Development of a Hybrid Algorithm for Efficiently Solving Mixed Integer-Continuous Optimization Problems

Abstract

Problems with mixed integer-continuous design variables are a class of complicated optimization problems that commonly exist in practical engineering design work. In this paper, a hybrid algorithm combining metamodel-based Multipoint Approximation Method (MAM) and Hooke-Jeeves direct search technique is presented to efficiently seek the optimum solutions for mixed integer-continuous optimization problems. First, optimal continuous values are obtained by the Sequential Quadratic Programming method (SQP) on the approximated functions in a current trust region. Then, continuous values are rounded to the nearest integer values for discrete variables. Utilizing integer values as a starting point, the Hooke-Jeeves assisted MAM is applied to search for the discrete optimal solution in the sub-space of discrete variables as well as accordingly update the sub-optimal values for continuous design variables by SQP. The proposed hybrid algorithm is examined by the well established benchmark example and the obtained results demonstrate the superiority of the developed algorithm over GA in terms of computational cost and the quality of solutions.

Efficient hybrid algorithms to solve mixed discrete-continuous optimization problems

“…Fixing the values for discrete design variables and then updating the optimal values only for continuous design variables by performing SQP on the approximation model The end of Step Two Figure 3 Flowchart for the coordinate search technique in Step Two (3) Hooke-Jeeves direct search technique (Kolda et al 2003, Garcia et al 2006, Brauna et al 2015, Liu 2016), a more robust approach than the first two algorithms, can more efficiently and effectively exploit the design space of discrete variables for the optimal solutions. The flowchart for the Hooke-Jeeves direct search technique is depicted in Figure 4.…”

“…Hooke–Jeeves direct search technique (Kolda et al , 2003; Garcia et al , 2006; Brauna et al , 2015; Liu, 2016), a more robust approach than the first two algorithms, can more efficiently and effectively exploit the design space of discrete variables for the optimal solutions. The flowchart for the Hooke–Jeeves direct search technique is depicted in Figure 4.…”