Enhancing Branch-and-Bound Method for Structural Optimization

Abstract

The branch-and-bound method was originally developed to cope with difficulties caused by discontinuous design variables in linear programming. When the branch-an~-bound method is applied to solve nonlinear programming (NLP) problems with a large number of mixed discontinuous and continuous design variables. the slow rate of convergence becomes a major drawback of the method. In thIs study. a number of enhancements are proposed to speed up the rate of convergence of the conventIOnal branch-an~~bound algorithm. Three NLP in the form of truss-design examples ar~tested to compare the capabilitIes and effIcIency of the proposed enhancements. It is shown that of the five CrIterIa for arranglllg the order III which the deSign variables are branched. the criterion of maximum cost difference dramatically reduces the number of branch nodes. thereby reducing the total number of continuous-optimization runs executed. Moreover. neighboring search. a branching procedure restricted in the neighborhood of the contllluous optImum. IS proven to be effective in speeding up the convergence. Investigation also shows that branching several deSign varIables simultaneously is not as efficient as sequentially branching one variable at a time. The proposed enhancements are incorporated along with a sequential quadratic programming algorithm mto a software package that IS shown to be very useful in the optimal design of engineering structures.

Mixed Variable Structural Optimization: Toward an Efficient Hybrid Algorithm

“…For that purpose, we chose the branch and bound algorithm, whose guiding principle is mainly due to [20], [21]. Many authors improved this method afterwards, for example in the field of structural optimization [22].…”

A two-phase computational scheme for solving bang-bang control problems

“…Hence, the algorithm developed in this paper is based on the AOCP but uses the enhanced branch-and-bound method (Tseng et al, 1995) to solve the optimal discrete-valued control problems. In each branching node of the branch-and-bound Initialization H(0) = I, Initial guess P (0) Cost function J 0 (P (k) ) Equality constraints h(P (k) ) Inequality constraints g(P (k) )…”

“…However, the large number of discontinuous design variables greatly increases the number of the continuous optimization sub-problems. Tseng et al (1995) presents an enhanced branch-and-bound method for reducing the number of executions of the continuous-optimization scheme by intelligently selecting the bounding route. Because such an enhanced branch-and-bound method dramatically reduces the total number of continuous optimization runs executed and speeds up its convergence (Tseng et al, 1995), it is adopted herein and integrated with the AOCP to develop a mixed integer NLP algorithm for solving time-optimal control problems (TOCP).…”

“…This method consists of two computational phases: in the first, switching times are calculated using existing optimal control methods; and in the second, the resulting information is used to compute the discrete-valued control strategy. The proposed algorithm, which integrates the existing optimal control solver with an enhanced branch-and-bound method (Tseng et al, 1995), is implemented and applied to some example systems, including that of the F-8 fighter aircraft.…”

Reliability Optimization Involving Mixed Continuous-Discrete Uncertainties

“…MOST is an optimization algorithm that combines SQP and branch-andbound algorithms to solve mixed continuous-discrete problems [31]. For comparison, we solved the problem three times, each using MCA, FFRA, and PFRA for reliability calculation.…”