A method to learn high-performing and novel product layouts and its application to vehicle design
Introduction
A central question in the field of Design Engineering is how to build optimal product design layouts. Tackling this question implies not only understanding, but also developing the effective search heuristics and knowledge representations that lead to relevant designing. Thus, developing such heuristics implies the realization of concrete procedures that map key features from the space of needs and functions to product configuration. How to build such heuristics?
Often, developing effective algorithms for product design have focused on building articulated rules that link preferential and functional requirements to concrete product parameters [2], [3], [4], [10], [12], [13]. Also, a natural answer to the above question comes from practical fields: artisans use (1) metaphoring, which is the process of mimicking the functions and features of pre-existing referential entities, and (2) tooling, which is the process of building systems by using modularity principles to enable scalability and hierarchical entities. Both metaphoring and tooling principles rely on search heuristics to find the relevant set of articulated rules that map the space of needs and functions to the key systems having specific parametric representations. Here, search heuristics are either performed artificially by using optimization algorithms or performed naturally by the artisan him(her)self.
However, considering matters of practical use and effective sampling of the design search space, it is cumbersome to perform the above effectively and efficiently. The main reason is that in certain design applications either (1) real-world experiments are expensive and dangerous, or (2) simulations are inaccurate to model and represent the real-world invariants reasonably well. Examples of this scenario include the design of the most complex existing systems in the world including vehicles, airplanes, large-space spacecrafts, and robots for critical environments.
In order to tackle the above limitations in the current approaches for product designs, in this paper we introduce a simple and complementary approach for tasks involving the optimal configuration of parametric product design layouts. Basically, we tackle the problem of how to learn the optimal mappings from functional and user requirements to concrete product definitions by using historical performance data and a newly applied novelty metric; so that the whole task of designing a product entity optimizes a set of user-defined and pre-stated goals in performance and uniqueness.
Generally speaking, inspired by the work of artisans whom usually build a relevant rule set by interaction, iteration, analysis and synthesis, it is natural to develop algorithms for product design that enable some form of metaphoring [2] and tooling [1]. These algorithms replicate, in a digital and conceptual sense, not only the process of mimicking the functions and features of pre-existing referents, but also the process of building modularity to scale toward sophisticated hierarchical, ontological entities.
However, the above artisan-inspired approaches to product design layout are resource-consuming: either time-consuming iterations in the realization of the product design are needed, or costly real-world experimentations become essential. Representative examples of research in this direction include achievements in the last decade to design new chemical reactors for failing batteries [6], and novel inhibitors for a new type of influenza [7].
Then, improving the efficiency in resource usage during the task of designing product layouts becomes essential. In that sense, one would like to use and learn the most optimal mappings from functional and user requirements to concrete product design definitions efficiently. Then, the optimal mapping aids the holistic task of designing to optimize a set of pre-stated goals. An example of research in this direction include the work of Wang et al. whom use evolutionary computation for product design and manufacturing [5]; and the work of Akai et al. whom use Simulated Annealing for the dynamic deployment of a product family under commonalization-oriented modularity and a discrete choice-based market model [28].
It is straightforward to use optimization heuristics to realize the optimal mappings between functional and user requirements to concrete design definitions. However, as described before, the direct use of such techniques requires using either real-world experimental tests or simulation experiments to evaluate a set of pre-defined metrics of performance. And, in the field of Design Engineering, approaches involving experiments followed by simulations have been used widely in a plethora of applications. Some examples include the use of Simulated Annealing to find optimal composition of parameters in chemical compounds through reactions modeled in directed graphs [6]. Also, Dynamic Programming and Gradient-based algorithms were used to optimize inhibitors against H1N1 influenza [7]. Evolutionary Algorithms were used to optimize not only the product design but also the manufacturing process [8]. Genetic Algorithms were used to learn the relationships between firm and market factors to enable rapid product design and development [9]. Furthermore, Fuzzy Logic helped modeling rules to facilitate the product screening to decide new product configurations [10], [11]. Data Envelopment Analysis was used to evaluate multiple factors during the evolutionary-based generation of ideas [3]. Clustering methods were used to build modular mechatronic systems [12]. Reinforcement Learning was used to map the function requirements to means realizations in a vehicle design problem [13].
In order to tackle the above problems, we propose a simple approach to search for optimal product designs under scenarios having restrictive simulations and experimentations. Basically, we use historical data in order to approximate a representative surrogate function that not only models, but also explains the performance of observed past design variables reasonably. Then, by using the learned surrogate performance function, along with a proposed novelty function, we optimize the product design layouts. The main goal and advantage of our approach is not only to map the representative approximations of the off-line learning (which is based on historical data) to the global refinements in parametric optimization (both in continuous space), so that the overall search heuristic focuses on sampling over the most meaningful (novel and high-performing) areas of the product layout search space. Our proposed approach aims at contributing towards the holistic design of product systems.
