Knowledge creation and visualisation by using trade-off curves to enable set-based concurrent engineering

The increased international competition forces companies to sustain and improve market share through the production of a high quality product in a cost effective manner and in a shorter time. Set‑based concurrent engineering (SBCE), which is a core element of lean product development approach, has got the potential to decrease time‑to‑market as well as enhance product innovation to be produced in good quality and cost effective manner. A knowledge‑based environment is one of the important requ irements for a successful SBCE implementation. One way to provide this environment is the use of trade‑off curves (ToC). ToC is a tool to create and visualise knowledge in the way to understand the relationships between various conflicting design parame ters to each other. This paper presents an overview of different types of ToCs and the role of knowledge‑based ToCs in SBCE by employing an extensive literature review and industrial field study. It then proposes a process of generating and using knowledg e‑based ToCs in order to create and visualise knowledge to enable the following key SBCE activities: (1) Identify the feasible design space, (2) Generate set of conceptual design solutions, (3) Compare design solutions, (4) Narrow down the design sets, (5) Achieve final optimal design solution. Finally a hypothetical example of a car seat structure is presented in order to provide a better understanding of using ToCs. This example shows that ToCs are effective tools to be used as a knowledge sou rce at the early stages of product development process

Seeding the Initial Population of Multi-Objective Evolutionary Algorithms: A Computational Study

Most experimental studies initialize the population of evolutionary algorithms with random genotypes. In practice, however, optimizers are typically seeded with good candidate solutions either previously known or created according to some problem-specific method. This "seeding" has been studied extensively for single-objective problems. For multi-objective problems, however, very little literature is available on the approaches to seeding and their individual benefits and disadvantages. In this article, we are trying to narrow this gap via a comprehensive computational study on common real-valued test functions. We investigate the effect of two seeding techniques for five algorithms on 48 optimization problems with 2, 3, 4, 6, and 8 objectives. We observe that some functions (e.g., DTLZ4 and the LZ family) benefit significantly from seeding, while others (e.g., WFG) profit less. The advantage of seeding also depends on the examined algorithm

Efficient Algorithms for k-Regret Minimizing Sets

A regret minimizing set Q is a small size representation of a much larger database P so that user queries executed on Q return answers whose scores are not much worse than those on the full dataset. In particular, a k-regret minimizing set has the property that the regret ratio between the score of the top-1 item in Q and the score of the top-k item in P is minimized, where the score of an item is the inner product of the item\u27s attributes with a user\u27s weight (preference) vector. The problem is challenging because we want to find a single representative set Q whose regret ratio is small with respect to all possible user weight vectors. We show that k-regret minimization is NP-Complete for all dimensions d>=3, settling an open problem from Chester et al. [VLDB 2014]. Our main algorithmic contributions are two approximation algorithms, both with provable guarantees, one based on coresets and another based on hitting sets. We perform extensive experimental evaluation of our algorithms, using both real-world and synthetic data, and compare their performance against the solution proposed in [VLDB 14]. The results show that our algorithms are significantly faster and scalable to much larger sets than the greedy algorithm of Chester et al. for comparable quality answers

One-Exact Approximate Pareto Sets

Papadimitriou and Yannakakis show that the polynomial-time solvability of a certain singleobjective problem determines the class of multiobjective optimization problems that admit a polynomial-time computable $(1+\varepsilon, \dots , 1+\varepsilon)$-approximate Pareto set (also called an $\varepsilon$-Pareto set). Similarly, in this article, we characterize the class of problems having a polynomial-time computable approximate $\varepsilon$-Pareto set that is exact in one objective by the efficient solvability of an appropriate singleobjective problem. This class includes important problems such as multiobjective shortest path and spanning tree, and the approximation guarantee we provide is, in general, best possible. Furthermore, for biobjective problems from this class, we provide an algorithm that computes a one-exact $\varepsilon$-Pareto set of cardinality at most twice the cardinality of a smallest such set and show that this factor of 2 is best possible. For three or more objective functions, however, we prove that no constant-factor approximation on the size of the set can be obtained efficiently

Efficiently Computing Succinct Trade-off Curves

Abstract. Trade-off (aka Pareto) curves are typically used to represent the trade-off among different objectives in multiobjective optimization problems. Although trade-off curves are exponentially large for typical combinatorial optimization problems (and infinite for continuous problems), it was observed in [PY1] that there exist polynomial size ɛ approximations for any ɛ> 0, and that under certain general conditions, such approximate ɛ-Pareto curves can be constructed in polynomial time. In this paper we seek general-purpose algorithms for the efficient approximation of trade-off curves using as few points as possible. In the case of two objectives, we present a general algorithm that efficiently computes an ɛ-Pareto curve that uses at most 3 times the number of points of the smallest such curve; we show that no algorithm can be better than 3-competitive in this setting. If we relax ɛ to any ɛ ′> ɛ, then we can efficeintly construct an ɛ ′-curve that uses no more points than the smallest ɛ-curve. With three objectives we show that no algorithm can be c-competitive for any constant c unless it is allowed to use a larger ɛ value. We present an algorithm that is 4-competitive for any ɛ ′> (1 + ɛ) 2 − 1. We explore the problem in high dimensions and give hardness proofs showing that (unless P=NP) no constant approximation factor can be achieved efficiently even if we relax ɛ by an arbitrary constant.