Discrete optimization

About: Discrete optimization is a research topic. Over the lifetime, 4598 publications have been published within this topic receiving 158297 citations. The topic is also known as: discrete optimisation.

Methods for Discrete Variable Structural Optimization

Abstract: Discrete design variables are encountered in most practical design applications. An overview of the optimization methods that can treat such design variables in their solution process is presented. Many times selection of an appropriate method depends on type of discrete variables and problem functions. Therefore, discrete design variable problems are classified into six different types. Methods suitable for each problem type are identified. Some recent applications of discrete variable optimization methods are described. Methods for structural optimization with available sections are discussed.

Discrete Monotonic Optimization with Application to a Discrete Location Problem

Abstract: A general discrete optimization problem is investigated that includes integer polynomial programs as special cases. To exploit the discrete monotonic structure of these problems, a special class of cuts called monotonicity cuts are developed and then adjusted according to a suitable procedure to accommodate discrete requirements. As illustration, the method is applied to solve a discrete location problem which is also a variant of the well known engineering problem of design centering. Computational results are reported for instances of the latter problem with up to 100 variables and 500 constraints.

Optimal Design of Latticed Towers Subjected to Earthquake Loading

Abstract: The problem of optimal design of latticed transmission towers subjected to normal operating loads and an earthquake load is formulated. A time history analysis of the structure is performed. The constraints given in a design code are imposed. Many of the constraints are time dependent; therefore methods to treat them are incorporated in the solution process. All members are treated as equal- ~unequal-! legged angle sections. The members are selected from the sections available in a manufacturer's catalog. Two methods are presented and evaluated for such discrete variable optimization problems. The first method, called the two-phase method, uses a combi- nation of continuous and discrete optimization algorithms, and the second one, called an adaptive discrete assignment method ~ADAM!, uses only a continuous optimization algorithm. The proposed methods are applicable to any discrete variable problem that can be formulated as a continuous problem. In addition, the problem is solved using a genetic algorithm ~GA!. The efficiency and practicality of the proposed methods are compared to those of the GA. From the results, it is concluded that the GA is a very straightforward method to use for discrete problems; however, it requires a significant amount of Central Processing Unit time. On the other hand, the two-phase method and the ADAM do not require as much computational effort but the discrete designs found with them are slightly more expensive. Also, numerical implementation of the two methods requires more effort.