Implementation of Discrete Capability into the Enhanced Multipoint Approximation Method for Solving Mixed Integer-Continuous Optimization Problems

Abstract

Multipoint appro ximation method (MAM) focuses on the development of metamodels for the objective and constraint functions in solving a mid-range optimization problem within a trust region. To develop an optimization technique applicable to mixed integer-continuous design optimization problems in wh ich the objective and constraint functions are computationally expensive and could be impossible to evaluate at some comb inations of design variables, a simple and efficient algorith m, coordinate search, is imp lemented in the MAM. Th is discrete optimization capability is examined by the well established benchmark problem and its effectiveness is also evaluated as the discreteness interval for discrete design variables is increased from 0.2 to 1. Furthermore, an application to the optimization of a lattice co mposite fuselage structure where one of design variables (number of helical ribs) is integer is also presented to demonstrate the efficiency of this capability.

Design and Optimization Lattice Endoprosthesis for Long Bones: Manufacturing and Clinical Experiment

“…The parameter varied from 0.25 to 2, in increments of 0.175. To find the influence function multipoint approximation method for solving a mixed integer-continuous optimization, problems were used [27]. To solve the mechanical properties of the lattice cell the method of the representative sample was used [28,29].…”

Extended Multipoint Approximation Method

“…Other than the surrogates built by Liu and Toropov [2], one new surrogate called the Taylor's Expansion surrogate is introduced in the extended MAM by the following equation:…”

“…This method is based on an assembly of multiple surrogates into a single surrogate using linear regression. The coefficients of the model assembly are not weights of the individual models but tuning parameters determined by the least squares method [2].…”

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

“…The Hooke-Jeeves direct search technique [12,[18][19] examines points near the current point (having the rounded values for discrete design variables) by perturbing design variables -one variable at a time -until an improved point is found. There is a similarity between Hooke-Jeeves technique and the coordinate search algorithm previously suggested in [11] in terms of the determination of the optimal search path for the solution. The Hooke-Jeeves search technique begins with the starting point, as well as 2N d coordinate points, where N d is the number of discrete design variables.…”

“…In general, it is only allowed to perform response function evaluations for points that have discrete values of the design variables [9]. New procedures for sampling, metamodel building, their use for solving an optimization problem with continuous and discrete properties within a trust region, and the trust region adaptation strategy have been developed to enhance the MAM with the discrete capability by authors [10,11].…”