Redundancy and delimitation of the Pareto front

The purpose of this paper is to investigate the constraints shaping the Pareto front in multi-objective linear programming, by applying recently proposed single-objective optimization methods to individual linear programming problems, constructed from the given problem. Considering the binding constraints of these individual linear programming problems, two new constraint sets are proposed, called union-binding and intersection-binding. A definition of binding constraints for a multiobjective problem is given and it is proved that at least the constraints that belonging to the union-binding set are binding constraints for the given multi-objective problem. Furthermore, it is proved that if the intersection-binding set is non-empty, then at least one point resulting from strictly satisfying these constraints belongs to the Pareto set. Hence, the exploration of union-binding and intersection-binding sets facilitates an understanding of both the constraints contributing to finding the Pareto set and those delimiting the Pareto front. Additionally, we interpret the union-binding and intersection-binding sets, using interpretive parameter variables derived from the original multi-objective problem, through a parallel exploitation of recently proposed LP algorithms, PRMac and Cosine. This interpretation leads to the conclusion that exploiting union-binding and intersection-binding sets holds promising prospects for future research. Finally, the present paper defines the minimal multi-objective linear programming problem and proposes a step-by-step solution for the multi-objective problem.