Optimization of Problems with Multi-Objective Functions and their Applications in Engineering

Abstract

Many real-world optimization issues typically have multiple competing goals. There is generally no solution in those multi-objective optimization problems that optimizes all objective functions at the same time. Rather, "efficient" in terms of all objective function’s solutions known as Pareto optimum solutions are presented. We typically have a large number of Pareto-optimal options. As a result, we must choose a final solution from among Pareto optimal solutions while considering the objective function balance; this process is known as "trade-off analysis." It is not hyperbole to state that trade-off analysis is the most crucial task in multi-objective optimization. As a result, the methodology's ease of use and comprehension for trade-off analysis should be highlighted. The set of Pareto optimal solutions in the objective function space, or Pareto frontier, can be represented somewhat simply in circumstances when there are two or three objective functions. We can fully understand the trade-off relationship between objectives when we see Pareto boundaries. Thus, in scenarios with two or three objectives, it would be the most appropriate technique to represent Pareto borders. Reading the trade-off relationship between objectives with three dimensions, however, may be challenging. Nonetheless, Pareto frontier cannot be represented in situations where there are more than three objectives. In this case, interactive techniques can assist us in performing a local trade-off analysis that reveals a "certain" Pareto optimal option. Many techniques have been devised, with variations in which the Pareto optimal solution is displayed. The main concerns of such multi-objective optimization techniques, especially as they relate to engineering design problems, are covered in this study.