Aspiration-Based Search Algorithm (ABSALG) for Multiple Objective Linear Programming Problems: Theory and Comparative Tests

Abstract

We develop an interactive method for multiple objective linear programming based on aspiration levels of a decision maker. The method assumes an unknown pseudoconcave preference structure of a decision maker throughout the decision process, and the decision maker's ability to select a preferred solution from p + 1 alternatives, where p is the number of objectives. In addition to presenting the supporting theory and algorithm, we perform a comparative study using a fictitious decision maker, comparing our approach to those of Steuer and Choo (Steuer, R. E., E. Choo. 1983. An interactive weighted Tchebycheff procedure for multiple objective programming. Math. Prog. 26 326–344.) and Reeves and Franz (Reeves, G. R., L. Franz. 1985. A simplified interactive multiple objective linear programming procedure. Comp. & Oper. Res. 12 589–601.). All three methods are interactive. During an iteration, each method presents several solution alternatives to the decision maker simultaneously. Our approach utilizes a Tchebycheff function that facilitates attainment of an optimum at a nonextreme point solution. The statistics collected in the comparative study provide insights into the nature of the algorithms and the behavior of the solution techniques with different categories of problem structure and different underlying utility functions.