Showing papers on "Discrete optimization published in 1986"

Optimization of stochastic systems

Abstract: This paper gives a short survey of Monte Carlo algorithms for stochastic optimization. Both discrete and continuous parameter stochastic optimization are discussed, with emphasis on the analysis of convergence rate. Some future research directions for the area are also indicated.

Models for simulation and discrete control of manufacturing systems

Abstract: A methodology is presented for constructing models of manufacturing processes for simulation and design of the discrete control logic. The models represent the discrete event evolution of the system as well as features of the underlying continuous processes. For applications such as discrete parts manufacture and assembly, the process is decomposed into operations with specified precedence relations. For each operation the required resources and associated discrete resource states are identified. Also associated with each resource is a set of resource attributes which are modified by the processes underlying each operation. The structure of the discrete-level control is modeled by modified Petri nets which are synthesized from single resource activity cycles. Construction of the net provides discrete control logic for error recovery loops and other real-time decision structures with guaranteed properties based on extensions of previous results in Petri net theory. The modeling methodology is applied to a two-arm robotic assembly cell example.

Consideration of Worst-Case Manufacturing Tolerances in Design Optimization

Abstract: The paper discusses the effect of manufacturing tolerances for the design variables on the solution to an optimization problem. Two formulations of the tolerance problem in an optimization context are presented. Linearization is employed to reduce the problems to quadratic and linear programming problems. The formulations and solutions of the two tolerance problems are illustrated with an example application.

Solving nonlinear integer programs with large-scale optimization software

Abstract: This paper describes recent experience in tackling large nonlinear integer programming problems using the MINOS large-scale optimization software. A technique is presented for extending the constrained search approach used in MINOS to exploring integer-feasible solutions once a continuous optimal solution is obtained. Computational experience with this approach is described for two classes of problems: quadratic assignment problems and pipeline network design problems.

Monte Carlo Optimization of Stochastic Systems: Two New Approaches.

Abstract: : The design of modern manufacturing systems presents a number of challenges. In particular, the stochastic nature of machine failures in combination with the large number of decision variables makes optimization of such systems difficult. This paper presents two new approaches to optimization of the complex stochastic systems that arise in a manufacturing context; both are Monte Carlo simulation-oriented, and are therefore broadly applicable. The first technique involves using a likelihood ratio gradient estimate to drive a Robbins-Monro algorithm, and is relevant to problems in which the decision variables are continuous. The second idea employs homotopy methods to follow an optimal path in decision variable space, and can be used for both discrete and continuous optimization.

On the connections between mathematical programming and discrete optimal control

Abstract: This paper gives a short review of different theories and topics in the fields of Mathematical Programming and Discrete-time Optimal control Theory. Well-known and new results (for instance, the generalized Maximum Principle) are presented within a unified framework. Emphasis is placed in the trends of interplay. New research areas are also identified.

Simulator for multilevel optimization research

Abstract: A computer program designed to simulate and improve multilevel optimization techniques is described. By using simple analytic functions to represent complex engineering analyses, the simulator can generate and test a large variety of multilevel decomposition strategies in a relatively short time. This type of research is an essential step toward routine optimization of large aerospace systems. The paper discusses the types of optimization problems handled by the simulator and gives input and output listings and plots for a sample problem. It also describes multilevel implementation techniques which have value beyond the present computer program. Thus, this document serves as a user's manual for the simulator and as a guide for building future multilevel optimization applications.

Some experience in applying a stochastic method to location problems

Abstract: Stochastic methods have recently been applied to continuous non-linear optimization problems. In this paper we begin to investigate whether these methods could be useful for discrete optimization problems. Specifically we focus our attention on sampling and clustering methods, to investigate whether they help in reducing the computational effort needed to solve uncapacitated and capacitated location problems.

A finite descent method for Steiner's problem of inpolygons with minimal circumference

Abstract: A finite descent method is proposed to solve the problem of determining an inpolygon with minimal circumference. The algorithm is based on Schwabz' reflection principle and the idea of coordinate-wise descent. Four examples illustrate the efficiency of the algorithm.

Stability of linear discrete-time systems

Abstract: A computationally efficient and simple method is suggested for determining the stability of digital systems. The new method is then compared with other existing methods.

On the derivation of bilinear models for optimization of the sampling periods in discrete systems

Abstract: This paper deals with the development of some bilinear models for non-periodic sampling in continuous plants by modelling the sampling interval as a component of the input vector. Using such models, simple optimization techniques, which are valid for on-line computation of the sampling intervals, are derived.

Evolutionary method in discrete programming

Abstract: The paper deals with the two-level partially stochastic optimization method named evolutionary method. The aim of the paper is to present a formal description of the method and its application in discrete programming. The algorithm for planning of investments in chemical industry, based on the method, has been presented.

Semi-discrete geometric programming

Abstract: An approach is proposed to solve a class of mixed-integer nonlinear programs based on the use of the Benders' decomposition partitioning scheme. This kind of problem contains continuous and discrete variables and is one of the most-difficult problems in mathematical programming because of the discontinuities in the feasible region, introduced by the discrete variables. Embedded in this problem there is a discrete optimization problem for which there are not general efficient techniques to this date. Benders' decomposition has been successfully applied to mixed-integer linear-programming problems and to mixed-integer nonlinear problems where the continuous and noncontinuous variables appear in separate terms. The class of problems considered allows the continuous and discrete variables to appear together in polynomial expressions. Geometric programming results are used to obtain separability of the variables and thus to apply Bender's scheme. The approach is an iterative one, that alternates between solving continuous geometric programming problems and linear discrete programming problems. The numerical efficiency of the method is assessed for a sample of test problems and depends on the methods used to solve these two derived problems. Several alternatives are studied.

On the Real-Time Design of Changing Sampling Periods by Using Bilinear Models

Abstract: This paper describes a method to obtain a kind of bilinear model for discrete systems. In such models, the sampling period plays the role of an additional input component.