A General Purpose Interactive Goal Programming Algorithm

Abstract

This paper reviews currently available goal programming (GP) and multi-objective programming (MOP) interactive algorithms and discusses design issues of interactive algorithms specifically for GP. Two factors which distinguish GP applications from most MOP application are the capability to incorporate a large number of objectives in the modelling and solution practice, and the possible use of a lexicographic priority structure. Therefore any interactive GP or adapted MOP algorithm should be capable of performing well under these conditions. In practice, many existing algorithms fail to operate efficiently under these conditions due to a large amount of information required from, or presented to, the decision maker or the time taken per interactive iteration. The use of the lexicographic structure also adds an extra degree of complexity and may cause problems with utility function based algorithms. Therefore, the remainder of this paper presents a general purpose GP interactive algorithm capable of handling both large scale, and lexicographic, goal programmes. The algorithm is designed to present a suitable amount of information to the decision maker and be efficient both in number of interactive iterations and in time taken per interactive iteration.