Vector maximisation over a finite set of alternatives

This paper examines the computational complexity of solving the vector maximisation problem defined over a finite set of alternatives. It is shown that the computational requirements and the number of efficient solutions may be prohibitive. The paper presents an effective algorithm for generating a family of a ‘tolerable’ number of efficient solutions for multi-objective generalisations of non-linear knapsack and distribution of effort/resource allocation problems involving one separable non-linear objective function and m linear objective functions defined over a finite set of alternatives. The embedding of the algorithm within interactive search methods and the determination of a representative set of efficient solutions for selecting a ‘satisfactory’ compromise solution are briefly discussed. A numerical example is used to illustrate the algorithm.