Solving multi-objective convex programming problems with a distance-based methodology

Purpose This work introduces a novel model for weighted sum approaches of goal programming that finds the optimum compromise solution for multi-objectives convex programming problem (MOCPP) by minimizing the distance between the ideal solution and the feasible solution space. For any MOCPP, the number of convex objectives must be minimized across a convex set of constraints. When these objectives conflict, several compromise solutions are usually found rather than a single ideal solution. Accordingly, for decision-makers, the best compromise solution is crucial because it takes into account the fundamentals of optimization problems with multiple objectives. Design/methodology/approach To find the best compromise efficient solution to multi-objective convex programming problems, we used the suggested approach to convert MOCPP into a sum of single problem. Then, minimize the distance between the ideal solution and the practical solution. For any number of objectives, the solution determined by the proposed method is valid, which calculates the efficient solution of the given objectives. Findings This technique is demonstrated with examples, and the results are compared with existing works in the literature. Remarkably, the results show how reliable and successful the proposed methodology is at solving these kinds of problems with conflicting objectives. Research limitations/implications Thank you for your comment. The main limitation of the proposed work is when the objectives are non-convex functions, where the proposed method works only for convex cases. Moreover, in multi-objective convex programming problems, it is easy to find the ideal objective vector, which may not always be achievable in real-world situations. This dependence could affect the outcomes if the ideal point is not achievable for feasible solutions. Furthermore, the method’s effectiveness can be sensitive by assigning weights to prioritize objectives, which may vary depending on the problem’s specific characteristics. Originality/value This work is original and not submitted anywhere else.