In line of the above, neither real-world experiments nor simulation tests consider novelty metrics in a meaningful way, such as the work of Grignon and Fadel [14]. Basically, novelty is an important factor in design because it enables the meaningful, the complete and the uniform sampling of the design search space; where novelty is defined as the maximum dissimilarity of the sampled product design compared to the convex hull of observed (historical) clusters.
Computational experiments using historical data of more than twenty thousand vehicles and rigorous computational experiments using Genetic Programming and eight representative gradient-free optimization algorithms, described subsequently, show that our proposed scheme works well: (1) a competitive performance function is generated within 10 h, (2) the breadth of Genetic Programming models is a key parameter to learn vehicle performance functions, and (3) it is possible to obtain unique and high-performing vehicle layouts when the search space is both constrained and unconstrained by history.
The main contributions in this paper are summarized as follows:
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We provide a simple and effective approach for optimizing the product design layout using a performance function, learned from historical data, and newly proposed novelty metric.
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Time for generating vehicle design layouts is feasible experimentally, and the possibility for generating unique and high-performing vehicle layouts are confirmed by rigorous and extensive computational experiments involving more than twenty thousand vehicle layouts and representative gradient-free algorithms in the literature.
The basic ideas and building blocks developed in this paper were firstly introduced at ICONIP 15’ [26]. In this paper, we further develop our proposed approach in the following points:
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Inclusion of constraints to consider technical constraints in sheet thickness, vehicle lengths, movable free-space inside the vehicle and feasible bounds on vehicle mileage performance.
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Rigorous sensitivity analysis on a number of relevant Genetic Programming parameters when learning vehicle performance functions, that is a rigorous study on the convergence time and the quality of the learned functions with regard to the number of multi-trees, population size, and tree depth.
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Rigorous study of the vehicle layout problem, under tight and relaxed box-bounding constraints, by using significant gradient-free optimization algorithms that consider multimodality, parameter adaptation, search memory, selection pressure, probability distribution, neighborhood concepts, search space partitioning and adaptive meshing.
The rest of this paper is organized as follows. Section 2 describes the problem. Section 3 shows a case study using real world data for a vehicle design layout problem and Section 4 concludes the paper.
Section snippets
Main problem
In this paper, we formulate the problem of product design layout as follows: where x is the product design variable, X is the box-bounding restriction on the variables, N(x) is the novelty function of the design variable x, and f(x) is the performance of the design variable x ∈ Rn. Then, we aim at tackling the above problem, for which the coming sub-sections describe both how to compute the novelty factor N(x) and the performance factor f(x).
Summary
Fig. 1 introduces the main steps
Computational experiments
In this section we describe the computational experiments performed to evaluate the effectiveness and usefulness of our method.
Conclusion
In this paper we propose a new approach to search for unique and high-performing vehicle design layouts given observations of historical data. The basic idea in our proposal is to first learn a surrogate vehicle performance function that approximates the real-world features from past historical data, and then optimize the learned function, along with a newly propose novelty metric, to enable high-performance and uniqueness. The proposed novelty function is defined as the dissimilarity degree
Acknowledgment
We acknowledge the support from Kakenhi No. 15K18095 to fund this work.
Victor Parque is Assistant Professor at the Department of Modern Mechanical Engineering, Waseda University, as well as Associate Professor at Egypt–Japan University of Science and Technology. After joining Engineering Complex in 2003, he obtained the MBA degree from Esan University in 2009, and obtained the doctoral degree from Waseda University in 2011. He was a PostDoctoral Fellow at Toyota Technological Institute from 2012 to 2014. His research interests include Learning and Intelligent
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Victor Parque is Assistant Professor at the Department of Modern Mechanical Engineering, Waseda University, as well as Associate Professor at Egypt–Japan University of Science and Technology. After joining Engineering Complex in 2003, he obtained the MBA degree from Esan University in 2009, and obtained the doctoral degree from Waseda University in 2011. He was a PostDoctoral Fellow at Toyota Technological Institute from 2012 to 2014. His research interests include Learning and Intelligent Systems and its applications to Design Engineering and Control.
Tomoyuki Miyashita is Professor at the Department of Modern Mechanical Engineering, Waseda University. After joining Nippon Steel Co. Ltd. in 1992, He obtained the doctoral degree from Waseda University in 2000. He was Research Associate at Waseda University and Ibaraki University since 2000 and 2002, respectively. He became Associate Professor and Professor at Waseda University in 2005 and 2007, respectively. His research interests are Design Process, Design Optimization, Organ Deformation.