Having developed multiobjective optimization algorithms using evolutionary optimization methods and demonstrated their niche on various practical problems involving mostly two and three objectives, there is now a growing need for developing evolutionary multiobjective optimization (EMO) algorithms for handling many-objective (having four or more objectives) optimization problems. In this paper, we recognize a few recent efforts and discuss a number of viable directions for developing a potential EMO algorithm for solving many-objective optimization problems. Thereafter, we suggest a reference-point-based many-objective evolutionary algorithm following NSGA-II framework (we call it NSGA-III) that emphasizes population members that are nondominated, yet close to a set of supplied reference points. The proposed NSGA-III is applied to a number of many-objective test problems with three to 15 objectives and compared with two versions of a recently suggested EMO algorithm (MOEA/D). While each of the two MOEA/D methods works well on different classes of problems, the proposed NSGA-III is found to produce satisfactory results on all problems considered in this paper. This paper presents results on unconstrained problems, and the sequel paper considers constrained and other specialties in handling many-objective optimization problems.

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An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based Nondominated Sorting Approach, Part I: Solving Problems With Box Constraints

Over the past several decades, a noticeable amount of research efforts has been directed to minimising injuries and death to people inside a structure that is subjected to an impact loading. Thin-walled (TW) tubular components have been widely employed in energy absorbing structures to alleviate the detrimental effects of an impact loading during a collision event and thus enhance the crashworthiness performance of a structure. Comprehensive knowledge of the material properties and the structural behaviour of various TW components under various loading conditions is essential for designing an effective energy absorbing system. In this paper, based on a broad survey of the literature, a comprehensive overview of the recent developments in the area of crashworthiness performance of TW tubes is given with a special focus on the topics that emerged in the last ten years such as crashworthiness optimisation design and energy absorbing responses of unconventional TW components including multi-cells tubes, functionally graded thickness tubes and functionally graded foam filled tubes. Due to the huge number of studies that analysed and assessed the energy absorption behaviour of various TW components, this paper presents only a review of the crashworthiness behaviour of the components that can be used in vehicles structures including hollow and foam-filled TW tubes under lateral, axial, oblique and bending loading.

https://myresearchspace.uws.ac.uk/ws/files/1765038/Paper_2.pdf

On the crashworthiness performance of thin-walled energy absorbers: Recent advances and future developments

Taking both convergence and diversity into consideration, this paper suggests a vector angle-based evolutionary algorithm for unconstrained (with box constraints only) many-objective optimization problems. In the proposed algorithm, the maximum-vector-angle-first principle is used in the environmental selection to guarantee the wideness and uniformity of the solution set. With the help of the worse-elimination principle, worse solutions in terms of the convergence (measured by the sum of normalized objectives) are allowed to be conditionally replaced by other individuals. Therefore, the selection pressure toward the Pareto-optimal front is strengthened. The proposed method is compared with other four state-of-the-art many-objective evolutionary algorithms on a number of unconstrained test problems with up to 15 objectives. The experimental results have shown the competitiveness and effectiveness of our proposed algorithm in keeping a good balance between convergence and diversity. Furthermore, it was shown by the results on two problems from practice (with irregular Pareto fronts) that our method significantly outperforms its competitors in terms of both the convergence and diversity of the obtained solution sets. Notably, the new algorithm has the following good properties: 1) it is free from a set of supplied reference points or weight vectors; 2) it has less algorithmic parameters; and 3) the time complexity of the algorithm is low. Given both good performance and nice properties, the suggested algorithm could be an alternative tool when handling optimization problems with more than three objectives.

A Vector Angle-Based Evolutionary Algorithm for Unconstrained Many-Objective Optimization

Optimization for structural crashworthiness and energy absorption has become an important topic of research attributable to its proven benefits to public safety and social economy. This paper provides a comprehensive review of the important studies on design optimization for structural crashworthiness and energy absorption. First, the design criteria used in crashworthiness and energy absorption are reviewed and the surrogate modeling to evaluate these criteria is discussed. Second, multiobjective optimization, optimization under uncertainties and topology optimization are reviewed from concepts, algorithms to applications in relation to crashworthiness. Third, the crashworthy structures are summarized, from generically novel structural configurations to industrial applications. Finally, some conclusions and recommendations are provided to enable academia and industry to become more aware of the available capabilities and recent developments in design optimization for structural crashworthiness and energy absorption.

On design optimization for structural crashworthiness and its state of the art

Crashing analysis and multiobjective optimization for thin-walled structures with functionally graded thickness

In automotive industry, structural optimization for crashworthiness criteria is of special importance. Due to the high nonlinearities, however, there exists substantial difficulty to obtain accurate continuum or discrete sensitivities. For this reason, metamodel or surrogate model methods have been extensively employed in vehicle design with industry interest. This paper presents a multiobjective optimization procedure for the vehicle design, where the weight, acceleration characteristics and toe-board intrusion are considered as the design objectives. The response surface method with linear and quadratic basis functions is employed to formulate these objectives, in which optimal Latin hypercube sampling and stepwise regression techniques are implemented. In this study, a nondominated sorting genetic algorithm is employed to search for Pareto solution to a full-scale vehicle design problem that undergoes both the full frontal and 40% offset-frontal crashes. The results demonstrate the capability and potential of this procedure in solving the crashworthiness design of vehicles.

Multiobjective optimization for crash safety design of vehicles using stepwise regression model

Structural optimization related to crashworthiness and impact energy absorption capability is of particular importance to the automotive industry, which involves highly nonlinear computational analysis and design with many material and structure parameters. Unfortunately, conventional design analysis techniques can only improve the structural crashworthiness to a limited extent, which frequently undergo significant difficulties to achieve a global optimized performance in a nonlinear analysis and design framework.

Xingtao Liao

Papers

Multiobjective optimization for crash safety design of vehicles using stepwise regression model

Optimization Studies for Crashworthiness Design using Response Surface Method