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multiobjective discrete optimization algorithm based on Entropy-AHP weighted TOPSIS for pedestrian lower limb protection

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART D-JOURNAL OF AUTOMOBILE ENGINEERING 2025年

作者： Wang, Muyang Peng, Weiqiang Zhou, Dayong Yao, Ruyang Lv, Xiaojiang Harbin Univ Sci & Technol Sch Mech & Power Engn Harbin Heilongjiang Peoples R China Geely Automobile Res Inst Ningbo Co Ltd Zhejiang Key Lab Intelligent Vehicle Comprehens Sa Ningbo Zhejiang Peoples R China China Automot Technol & Res Ctr Co Ltd Tianjin Peoples R China Hunan Univ State Key Lab Adv Design & Mfg Vehicle Body Changsha Hunan Peoples R China

Globally, the tibia, femur, and knee joints of the lower limbs frequently sustain severe injuries in vehicle-to-vulnerable road user (VRU) accidents. The design of vehicle structures is crucial for absorbing impact energy and reducing VRU injuries. The advanced pedestrian legform impactor (APLI) offers more precise biomechanical performance for evaluating lower limb injuries compared to other legform impactors. Traditional structural optimization methods often overlook the discrete nature of vehicle structures and the complexity of biomechanical models, where injury responses are highly nonlinear. This study investigates a multiobjective discrete optimization (MODO) algorithm tailored for vehicle structures in APLI impacts. The proposed MODO algorithm integrates a multiple attribute decision making (MADM) model, using the TOPSIS method, with weight coefficients derived from Entropy and AHP methods. Iterative refinement through successive orthogonal experiments efficiently manages numerous design variables and levels. The results demonstrate that the MODO algorithm achieves optimal design by integrating seamlessly with the MADM model. Additionally, this algorithm shows significant potential for addressing other complex engineering challenges.

关键词： multiobjective discrete optimization vehicle structures pedestrian protection APLI TOPSIS Entropy-AHP weighting method MADM

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multiobjective discrete optimization using the TOPSIS and entropy method for protection of pedestrian lower extremity

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THIN-WALLED STRUCTURES 2020年 152卷 106349-106349页

作者： Lei, Fei Lv, Xiaojiang Fang, Jianguang Sun, Guangyong Li, Qing Hunan Univ State Key Lab Adv Design & Mfg Vehicle Body Changsha 410082 Hunan Peoples R China Geely Automobile Res Inst Zhejiang Key Lab Automobile Safety Technol Ningbo 315336 Zhejiang Peoples R China Univ Technol Sydney Sch Civil & Environm Engn Sydney NSW 2007 Australia Univ Sydney Sch Aerosp Mech & Mechatron Engn Sydney NSW 2006 Australia

Design of vehicle frontal structures signifies an important topic of studies on protection of pedestrian lower extremity. Conventional optimization has been largely focused on continuous variable problems without involving complexity of human model. Nevertheless, design of frontal structures is commonly discrete from a manufacturing perspective and the responses of the lower extremity of pedestrian are highly nonlinear in nature. For this reason, this study aimed to develop a multiobjective discrete optimization (MODO) algorithm for design of frontal structures involving a pedestrian model. In the proposed MODO method, the order preference by similarity to ideal solution (TOPSIS) was coupled with the entropy algorithm to develop a multiple attribute decision making (MADM) model for converting multiple conflicting objectives into a unified single cost function. The presented optimization procedure is iterated using the successive orthogonal experiment to deal with a large number of design variables and design levels. In this study, the proposed method was first verified by two benchmark examples;and then was applied to a more sophisticated real-life design case of vehicle frontal structure to better protect pedestrian lower extremity from impacting injury. The finite element model was validated via experimental tests first and the optimized design was then prototyped for the further physical tests. The results showed that the algorithm is able to achieve an optimal design in a fairly efficient manner. The proposed algorithm exhibits considerable potential to solve other complex engineering design problems.

