constrained optimization tasks.
ZIVARI-TLBO is a grouped Teaching-Learning-Based Optimization (TLBO) method that augments an existing population-state controller with a fixed inter-group evaluated-elite relay. At each scheduled event, every group offers its already evaluated elite to the next group in a fixed ring; the elite replaces the receiver's worst eligible learner only when its stored objective value is better. Because the exact relay copies an already evaluated solution and its stored fitness, it requires no additional objective-function calls. The frozen gts-v4-cm-fixed implementation is evaluated under equal 10,000-evaluation budgets on eight classical functions at dimensions 10, 30, 50, and 100, with 30 matched seeds, and on five constrained engineering problems. A direct ablation against the same grouped landscape-aware controller without relay records 728/11/221 wins/ties/losses and a rank-biserial effect size of 0.624 across dimensions. In an eight-method multidimensional comparison, WOA obtains the best average rank (2.914) and ZIVARI-TLBO ranks second (3.382); ZIVARI-TLBO significantly outperforms TLBO, MCTLBO, DE, PSO, and GWO, loses significantly to WOA, and is not significantly different from HHO after Holm adjustment. Feasibility-aware engineering results are mixed and sensitive to the current static-penalty formulation. The evidence supports a scoped relay contribution and budget-consistent information-sharing mechanism, but not universal state-of-the-art, global-convergence, engineering-dominance, or CEC superiority claims.
Hiba Ahmed, Alexander E. I. Brownlee, Jason Adair +1cs.AI
Renewable energy is essential for meeting future energy demands; however, solar energy generation, which occurs only during daylight hours often does not align with household consumption patterns. Appliances such as cookers, washing machines, and dryers are typically operated according to user preferred schedules rather than solar energy availability, creating a scheduling optimization problem. The objective is to determine optimal appliance start times to maximize renewable energy utilization while minimizing user inconvenience and adhering to system constraints. This paper presents a metaheuristic approach using Iterated Local Search (ILS) and Simulated Annealing (SA) to optimize appliance start times, while considering appliance operating durations, power consumption, inverter limit, battery state of charge constraints, and solar generation forecasts. Unlike most existing work, the scheduling is extended beyond a single day to accommodate unfinished tasks from previous days (spillover), ensuring operational continuity and enabling sequential operation across multiple days. Experimental results show that the sequential multi-day scheduling framework effectively manages system constraints while ensuring user convenience under exclusive solar generation. These findings also open opportunities for future research on multi-objective trade-offs between investment in equipment of various sizes, return on that investment, and user satisfaction.
Deriving governing equations from empirical observations is a longstanding challenge in science. Although artificial intelligence (AI) has demonstrated substantial capabilities in function approximation, the discovery of explainable and extrapolatable equations remains a fundamental limitation of modern AI, posing a central bottleneck for AI-driven scientific discovery. Here, we present machine collective intelligence, a unified paradigm that integrates two fundamental yet distinct traditions in computational intelligence--symbolism and metaheuristics--to enable autonomous and evolutionary discovery of governing equations. It orchestrates multiple reasoning agents to evolve their symbolic hypotheses through coordinated generation, evaluation, critique, and consolidation, enabling scientific discovery beyond single-agent inference. Across scientific systems governed by deterministic, stochastic, or previously uncharacterized dynamics, machine collective intelligence autonomously recovered the underlying governing equations without relying on hand-crafted domain knowledge. Furthermore, the resulting equations reduced extrapolation error by up to six orders of magnitude relative to deep neural networks, while condensing 0.5-1 million model parameters into just 5-40 interpretable parameters. This study marks an important shift in AI toward the autonomous discovery of principled scientific equations.