Bilevel multiobjective packaging optimization for automotive design

Dandurand, Brian; Guarneri, Paolo; Fadel, Georges; Wiecek, Margaret M.

doi:10.1007/s00158-014-1120-0

Cited by 19 publications

(7 citation statements)

References 35 publications

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“…Guo and Xu [21] developed a BMPP model to study the seismic risk of transportation system reconstruction in large construction projects, and fuzzy random variable transformation and fuzzy variable decomposition methods were proposed to solve the model. Brian et al [22] proposed a BMPP model for coordinating multiple design problems according to conflicting criteria. The design of a hybrid vehicle layout was expressed as a twostage decomposition problem including vehicle class and battery class, and a multiobjective decomposition algorithm was developed.…”

Section: Related Workmentioning

confidence: 99%

Evolutionary algorithm using surrogate models for solving bilevel multiobjective programming problems

Liu

2020

PLoS ONE

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A bilevel programming problem with multiple objectives at the leader’s and/or follower’s levels, known as a bilevel multiobjective programming problem (BMPP), is extraordinarily hard as this problem accumulates the computational complexity of both hierarchical structures and multiobjective optimisation. As a strongly NP-hard problem, the BMPP incurs a significant computational cost in obtaining non-dominated solutions at both levels, and few studies have addressed this issue. In this study, an evolutionary algorithm is developed using surrogate optimisation models to solve such problems. First, a dynamic weighted sum method is adopted to address the follower’s multiple objective cases, in which the follower’s problem is categorised into several single-objective ones. Next, for each the leader’s variable values, the optimal solutions to the transformed follower’s programs can be approximated by adaptively improved surrogate models instead of solving the follower’s problems. Finally, these techniques are embedded in MOEA/D, by which the leader’s non-dominated solutions can be obtained. In addition, a heuristic crossover operator is designed using gradient information in the evolutionary procedure. The proposed algorithm is executed on some computational examples including linear and nonlinear cases, and the simulation results demonstrate the efficiency of the approach.

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Section: Related Workmentioning

confidence: 99%

Evolutionary algorithm using surrogate models for solving bilevel multiobjective programming problems

Liu

2020

PLoS ONE

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“…So-called semivectorial bilevel optimization problems, where only p := 1 and K := R + are demanded in (BPP), i.e., only the underlying parametric optimization problem (P(x)) possesses multiple objective functions, provide a much more general model paradigm and have been investigated, e.g., in [8,10,17,19,39,57]. The even more general situation where the objective functions of both decision makers in (BPP) are allowed to be vector-valued has been considered, e.g., in [11,24,25,27,37,50]. For formal completeness, let us also mention that the setting where q := 1 and C := R + hold while the objective function of (BPP) is vector-valued is also reasonable, see e.g.…”

Section: Introductionmentioning

confidence: 99%

Notes on the value function approach to multiobjective bilevel optimization

Hoff¹,

Mehlitz²

2023

Preprint

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This paper is concerned with the value function approach to multiobjective bilevel optimization which exploits a lower level frontier-type mapping in order to replace the hierarchical model of two interdependent multiobjective optimization problems by a single-level multiobjective optimization problem. As a starting point, different value-function-type reformulations are suggested and their relations are discussed. Here, we focus on the situations where the lower level problem is solved up to efficiency or weak efficiency, and an intermediate solution concept is suggested as well. We study the graph-closedness of the associated efficiency-type and frontier-type mappings. These findings are then used for two purposes. First, we investigate existence results in multiobjective bilevel optimization. Second, for the derivation of necessary optimality conditions via the value function approach, it is inherent to differentiate frontier-type mappings in a generalized way. Here, we are concerned with the computation of upper coderivative estimates for the frontier-type mapping associated with the setting where the lower level problem is solved up to weak efficiency. We proceed in two ways, relying, on the one hand, on a weak domination property and, on the other hand, on a scalarization approach. Throughout the paper, illustrative examples visualize our findings, the necessity of crucial assumptions, and some flaws in the related literature.

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“…Decomposable MOPs are frequently employed to model certain engineering design problems whose complexity necessitates a specialization along distinct disciplines [39,44,34]. For example, a bilevel automotive design problem [14,15] is presented as a collection of subproblems including a vehicle-level subproblem and component-level subproblems. The subproblems correspond to disparate design-team organizational structures and require disparate solution methodologies and software interfaces, and so a distributed solution approach based on the specified subproblem decomposition is necessary.…”

Section: Introductionmentioning

confidence: 99%

Distributed Computation of Pareto Sets

Dandurand¹,

Wiecek²

2015

SIAM J. Optim.

Self Cite

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The needs of multidisciplinary engineering design have motivated the development of distributed solution approaches to computing efficient solutions to decomposable multiobjective optimization problems (MOPs). The decomposition is necessary due to the assumption that the overall MOP is not solvable since access to its solution space is subproblem-restricted. The state-of-the-art analyses for distributed solution approaches such as the alternating direction method of multipliers (ADMM) and the block coordinate descent (BCD) method were developed in the context of problem decomposition originating in a single objective setting and are not immediately applicable to MOPs. Applying certain scalarization techniques well-suited for nonconvex MOPs, the decomposable MOP is reformulated into a single objective problem (SOP) but the decomposability is not preserved and the SOP is not suitable for the application of ADMM. Furthermore, coupling between the subproblems makes BCD in its current form likewise inadequate. To address these challenges to distributed multiobjective optimization, existing theory is extended for (1) iterative augmented Lagrangian coordination techniques and (2) the block coordinate descent method. For the former, each augmented Lagrangian subproblem is subject to convex constraints and is solved approximately for solutions satisfying a necessary condition for optimality (but not necessarily optimal). For the latter, existing convergence proofs under generalized convexity assumptions are redeveloped so that new insights and convergence results become evident. An integration of the above two convergence analyses yields convergence results for a distributed solution approach that addresses coupling between subproblems and does not require convergence of the generated sequence of solution-multiplier pairs. Based on this study, a multi-objective decomposition algorithm is developed for the distributed generation of efficient solutions to nonconvex decomposable MOPs.

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Bilevel multiobjective packaging optimization for automotive design

Cited by 19 publications

References 35 publications

Evolutionary algorithm using surrogate models for solving bilevel multiobjective programming problems

Evolutionary algorithm using surrogate models for solving bilevel multiobjective programming problems

Notes on the value function approach to multiobjective bilevel optimization

Distributed Computation of Pareto Sets

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