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Many methods have been developed for structural size and configuration optimization in which cross-sectional areas are usually assumed to be continuous. In most practical structural engineering design problems, however, the design variables are discrete. This paper proposes two efficient structural optimization methods based on the harmony search (HS) heuristic algorithm that treat both discrete sizing variables and integrated discrete sizing and continuous geometric variables. The HS algorithm uses a stochastic random search instead of a gradient search so the former has a new-paradigmed derivative. Several truss examples from the literature are also presented to demonstrate the effectiveness and robustness of the new method, as compared to current optimization methods.

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This study uses an elitist Genetic Algorithm (GA) to optimize material costs in one-way reinforced concrete slabs, adhering to ACI 318-19. A sensitivity analysis demonstrated the critical role of elitism in GA performance. Without elitism, the GA consistently failed to reach the target objective, with success rates often nearing zero across various crossover fractions. Incorporating elitism dramatically increased success rates, highlighting the importance of preserving high-performing individuals. With an optimal configuration of 0.3 crossover fraction and 0.45 elite percentage, a 92% success rate was achieved, finding a cost of 24.91 in 46 of 50 runs for a simply supported slab. This optimized design, compared to designs based on ACI 318-99 and ACI 318-08, yielded material cost savings of between 5.8% to 8.6% for simply supported, one-end continuous, both-ends continuous, and cantilevered slabs. The influence of slab dimensions on cost was evaluated across 64 scenarios, varying slab lengths from 5 to 20 feet for each support condition. Resulting cost versus slab length diagrams illustrate the economic benefits of GA optimization.