Abstract
Generally, the inconvenience of establishing the mathematical optimization models directly and the conflicts of preventing simultaneous optimization among several objectives lead to the difficulty of obtaining the optimal solution of a practical engineering problem with several objectives. So in this paper, a generate-first-choose-later method is proposed to solve the multiobjective engineering optimization problems, which can set the number of Pareto solutions and optimize repeatedly until the satisfactory results are obtained. Based on Frisch’s method, Newton method, and weighed sum method, an efficient hybrid algorithm for multiobjective optimization models with upper and lower bounds and inequality constraints has been proposed, which is especially suitable for the practical engineering problems based on surrogate models. The generate-first-choose-later method with this hybrid algorithm can calculate the Pareto optimal set, show the Pareto front, and provide multiple designs for multiobjective engineering problems fast and accurately. Numerical examples demonstrate the effectiveness and high efficiency of the hybrid algorithm. In order to prove that the generate-first-choose-later method is rapid and suitable for solving practical engineering problems, an optimization problem for crash box of vehicle has been handled well.
Highlights
Most of the practical engineering optimization problems are multiobjective
The models of multiobjective engineering optimization problems in this paper are established by response surface methods, and the constraints are handled by log functions
The solutions of multiobjective optimization problems, which are obtained by the algorithms based on weighted sum method, are not well distributed in the Pareto optimal front
Summary
Most of the practical engineering optimization problems are multiobjective. For example, an airplane design problem might require maximizing fuel efficiency and payload, while minimizing the weight of the structure [1]. Researchers have proposed various methods with the fast development of multiobjective optimization These methods can be divided into scalar methods and evolution methods by way of solving the optimization problems. Most references relative to these fields adopted evolutionary methods This is because the derivatives of practical engineering optimization problems may not always be obtained, which leads the scalar methods out of work [24]. This paper takes weighted sums method to solve the multiobjective optimization problems, in order to get satisfactory Pareto optimal solutions rapidly. The surrogate models of vehicle’s crash box have been constructed and optimized by the proposed method, in order to provide detailed advice for designers rapidly.
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