Metaheuristics

Optimization · Axiom Academy

High-level strategies for guiding optimization through complex search spaces Metaheuristics are master strategies that coordinate simple heuristics to effectively explore search spaces. They balance two key principles: Exploration: Discovering new, diverse regions of the search space Exploitation: Refining promising solutions already found This balance prevents getting stuck in local optima while efficiently converging toward high-quality solutions. Common metaheuristics include simulated annealing, genetic algorithms, and tabu search. Inspired by the metallurgical annealing process, this method starts with high "temperature" allowing exploration, then gradually "cools" to exploit good solutions. Temperature Schedule: Controls the exploration-exploitation tradeoff over time Acceptance Probability: Worse solutions may be accepted with probability based on temperature and solution quality At iteration t, a neighbor solution is accepted if it improves the objective, or with acceptance probability: Inspired by natural evolution, genetic algorithms maintain a population of solutions that evolve over generations through biological operators: Selection: Fitter individuals more likely to reproduce Crossover: Combine genetic material from two parents Mutation: Random changes to maintain diversity The fitness function evaluates solution quality, guiding the evolutionary process toward better solutions through successive generations.

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