Mixed-integer Non-linear Programming in Civil Engineering

Abstract

Abstract. The paper discusses the Mixed-Integer Non-linear Programming (MINLP) of problems in civil engineering. The MINLP enables the optimization of continuous parameters simultaneously with discrete alternatives. While continuous parameters are in structural optimization structural costs, masses, loads, stresses, resistances and deflections, as well as the discrete alternatives are in most cases defined as different topologies, standard sizes and materials. The continuous parameters are in the models expressed by continuous variables, whilst the discrete alternatives by discrete (0-1) variables. The MINLP optimization of a structure is usually a comprehensive and highly non-linear calculation process. The MINLP approach requires that a structure is generated as an MINLP superstructure including a number of structure alternatives. One of them is the optimal one. For each optimization problem/structure, an MINLP optimization model of the structure must be developed, where the cost or mass objective function of the structure is subjected to structural analysis and dimensioning equality/inequality constraints. The Modified Outer-Approximation/Equality-Relaxation algorithm and a threephase MINLP strategy are applied. Three numerical examples, i.e. the MINLP optimization of a cantilever beam, composite floor and high-pressure penstock are presented at the end of the paper.