Showing papers on "Discrete optimization published in 1970"
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01 Jan 1970
450 citations
TL;DR: Jacobi-type conditions for singular optimization problems obtained by transformation to nonsingular form adaptable to linear quadratic optimal control theory have been proposed in this paper, where the transformation is based on a transformation to a non-singular form.
Abstract: Jacobi-type conditions for singular optimization problems obtained by transformation to nonsingular form adaptable to linear quadratic optimal control theory
29 citations
TL;DR: In this paper, a combination of partial and random search is used to solve general linear 0-1 restricted optimization problems on a digital computer, where partial search moves from randomly selected starting points, through the space, to precisely characterized local optima.
Abstract: An approach to solving general linear 0-1 restricted optimization problems on a digital computer is presented. The approach used employs a combination of partial and random search conducted over the space of 2 '~ n-dimensional binary vectors. The partial search moves from randomly selected starting points, through the space, to precisely characterized local optima. Random search is then reapplied in an attempt to overcome the problem of generating a locally optimum solution which is not globally optimum. The resulting algorithm has been implemented on the GE 635 computer. Computational experience obtained thus far indicates that the approach taken is feasible for solving such problems and offers the possibilities of obtaining good solutions to large problems at modest computation costs.
19 citations
TL;DR: A criterion for ranking the decomposition procedures is developed, the properties of the optimal decompositions are discussed, and an algorithm for finding the best decomposition in the case of no storage limitation is given.
Abstract: This paper deals with the solution to a discrete optimization problem by decomposition. It develops a criterion for ranking the decomposition procedures, discusses the properties of the optimal decompositions, and gives an algorithm for finding the best decomposition in the case of no storage limitation.
18 citations
TL;DR: A closed-form evaluation of the infinite series of time-weighted squared errors associated with linear discrete systems is presented.
Abstract: A closed-form evaluation of the infinite series of time-weighted squared errors associated with linear discrete systems is presented. The method of evaluation does not require the system to be of low order or take a specific form.
16 citations
TL;DR: Optimal solutions and algorithms are presented for both continuous and discrete optimization problems for S-convex and symmetric objective and feasibility regions.
Abstract: Mathematical programs with S-convex and with symmetric objective and feasibility regions are investigated. Optimal solutions and algorithms are presented for both continuous and discrete optimization problems.
9 citations
4 citations
01 Jan 1970
TL;DR: A hybrid computer Monte Carlo technique for the simulation and optimization of systems with random parameters is presented, applied to the simultaneous optimization of the means and variances of two parameters in the radar-homing missile problem treated by McGhee and Levine.
Abstract: A hybrid computer Monte Carlo technique for the simulation and optimization of systems with random parameters is presented The method is applied to the simultaneous optimization of the means and variances of two parameters in the radar-homing missile problem treated by McGhee and Levine
TL;DR: The maximum principle is applied to minimum-time optimal-control problems, and an optimization algorithm is presented which can be implemented on a hybrid computer.
TL;DR: In this paper, a new discrete model for the study of dynamic interaction phenomena between adjacent, rigid foundations on a homogeneous, linear elastic half-space is presented, where each dynamic degree of freedom of the foundations consists of a mass connected to a rigid support through frequency independent springs and dashpots.
Abstract: A new discrete model for the study of dynamic interaction phenomena between adjacent, rigid foundations on a homogeneous, linear elastic half-space is presented. Each dynamic degree of freedom of the foundations consists of a mass connected to a rigid support through frequency independent springs and dashpots. The interaction between the foundations is achieved by imposing spring and damping couplings developed in this work. The time lagging effects of coupled dynamic input due to wave propagation is also considered through a proposed modified vector approach.
TL;DR: In this paper, a nonlinear multi-objective optimization model for machining process parameters is presented, which allows different priority level for each manufacturing objective and the resulting nonlinear optimization problem is solved using unconstrained optimization techniques.
Abstract: Multi-objective optimization applications in manufacturing of structural components have been mostly in the area of scheduling and process planning. Until now most well developed multi-objective optimization codes are linear. Due to the high level of nonlinearity, few applications have been reported in the area of multi-objective optimization of manufacturing processes parameters. This paper presents a general nonlinear multi-objective optimization model for machining processes parameters. The developed nonlinear multi-objective optimization model allows different priority level for each manufacturing objective. The resulting nonlinear optimization problem is solved using unconstrained optimization techniques. This reduces the effort required to model the manufacturing process problem since linearization is not required. The optimum solution can also be achieved from any starting point, since no feasibility conditions are required. The application and efficiency of the developed model is studied using a machining process test case with different manufacturing priority.
TL;DR: Results previously derived for 1st-order discrete-time systems are extended to higher-order systems to solve the inequality of the following type: For example, in the case of LaSalle's inequality, the inequality between theorems of 1st and 2nd order systems is fixed.
Abstract: Results previously derived for 1st-order discrete-time systems are extended to higher-order systems.
TL;DR: In this article, a Linked Multilevel Hierarchical (LMH) approach to the Mixed-Integer Nonlinear Programming (MINLP) synthesis of mechanical structures is presented, by which the original MINLP problem is hierarchically decomposed into material, topology and standard dimension levels to be solved sequentially.
Abstract: The paper present a Linked Multilevel Hierarchical (LMH) approach to the Mixed-Integer Nonlinear Programming (MINLP) synthesis of mechanical structures, by which the original MINLP problem is hierarchically decomposed into material, topology and standard dimension levels to be solved sequentially. We introduce a special case of a simplified MINLP model formulation for mechanical superstructures (MINLP-S), which are supposed to contain a number of (sub)groups of equal structural elements. The objective is to perform a continuous parameter optimization of the superstructure simultaneously with a discrete optimization of its material, topology and standard dimension alternatives. The Modified OuterApproximation/Equality-Relaxation (OA/ER) algorithm has been used for the optimization. In order to demonstrate this approach, we have included a practical example of a vacuum chamber structural synthesis for the high-frequency dryer for timber.
01 Mar 1970