Heuristic Solution Procedure Research Articles

Network layout procedure for printed - circuit design

This paper describes a heuristic solution procedure for laying out the conductors of a printed circuit on the two sides of a plate of nonconducting material. There must be no overlap between conductors on the same side of the plate as they are uninsulated. For certain layouts it is necessary to drill holes in the plate and pass conductors through the holes to avoid overlap. The problem is to identify the layout which requires the minimum number of holes. The solution procedure uses a computer subroutine in conjunction with an iconic model of the plate. The subroutine is based on a method of Nicholson 1 which attempts to lay out a given circuit on one side of a plate to minimize the number of overlaps. The iconic model of the plate used in this research consisted of a pair of plastic sheets, representing the two sides of the plate, overlaid one on top of the other. The nodes and connections were drawn on them with felt-tip pens. The procedure is iterative and takes advantage of the fact that the problem can be viewed in terms of graph theory. The procedure is suitable for an interactive computer terminal system. Computational experience is limited but encouraging. However there is no guarantee that solutions produced by the procedure will be optimal in the sense that an absolute minimum number of holes will be required to be drilled.

Sequencing Highway Network Improvements: A Case Study of South Sulawesi

A common problem in transportation planning studies is to determine which improvements or additions to a transportation network should be made within some given planning horizon, and then to sequence the construction of these projects in some optimal manner. Mathematical programming models capable of solving simultaneously the project selection and timing problems are computationally demanding, and, as a result, it is often necessary to resort to various heuristic solution procedures. In this paper a number of heuristic approaches are compared and evaluated with respect to a complete intertemporal specification of this investment problem. The evaluation is based on the results of a transportation planning study for the province of South Sulawesi, Indonesia.

Decomposition of a Multi-Period Media Scheduling Model in Terms of Single Period Equivalents

This paper develops a method for choosing advertising media plans for the next T-periods in order to maximize net discounted profits. Using the discrete maximum principle of Optimal Control Theory, it is shown that under certain conditions a T-period media model can be decomposed into a sequence of T one-period models together with the determination of the corresponding carry-over effects using an iterative procedure. The single period models with their objective functions modified to include the carry-over effects can be solved by conventional methods. Although the conditions for decomposition are not always satisfied, the heuristic solution procedure defined by the decomposition approach has been found to give close to optimal solutions in randomly generated test problems. The solutions obtained in these tests are usually better than the corresponding solutions obtained by the Little and Lodish type of heuristic applied to the present model. Finally, the T-period model is specialized to derive a steady-state formulation of an infinite horizon media planning problem.

Integer Programming Models for Sales Territory Alignment to Maximize Profit

A recent article described a mathematical programming model and heuristic solution procedure to realign sales territories. This report presents two linear integer programming models for sales territory alignment to maximize profit. Emphasis is placed on the development of models which are easy to implement.

Sales Territory Alignment to Maximize Profit

A mathematical programming model and heuristic solution procedure are developed to realign sales territories. Unique model aspects are: (1) the objective function is the anticipated profit generated by the sales force; (2) the interrelated problem of account specific call frequency determination is simultaneously considered; (3) travel time is considered, including combining calls on accounts into trips.

On Covering Problems and the Central Facilities Location Problem

AbstractA number of variations of facilities location problems have appeared in the research literature in the past decade. Among these are problems involving the location of multiple new facilities in a discrete solution space, with the new facilities located relative to a set of existing facilities having known locations. In this paper a number of discrete solution space location problems are treated. Specifically, the covering problem and the central facilities location problem are shown to be related.The covering problem involves the location of the minimum number of new facilities among a finite number of sites such that all existing facilities (customers) are covered by at least one new facility. The central facilities location problem consists of the location of a given number of new facilities among a finite number of sites such that the sum of the weighted distances between existing facilities and new facilities is minimized. Computational experience in using the same heuristic solution procedure to solve both problems is provided and compared with other existing solution procedures.

Heuristic Solution of a Signal Design Optimization Problem

This paper discusses a heuristic solution procedure for a combinatorial optimization problem that originates in designing signal constellations for modems. The design problem is to place m signals in a two-dimensional space to minimize the average error rate under specified noise conditions, using a maximum-likelihood decoding scheme. Intuitively, it amounts (roughly) to spreading the signal points as far apart as possible, according to the distance measurement implied by the noise function. We show how this problem can be reduced to a discrete one: Given an l by n matrix P, and m 1 , …, i m } of the rows of P that maximizes and then describe an efficient procedure for finding this maximizing set. Experiments indicate that the procedure is a useful tool, both for analysis of existing and proposed signal constellations and for finding new, near-optimum ones.

A Heuristic Solution Procedure for Linear Programming Problems with Special Structure

Abstract A heuristic method is developed for linear programming problems with homogeneous costs in the objective function and upper bounds on the variables. The iterative procedure developed starts with an initial nontrivial feasible solution vector and improves the objective function value at each iteration by improvement on the value of a variable in the solution vector. No artificial or slack variables are used in the solution of the problem. Computational experience with the method and comparison with standard LP codes are presented. Advantages and disadvantages of the method are also discussed.

Quasi-Convex Programming

Quasi-Convex Programming

Soil erosion

This paper deals with the dynamic multi-item capacitated lot-sizing problem under random period demands (SCLSP). Unfilled demands are backordered and a fill rate constraint is in effect. It is assumed that, according to the static-uncertainty strategy of Bookbinder and Tan [1], all decisions concerning the time and the production quantities are made in advance for the entire planning horizon regardless of the realization of the demands. The problem is approximated with the set partitioning model and a heuristic solution procedure that combines column generation and the recently developed ABCβ heuristic is proposed.