Ideal Cone: A New Method to Generate Complete Pareto Set of Multi-criteria Optimization Problems

Abstract

In this paper, a new classical method, entitled ideal cone (IC), is presented to generate complete Pareto set of multi-criteria optimization problems (MOP). Systematically changing a parameter, which is independent of decision maker’s (DM) preferences, the method seeks Pareto optimal solutions sequentially. Parameter of the proposed classical method is independent of objective functions of the problem. Formulated method is a non-gradient direction-based technique. Directions of the method essentially lie on \(k\)-dimensional unit sphere for \(k\)-criteria problems. Though proposed method is a direction-based method, it bears necessary and sufficient condition for globally weak Pareto optimality. It is shown that a simple modification of the presented method can attain \(D\)-Pareto optimal points of the problem, where \(D\) is any pointed convex cone. Thus, formulated technique not only can generate Pareto set, but also obtain general \(D\)-Pareto set. A brief comparison of the proposed method with the existing similar classical methods is also made. Developed method is supported by several numerical and pictorial illustrations.