Enhancing the multiobjective optimum design of structural trusses with evolutionary algorithms using DENSEA

Abstract

The multiobjective or multicriteria optimum design of structural trusses is handled in this paper. A double minimization is taken into account: constrained mass and number of different cross-section types. The first fitness function, the constrained mass, considers constraints in terms of stresses, buckling effect and displacements of certain nodes, and responds to the requirement of reducing the acquisition cost of raw material, which in case of a metallic structure is directly related to the whole mass of the design. The constraints (required for assuring the structure to complain its mission) are evaluated by the direct stiffness method. The second fitness function, number of different cross section types, supposes a condition of constructive order, and with special relevancy in structures with high number of bars. It helps to a better quality control during the execution of the building site and its calculation is done by successive comparisons among the existing cross-section types in a particular design. This is a discrete domain problem, being the cross-section types chosen among normalized cross-section types included in codes and / or acquirable in the market. The optimization process is performed through evolutionary multiobjective algorithms, which allow a global optimization due to its populational search and obtain a multiobjective non-dominated front of solutions in one single execution. Moreover, they consider discrete search variables (the structural trusses cross-section types) in discrete search spaces (the second objective is a discrete one). The maintenance of the population diversity through the search process seems to be critical in this type of problem as results indicate. A new evolutionary multiobjective algorithm called DENSEA is introduced in this paper. It takes advantage of good diversity maintenance of the population individuals through three different mechanisms of the algorithm. The DENSEA approach is compared versus two well known multicriteria evolutionary algorithms which are among the top of the most recent state of the art: the Non-dominated Sorting Genetic Algorithm II (NSGA-II) and the Strength Pareto Evolutionary Approach 2 (SPEA2). Thirty independent executions for each algorithm, different population sizes and mutation rates are considered in the comparison. Some structural trusses test-cases taken from the known field references are handled. The comparative statistical results of the test case cover a convergence study during evolution by means of certain metrics that measure front amplitude and distance to the optimal front not only in final values, but also during the whole convergence process. Results indicate that the DENSEA approach outperforms the other algorithms solving successfully the multiobjective optimum design problem.