A New Proposed Method for Solving Multi-Objective Optimization Problems (MOP)
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Abstract
Multi-objective Optimization Problems (MOP) (or Pareto optimization) are deeply rooted as an alternative concept of actual optimization where multi-objective identifies the conception of the optimization, as is common in the fields of Operations Research (OR) and decision science. These are often constrained problems where the search for an optimal solution requires some form of analyzing objective achievement trade-offs. Because there are no trade-offs along a Linear Programming (LP), optimization is an essential concept of multiple objectives. In other words, a Decision-Making (DM) process for LP optimization is a traditional method that depends on finding the optimal solution for a single objective function. However, in real life, this logic is considerably classical, where researchers often encounter situations that contain more than one objective function, and these functions usually conflict with each other. It means that when one objective value is either increased or decreased, it comes at the expense of the other in the opposite way. Problems of this type are called MOP, which seeks to find a set of nondominated solutions (or Pareto optimal solution) to satisfy the decision maker. This paper expands and develops the multi-objective optimization concept by using a proposed new method for solving all objective functions together without converting to an individual objective problem, as is common in solving MOP. The paper also introduces a tabular and graphical comparison with a simple numerical problem showing the difference between the proposed method and some essential multiple optimality methods (such as compromise programming, relative weighting, and constraint programming). The suggested method provides a practical initiatory framework for future MOP research and applications.
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