关键词： multiobjective discrete optimization Vehicle frontal structures Pedestrian protection TOPSIS Entropy method Successive orthogonal experiment Injury mechanics Biomechanics

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Computing the nadir point for multiobjective discrete optimization problems

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JOURNAL OF GLOBAL optimization 2015年第1期62卷 79-99页

作者： Kirlik, Gokhan Sayin, Serpil Koc Univ Grad Sch Sci & Engn TR-34450 Istanbul Turkey Koc Univ Coll Adm Sci & Econ TR-34450 Istanbul Turkey

We investigate the problem of finding the nadir point for multiobjective discrete optimization problems (MODO). The nadir point is constructed from the worst objective values over the efficient set of a multiobjective optimization problem. We present a new algorithm to compute nadir values for MODO with objective functions. The proposed algorithm is based on an exhaustive search of the -dimensional space for each component of the nadir point. We compare our algorithm with two earlier studies from the literature. We give numerical results for all algorithms on multiobjective knapsack, assignment and integer linear programming problems. Our algorithm is able to obtain the nadir point for relatively large problem instances with up to five-objectives.

关键词： Nadir point multiobjective optimization multiobjective discrete optimization

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A multiobjective discrete combination optimization method for dynamics design of engineering structures

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International Journal of Mechanical System Dynamics 2022年第1期2卷 108-116页

作者： Wenjie Ding Yanchen Ji Haitao Liao Daining Fang Institute of Advanced Structure Technology Beijing Institute of TechnologyBeijingChina

This paper presents a new multiobjective discrete optimization method for the engineering design of dynamic problems.A discrete combinatorial optimization problem is solved using a particle swarm optimization algorithm coupled with a stair‐form interpolation *** address multiobjective optimization issues,a weighted average approach is implemented to convert the multiobjective optimization problem into an equivalent single‐objective optimization *** con-straints are taken into consideration by using the penalty function *** proposed method is first verified with a 10‐bar truss structure design problem,where the cross‐sectional area of each bar is optimized to minimize both volume and node ***,the dynamic issue for hybrid composite laminates is investigated by maximizing the fundamental frequency and minimizing the *** results reveal that the optimized results generated by the proposed method agree well with those from other approaches.

关键词： multiobjective discrete optimization stair‐form interpolation model particle swarm optimization dynamic issue

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Representation of the non-dominated set in biobjective discrete optimization

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COMPUTERS & OPERATIONS RESEARCH 2015年第Nov.期63卷 172-186页

作者： Vaz, Daniel Paquete, Luis Fonseca, Carlos M. Klamroth, Kathrin Stiglmayr, Michael Max Planck Inst Informat D-66123 Saarbrucken Germany Univ Coimbra Dept Informat Engn CISUC P-3000 Coimbra Portugal Univ Wuppertal Dept Math & Nat Sci Wuppertal Germany

This paper introduces several algorithms for finding a representative subset of the non-dominated point set of a biobjective discrete optimization problem with respect to uniformity, coverage and the epsilon-indicator. We consider the representation problem itself as multiobjective, trying to find a good compromise between these quality measures. These representation problems are formulated as particular facility location problems with a special location structure, which allows for polynomial-time algorithms in the biobjective case based on the principles of dynamic programming and threshold approaches. In addition, we show that several multiobjective variants of these representation problems are also solvable in polynomial time. Computational results obtained by these approaches on a wide range of randomly generated point sets are presented and discussed. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： multiobjective discrete optimization Representation Dynamic programming Threshold algorithm

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Bound sets for biobjective combinatorial optimization problems

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COMPUTERS & OPERATIONS RESEARCH 2007年第9期34卷 2674-2694页

作者： Ehrgott, Matthias Gandibleux, Xavier Univ Auckland Dept Engn Sci Auckland New Zealand Univ Nantes LINA FRE 2729 CNRS F-44322 Nantes 03 France

In this paper we introduce the concept of bound sets for multiobjective discrete optimization. We prove general results on lower and upper bound sets for combinatorial optimization problems with multiple objectives. We present general algorithms for constructing lower and upper bound sets for biobjective problems and provide numerical results on five different problem types. (c) 2005 Elsevier Ltd. All rights reserved.

