Simulated Annealing Techniques in Global Optimization

Simulated annealing is a probabilistic metaheuristic inspired by the physical process of annealing in metallurgy, where controlled cooling enables a metal to reach a low-energy crystalline state. In the context of global optimisation, the algorithm explores a solution space by accepting not only improvements but occasionally inferior solutions according to a temperature-dependent probability. This mechanism permits escape from local optima and enhances the likelihood of attaining a global optimum. Key components include the initial temperature, cooling schedule and acceptance criterion, all of which determine convergence speed and solution quality. Over recent decades, advances have encompassed adaptive cooling schedules, surrogate-model guidance and multi-agent or population-based variants that balance exploration and exploitation more effectively. Integration with machine learning methods has yielded self-tuning annealing laws that respond dynamically to search history. Practical applications span engineering design, logistics and computational physics, addressing problems as varied as shape optimisation of mechanical components, supply-chain order allocation and scheduling of complex networks. By accommodating non-convex, high-dimensional or discontinuous objective functions, simulated annealing continues to serve as a versatile tool for real-world global optimisation challenges.

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Recent work in inventory management has introduced a modified simulated annealing algorithm featuring multiple cooperating agents and adaptive attraction toward the current best solution. Applied to a non-linear economic order quantity problem with freight-rate complexities, this algorithm demonstrated accelerated convergence and robust avoidance of local minima, outperforming traditional single-agent strategies. In automotive design, a surrogate-model approach has been employed to tune annealing parameters for shape optimisation of rubber bumpers. By constructing a support-vector regression model and sampling via Latin hypercube design, researchers have been able to fine-tune temperature schedules and search bounds without repeated expensive finite-element simulations, achieving near-optimal designs with minimal evaluation cost. For combinatorial routing problems, enhancements to the classic algorithm have been proposed through modified inner–outer loop interactions in the travelling salesman problem. The revised structure yielded lower variance and faster runtimes across multiple benchmark instances, demonstrating the algorithm’s adaptability to grid and random node distributions. Collectively, these studies underscore the breadth of simulated annealing’s applicability and its ongoing evolution through hybridisation with statistical models and parallel search frameworks.

Simulated Annealing Techniques in Global Optimization publication trend

The graph below shows the total number of articles in simulated annealing techniques in global optimization across all publications each year (not limited to Nature Index journals).

Technical terms

Metropolis criterion: A rule that probabilistically accepts a new solution based on energy difference and current temperature, allowing uphill moves to escape local minima.

Cooling schedule: A predefined or adaptive function that governs the reduction of temperature over iterations, critically affecting convergence rate and solution quality.

Annealing schedule: The sequence of temperature values and iteration counts applied to guide the search from exploration toward exploitation.

Surrogate model: An approximate representation of the true objective function, used to predict outcomes and reduce the number of expensive evaluations.

Global optimum: The best possible solution across the entire search space, as opposed to local optima which are best only within a limited region.

State space: The set of all feasible solutions over which the algorithm explores, each representing a distinct configuration of decision variables.

References

1. A Modified Simulated Annealing (MSA) Algorithm to Solve the Supplier Selection and Order Quantity Allocation Problem with Non-Linear Freight Rates. Axioms (2023).
2. Surrogate Model-Based Parameter Tuning of Simulated Annealing Algorithm for the Shape Optimization of Automotive Rubber Bumpers. Applied Sciences (2022).
3. Numerical Approach of Symmetric Traveling Salesman Problem Using Simulated Annealing. Jurnal RESTI (Rekayasa Sistem dan Teknologi Informasi) (2021).
4. A Self-Tuned Simulated Annealing Algorithm Using Hidden Markov Model. International Journal of Electrical and Computer Engineering (IJECE) (2018).