Showing papers on "Discrete optimization published in 1982"

Multicriteria dynamic programming with an application to the integer case

Abstract: Fundamental dynamic programming recursive equations are extended to the multicriteria framework. In particular, a more detailed procedure for a general recursive solution scheme for the multicriteria discrete mathematical programming problem is developed. Definitions of lower and upper bounds are offered for the multicriteria case and are incorporated into the recursive equations to aid problem solution by eliminating inefficient subpolicies. Computational results are reported for a set of 0–1 integer linear programming problems.

An Overview of Complexity Theory in Discrete Optimization: Part II. Results and Implications

Abstract: Over the past decade, complexity theory has emerged from a branch of computer science almost unknown in the operations research community into a topic of widespread interest and research. Part I of this tutorial overview of the subject (TRANSACTIONS, March 1982) developed important background concepts of the theory. This paper uses that background to define and investigate the implications of NP-Hardness, NP-Completeness, NP-Equivalency, the NP≠NP conjecture, and various approximations.

Discrete Optimization by Relational Constraint Satisfaction

Abstract: In pattern matching a basic problem is to determine one or more vectors X that maximize an objective function which is a sum of functions of components of X. When this problem is solved by dynamic programming CPU time and storage requirements grow explosively as the amount of intervariable interaction in the objective function increases. This explosion may be reduced by departing from the traditional dynamic programming method of eliminating successive variables and instead determining a constraint relation between each variable and all others with which it interacts. Discrete relaxation is used to accelerate a backtrack search to find all vectors that satisfy all such constraints. Optimization is achieved by evaluating the objective function for all such vectors. This new method of optimization has been experimentally compared with a classical dynamic programming algorithm running with the same pseudorandomly generated objective functions.

Combining analysis with optimization at Langley Research Center - An evolutionary process

Abstract: The evolutionary process of combining analysis and optimization codes was traced with a view toward providing insight into the long term goal of developing the methodology for an integrated, multidisciplinary software system for the concurrent analysis and optimization of aerospace structures. It was traced along the lines of strength sizing, concurrent strength and flutter sizing, and general optimization to define a near-term goal for combining analysis and optimization codes. Development of a modular software system combining general-purpose, state-of-the-art, production-level analysis computer programs for structures, aerodynamics, and aeroelasticity with a state-of-the-art optimization program is required. Incorporation of a modular and flexible structural optimization software system into a state-of-the-art finite element analysis computer program will facilitate this effort. This effort results in the software system used that is controlled with a special-purpose language, communicates with a data management system, and is easily modified for adding new programs and capabilities. A 337 degree-of-freedom finite element model is used in verifying the accuracy of this system.

A discrete optimization method for high-order FIR filters with finite wordlength coefficients

Abstract: This paper suggests a discrete optimization method which can solve high order FIR filter problems within a practically reasonable computing time. The error spectrum caused by rounding off the coefficients is shaped through the discrete optimization so to be effectively cancelled, in the L 2 norm sense, by other factors connected in cascade. In order to save computing time, the error spectrum is evaluated in a time domain, and parameters are divided into small groups during searching for the optimum solution. LPF and BPF design examples, with 200 lengths, show the proposed approach can reduce coefficient wordlengths by 2 or 3 bits, compared with results obtained by only rounding off. The execution time on the general purpose computer, ACOS System 900, is 97 seconds.

Optimization of building systems

Abstract: In this paper a class of building systems is defined, to which optimization methods based on the decomposition and coordination might be applicable. Using graph theory, the properties of this class are described. These depend on the flow of effect through the subsystems and determine the structure of constraints in the mathematical optimization model of the system. An approach to the solution of the optimization problem is presented.

More on independence systems

Abstract: The equivalence of the notions of independence systems and monotone boolean functions is proved. This result permits to establish some new connections between discrete analysis and discrete optimization. We discuss possible directions of research following from these connections. Some Questions connected with the reducibility of general in-dependence systems to threshold ones are also considered.

Discrete Optimization of Finite-Element Solutions: A Concept Discussed for the Diffusion-Advection Problem

Abstract: We consider the equation $$ Lu = f{\text{ }}in{\text{ }}\Omega $$ (1) , where L:D(L) ⊂ E → F is a linear differential-operator.

Algorithms for parameter optimization probiems of nonlinear discrete systems

Abstract: This paper presents two algorithms for a class of optimization problems of the following form : min I (x) subject to the constraints Open image in new window The constraints of this form come from the stability condition. The great difficulty of this problem is that there exists no method to check whether a point x is strictly in the feasible region.