Abstract
Various engineering design problems are formulated as constrained multi-objective optimization problems. One of the relevant and popular methods that deals with these problems is the weighted method. However, the major inconvenience with its application is that it does not yield a well distributed set. In this study, the use of the Normal Boundary Intersection approach (NBI) is proposed, which is effective in obtaining an evenly distributed set of points in the Pareto set. Given an evenly distributed set of weights, it can be strictly shown that this approach is absolutely independent of the relative scales of the functions. Moreover, in order to ensure the convergence to the Global Pareto frontier, NBI approach has to be aligned with a global optimization method. Thus, the following paper suggests NBI-Simulated Annealing Simultaneous Perturbation method (NBI-SASP) as a new method for multiobjective optimization problems. The study shall test also the applicability of the NBI-SASP approach using different engineering multi-objective optimization problems and the findings shall be compared to a method of reference (NSGA). Results clearly demonstrate that the suggested method is more efficient when it comes to search ability and it provides a well distributed global Pareto Front.
Highlights
Optimization in engineering has become a vital component with the growth of the capabilities of computers nowadays
Normal Boundary Intersection is a method developed in 1998 by Das and Dennis. It aims to identify the Pareto front for a multi-objective optimization problem, it is proven that this method has succeeded in producing a uniform set of Pareto front points, and this gives Normal Boundary Intersection approach (NBI) an advantage over the other methods used before, weighting method and e-constrain method
Taking into account the whole analysis, it can be deduced that the NBI SPSA solutions are better NSGA-II with regards to both the closeness to the true optimum and their spread for all test problems employed in the study
Summary
Optimization in engineering has become a vital component with the growth of the capabilities of computers nowadays. What characterizes any problem of engineering design is the presence of various objectives [5,6] When all these objectives are taken into account, their conflicting nature finds it challenging to find an optimal solution to the problem. A set of solutions in which improving one objective can deteriorate the other ones is referred to as the Pareto set of non-dominated solutions and approximating it contributes to understanding it in depth as well as. A simulation of the results on various difficult test problems shall reveal that NBI-SASP outperforms NSGA-II with regards to detecting a diverse set of solutions and converging near the true Paretooptimal set
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