Computational tools have been used in structural engineering design for numerous objectives, typically focusing on optimizing a design process. We first provide a detailed literature review for optimizing truss structures with metaheuristic algorithms. Then, we evaluate an effective solution for designing truss structures used in structural engineering through a method called the mountain gazelle optimizer, which is a nature-inspired meta-heuristic algorithm derived from the social behavior of wild mountain gazelles. We use benchmark problems for truss optimization and a penalty method for handling constraints. The performance of the proposed optimization algorithm will be evaluated by solving complex and challenging problems, which are common in structural engineering design. The problems include a high number of locally optimal solutions and a non-convex search space function, as these are considered suitable to evaluate the capabilities of optimization algorithms. This work is the first of its kind, as it examines the performance of the mountain gazelle optimizer applied to the structural engineering design field while assessing its ability to handle such design problems effectively. The results are compared to other optimization algorithms, showing that the mountain gazelle optimizer can provide optimal and efficient design solutions with the lowest possible weight.

The k-means algorithm aims at minimizing the variance within clusters without considering the balance of cluster sizes. Balanced k-means defines the partition as a pairing problem that enforces the cluster sizes to be strictly balanced, but the resulting algorithm is impractically slow O(n³). Regularized k-means addresses the problem using a regularization term including a balance parameter. It works reasonably well when the balance of the cluster sizes is a mandatory requirement but does not generalize well for soft balance requirements. In this paper, we revisit the k-means algorithm as a two-objective optimization problem with two goals contradicting each other: to minimize the variance within clusters and to minimize the difference in cluster sizes. The proposed algorithm implements a balance-driven variant of k-means which initially only focuses on minimizing the variance but adds more weight to the balance constraint in each iteration. The resulting balance degree is not determined by a control parameter that has to be tuned, but by the point of termination which can be precisely specified by a balance criterion.