关键词： multiobjective discrete optimization lower bound upper bound heuristics relaxation

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A parallel MOEA with criterion-based selection applied to the Knapsack Problem

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APPLIED SOFT COMPUTING 2019年 80卷 358-373页

作者： Kantour, Nedjmeddine Bouroubi, Sadek Chaabane, Djamel USTHB LIFORCE Lab Fac Math Dept Operat Res PB 32 El Alia Algiers 16111 Algeria USTHB AMCD RO Lab Fac Math Dept Operat Res PB 32 El Alia Algiers 16111 Algeria

In this paper, we propose a parallel multiobjective evolutionary algorithm called Parallel Criterion-based Partitioning MOEA (PCPMOEA), with an application to the multiobjective Knapsack Problem (MOKP). The suggested search strategy is based on a periodic partitioning of potentially efficient solutions, which are distributed to multiple multiobjective evolutionary algorithms (MOEAs). Each MOEA is dedicated to a sole objective, in which it combines both criterion-based and dominance-based approaches. The suggested algorithm addresses two main sub-objectives: minimizing the distance between the current non-dominated solutions and the ideal point, and ensuring the spread of the potentially efficient solutions. Experimental results are included, where we assess the performance of the suggested algorithm against the above mentioned sub-objectives, compared with state-of-the-art results using well-known multi-objective metaheuristics. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Parallel evolutionary algorithms multiobjective discrete optimization multiobjective Knapsack Problem

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Split algorithms for multiobjective integer programming problems

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COMPUTERS & OPERATIONS RESEARCH 2022年 140卷 1页

作者： Karsu, Ozlem Ulus, Firdevs Bilkent Univ Dept Ind Engn TR-06800 Ankara Turkey

We consider split algorithms that partition the objective function space into - 1 dimensional regions so as to search for nondominated points of multiobjective integer programming problems, where is the number of objectives. We provide a unified approach that allows different split strategies to be used within the same algorithmic framework with minimum change. We also suggest an effective way of making use of the information on subregions when setting the parameters of the scalarization problems used in the -split structure. We compare the performances of variants of these algorithms both as exact algorithms and as solution approaches under time restriction, considering the fact that finding the whole set may be computationally infeasible or undesirable in practice. We demonstrate through computational experiments that while the (-1)-split structure is superior in terms of overall computational time, the-split structure provides significant advantage under time/cardinality limited settings in terms of representativeness, especially with adaptive parameter setting and/or a suitably chosen order for regions to be explored.

关键词： multiobjective discrete optimization multiobjective integer programming Pascoletti-Serafini scalarization Weighted sum scalarization Epsilon constraint scalarization

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Computing representations using hypervolume scalarizations

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COMPUTERS & OPERATIONS RESEARCH 2022年 137卷 105349-105349页

作者： Paquete, Luis Schulze, Britta Stiglmayr, Michael Lourenco, Ana C. Univ Coimbra CISUC Dept Informat Engn Coimbra Portugal Univ Wuppertal Sch Math & Nat Sci Wuppertal Germany

In this article, we use the hypervolume indicator as a scalarizing function for biobjective combinatorial optimization problems. In particular, we describe a generic solution approach that determines the nondominated set of a biobjective optimization problem by solving a sequence of hypervolume scalarizations with appropriate choices of the reference point. Moreover, this solution technique can also provide a compact representation of the efficient set that is a (1-1/e)-approximation to the optimal representation in terms of the hypervolume in an a priori manner. We illustrate these concepts for a particular variant of the biobjective knapsack problem and for a biobjective shortest path problem. Numerical results are presented for the former problem.

关键词： Hypervolume scalarization Representation multiobjective discrete optimization Greedy approximation

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A Multi-criteria discrete optimization Method for Design and Control of Large-scale Systems

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IFAC Proceedings Volumes 1989年第10期22卷 295-300页

作者： D.V. Ofitserov V.G. Tanaevsky Department of Control Automation Minsk Radioengineering Institute Minsk USSR

A new method for solving multi-criteria discrete optimization (MDO) problems is discussed to be used in design and control of large-scale systems. The general MDO problem statement is presented, and brief analysis of the methods employed for its solution is performed. A conceptual scheme of the method developed and its implementation in the form of MDO algorithm is discussed. The results of numerical experiment and possible application areas of the proposed method are given.

关键词： Large-scale systems multiobjective discrete optimization decision theory fuzzy set theory man-machine system

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