Showing papers on "Discrete optimization published in 1968"

An Extension of Lawler and Bell's Method of Discrete Optimization with Examples from Capital Budgeting

Abstract: The usefulness of integer programming as a tool of capital budgeting hinges on the development of an efficient solution technique. An algorithm based on partial enumeration has been developed by E. L. Lawler and M. D. Bell for solving integer linear programs with 0--1 decision variables; however their algorithm is not general enough to deal with all problems in which the objective function is quadratic. This paper extends Lawler and Bell's method so that it can be generally applied to integer quadratic programs. The new algorithm is illustrated by examples from capital budgeting.

Application of the Created Response Surface Technique to Structural Optimization

Abstract: : The Created Response Surface Technique was applied to some problems of structural optimization with multi-load conditions. The constrained optimization problem was converted to an unconstrained problem by the use of penalty functions that varied inversely with the distance of the design point from a constraint. Response surfaces also were introduced for optimization with discrete variables. The Rosenbrock Method of unconstrained optimization was used. The original method was modified to take advantage of the interaction between the optimization procedure and the response of the structure to change in discrete sections. This, when coupled with the r extrapolation procedure, resulted in considerable savings in computing time. To quantitatively evaluate the effectiveness of the techniques presented, a pilot computer program for the optimization of small-scale structures was developed. To minimize the effort involved in the development of the program a relatively inefficient analysis module was selected from a previously coded computer program. This analysis was limited to approximately 50 degrees of freedom and originally contained only an axial force member in the element library. This was considered sufficient for initial research. Two problems were investigated, that of the 3-bar truss studied by Schmit and Mallett and that of the 25-bar truss studied by Fox and Schmit. Fox and Schmit included buckling constraints and used tube diameter and thickness as the design variables. The cross-sectional areas of the circular tubes are used here as the design variables. The Euler criteria are included as stress limits for each member.

Two-level optimization techniques for dynamic systems†

Abstract: Techniques have been developed to date for the decomposition of complex interacting systems and their optimization through multilevel techniques. A second level Newton-Raphson controller that removes some of the restrictions of the second level gradient controller is developed in this paper. Simple examples are worked to demonstrate the techniques and to compare the two types of controllers. The re-optimization required of the subsystems after each iteration of the second level may be offset by the advantages of smaller subsystem optimization problems and the ability to use different optimization methods for different subsystems.

A method for optimizing control-free costs in systems with linear controllers

Abstract: Optimization problems for n -dimensional systems with m linear controls and cost functions not explicitly dependent on the control variables are transformed into equivalent problems involving only ( n-m ) state variables and m controls, and cost functions which are dependent on the controls. The equivalent problems can be solved by standard techniques, but at a considerable computational advantage stemming from the reduced dimensionality. An illustrative example is worked out for a discrete linear system.

Reciprocal variational techniques and the solution of optimization problems.

Abstract: DONALD J. EWING, Jr. was born in Toledo, Ohio in 1931. He received the BSEE from the University of Toledo in 1952 and the MSEE from MIT in 1954. He joined the electrical engineering staff of the University of Toledo in 1954 and has remained there since with the exception of a year-and-a-half pursuing further graduate work at the University of Wisconsin on a National Science Foundation Faculty Fellowship. Special areas of interest

Search and choice in transport systems planning. volume 3. applications of discrete optimization techniques to capital investment and network synthesis problems

Abstract: : The purpose of the work is to formulate and solve certain optimization problems arising in the fields of engineering economics, scarce resource allocation, and transportation systems planning. The scope and structure of optimization theory is presented in order to place subsequent work in proper perspective. A branch and bound algorithm is rigorously developed which can be applied to the optimization problems of interest. A rounding operation is defined, which provides a powerful rejection rule and permits the calculation, at each stage of the solution process, of an upper bound and a feasible solution in addition to the usual lower bound.