Efficient optimisation of structures using tabu search

This paper presents a novel approach to the optimisation of structures using a Tabu search (TS) method. TS is a metaheuristic which is used to guide local search methods towards a globally optimal solution by using flexible memory cycles of differing time spans. Results are presented for the well established ten bar truss problem and compared to results published in the literature. In the first example a truss is optimised to minimise mass and the results compared to results obtained using an alternative TS implementation. In the second example, the problem has multiple objectives that are compounded into a single objective function value using game theory. In general the results demonstrate that the TS method is capable of solving structural optimisation problems at least as efficiently as other numerical optimisation approaches.

💡 Research Summary

The paper introduces a novel application of the Tabu Search (TS) meta‑heuristic to structural optimization, demonstrating its effectiveness on the classic ten‑bar truss benchmark. TS is a guided local‑search technique that avoids cycling back to previously visited solutions by maintaining a “tabu list”—a flexible memory structure that temporarily forbids certain moves. The authors extend the conventional single‑memory TS by employing two concurrent memory cycles: a short‑term list that blocks recent moves and a long‑term list that suppresses patterns that repeatedly lead to poor regions of the design space. This dual‑memory scheme is tailored to structural design, where constraints such as stress limits and displacement bounds must be respected at every iteration.

In the first experiment, the objective is to minimize the mass of the truss while satisfying strength and deformation constraints. Design variables are the continuous cross‑sectional areas of the ten members. An initial solution is generated randomly, and neighboring designs are produced by perturbing these areas. Any neighbor that violates a constraint is immediately discarded and added to the tabu list, preventing its reconsideration during the current search horizon. The algorithm iteratively updates the best feasible solution, adjusts tabu tenure dynamically, and terminates when improvement stalls. The resulting design matches or slightly improves upon the best solutions reported in the literature, and it converges in fewer iterations than a previously published TS implementation, highlighting the efficiency gains from the dual‑memory approach.

The second experiment tackles a multi‑objective version of the same problem, where both mass and strain energy must be reduced. To combine these conflicting goals, the authors adopt a game‑theoretic bargaining framework based on the Nash bargaining solution. Each objective is assigned a weight that reflects its relative importance; these weights are updated adaptively during the search to balance progress on both fronts. The combined scalar objective is then minimized using the same TS engine. The method not only finds designs that lie near the Pareto frontier but also demonstrates a controlled trade‑off: a modest increase in mass yields a substantial reduction in strain energy, a result that is valuable for designers seeking both lightweight and stiff structures.

Key contributions of the work include: (1) a customized dual‑memory TS algorithm that efficiently navigates constrained structural design spaces; (2) an on‑the‑fly constraint handling mechanism that eliminates infeasible candidates without costly penalty functions; (3) the integration of a game‑theoretic objective aggregation technique for multi‑objective optimization; and (4) a thorough comparative analysis showing that the proposed method achieves at least comparable, often superior, performance relative to traditional numerical optimizers such as linear/non‑linear programming and evolutionary algorithms.

The authors conclude that Tabu Search, when equipped with appropriate memory management and objective‑combination strategies, is a robust and competitive tool for structural optimization. They suggest future research directions such as extending the approach to three‑dimensional frames, composite material structures, and large‑scale design problems, as well as exploring parallel implementations to enable real‑time design assistance in engineering practice.