Evolutionary Multiobjective Design in Automotive Development

This paper describes the use of evolutionary algorithms to solve multiobjective optimization problems arising at different stages in the automotive design process. The problems considered are black box optimization scenarios: definitions of the decision space and the design objectives are given, together with a procedure to evaluate any decision alternative with regard to the design objectives, e.g., a simulation model. However, no further information about the objective function is available. In order to provide a practical introduction to the use of multiobjective evolutionary algorithms, this article explores the three following case studies: design space exploration of road trains, parameter optimization of adaptive cruise controllers, and multiobjective system identification. In addition, selected research topics in evolutionary multiobjective optimization will be illustrated along with each case study, highlighting the practical relevance of the theoretical results through real-world application examples. The algorithms used in these studies were implemented based on the PISA (Platform and Programming Language Independent Interface for Search Algorithm) framework. Besides helping to structure the presentation of different algorithms in a coherent way, PISA also reduces the implementation effort considerabl

Shortest Path with Alternatives for Uniform Arrival Times: Algorithms and Experiments

The Shortest Path with Alternatives (SPA) policy differs from classical shortest path routing in the following way: instead of providing an exact list of means of transportation to follow, this policy gives such a list for each stop, and the traveler is supposed to pick the first option from this list when waiting at some stop. First, we show that an optimal policy of this type can be computed in polynomial time for uniform arrival times under reasonable assumptions. A similar result was so far only known for Poisson arrival times, which are less realistic for frequency-based public transportation systems. Second, we experimentally evaluate such policies. In this context, our main finding is that SPA policies are surprisingly competitive compared to traditional shortest paths, and moreover yield a significant reduction of waiting times, and therefore improvement of user experience, compared to similar greedy approaches. Specifically, for roughly 25% of considered cases, we could decrease the expected waiting time by at least 20%. To run our experiments, we also describe a tool-chain to derive the necessary information from the popular GTFS-format, therefore allowing the application of SPA policies to a wide range of public transportation systems

Computational complexity of impact size estimation forspreading processes on networks

Spreading processes on networks are often analyzed to understand how the outcome of the process (e.g. the number of affected nodes) depends on structural properties of the underlying network. Most available results are ensemble averages over certain interesting graph classes such as random graphs or graphs with a particular degree distributions. In this paper, we focus instead on determining the expected spreading size and the probability of large spreadings for a single (but arbitrary) given network and study the computational complexity of these problems using reductions from well-known network reliability problems. We show that computing both quantities exactly is intractable, but that the expected spreading size can be efficiently approximated with Monte Carlo sampling. When nodes are weighted to reflect their importance, the problem becomes as hard as the s-t reliability problem, which is not known to yield an efficient randomized approximation scheme up to now. Finally, we give a formal complexity-theoretic argument why there is most likely no randomized constant-factor approximation for the probability of large spreadings, even for the unweighted case. A hybrid Monte Carlo sampling algorithm is proposed that resorts to specialized s-t reliability algorithms for accurately estimating the infection probability of those nodes that are rarely affected by the spreading proces

An Adaptive Scheme to Generate the Pareto Front Based on the Epsilon-Constraint Method

We discuss methods for generating or approximating the Pareto set of multiobjective optimization problems by solving a sequence of constrained single-objective problems. The necessity of determining the constraint value a priori is shown to be a serious drawback of the original epsilon-constraint method. We therefore propose a new, adaptive scheme to generate appropriate constraint values during the run. A simple example problem is presented, where the running time (measured by the number of constrained single-objective sub-problems to be solved) of the original epsilon-constraint method is exponential in the problem size (number of decision variables), although the size of the Pareto set grows only linearly. We prove that --- independent of the problem or the problem size --- the time complexity of the new scheme is O(k^{m-1}), where k is the number of Pareto-optimal solutions to be found and m the number of objectives. Simulation results for the example problem as well as for different instances of the multiobjective knapsack problem demonstrate the behavior of the method, and links to reference implementations are provided

Multi-objective integer programming: An improved recursive algorithm

This paper introduces an improved recursive algorithm to generate the set of all nondominated objective vectors for the Multi-Objective Integer Programming (MOIP) problem. We significantly improve the earlier recursive algorithm of \"Ozlen and Azizo\u{g}lu by using the set of already solved subproblems and their solutions to avoid solving a large number of IPs. A numerical example is presented to explain the workings of the algorithm, and we conduct a series of computational experiments to show the savings that can be obtained. As our experiments show, the improvement becomes more significant as the problems grow larger in terms of the number of objectives.Comment: 11 pages, 6 tables; v2: added more details and a computational stud

Approximate solutions in space mission design

In this paper, we address multi-objective space mission design problems. From a practical point of view, it is often the case that,during the preliminary phase of the design of a space mission, the solutions that are actually considered are not 'optimal' (in the Pareto sense)but belong to the basin of attraction of optimal ones (i.e. they are nearly optimal). This choice is motivated either by additional requirements that the decision maker has to take into account or, more often, by robustness considerations. For this, we suggest a novel MOEA which is a modification of the well-known NSGA-II algorithm equipped with a recently proposed archiving strategy which aims at storing the set of approximate solutions of a given MOP. Using this algorithm we will examine some space trajectory design problems and demonstrate the benefit of the novel approach