97 research outputs found
A Parameterised Complexity Analysis of Bi-level Optimisation with Evolutionary Algorithms
Bi-level optimisation problems have gained increasing interest in the field of combinatorial optimisation in recent years. In this paper, we analyse the runtime of some evolutionary algorithms for bi-level optimisation problems. We examine two NP-hard problems, the generalised minimum spanning tree problem and the generalised travelling salesperson problem in the context of parameterised complexity. For the generalised minimum spanning tree problem, we analyse the two approaches presented by Hu and Raidl (2012) with respect to the number of clusters that distinguish each other by the chosen representation of possible solutions. Our results show that a (1+1) evolutionary algorithm working with the spanning nodes representation is not a fixed-parameter evolutionary algorithm for the problem, whereas the problem can be solved in fixed-parameter time with the global structure representation. We present hard instances for each approach and show that the two approaches are highly complementary by proving that they solve each other’s hard instances very efficiently. For the generalised travelling salesperson problem, we analyse the problem with respect to the number of clusters in the problem instance. Our results show that a (1+1) evolutionary algorithm working with the global structure representation is a fixed-parameter evolutionary algorithm for the problem
Multiobjective optimization for interwoven systems
In practical situations, complex systems are often composed of subsystems or subproblems with single or multiple objectives. These subsystems focus on different aspects of the overall system, but they often have strong interactions with each other and they are usually not sequentially ordered or obviously decomposable. Thus, the individual solutions of subproblems do not generally induce a solution for the overall system. Here, we strive to identify "re-composition architectures" of such "interwoven" systems. Our intention is to connect the subsystems adequately, analyze the resulting performance, model/solve the overall system, and improve the overall solution instead of just solving each subsystem separately. We review recent developments in this field and discuss modeling and solution paradigms in a general and unified framework using the example of an interwoven system consisting of two interacting subsystems
An integrated assignment, routing, and speed model for roadway mobility and transportation with environmental, efficiency, and service goals
Managing all the mobility and transportation services with autonomous
vehicles for users of a smart city requires determining the assignment of the
vehicles to the users and their routing in conjunction with their speed. Such
decisions must ensure low emission, efficiency, and high service quality by
also considering the impact on traffic congestion caused by other vehicles in
the transportation network.
In this paper, we first propose an abstract trilevel multi-objective
formulation architecture to model all vehicle routing problems with assignment,
routing, and speed decision variables and conflicting objective functions. Such
an architecture guides the development of subproblems, relaxations, and
solution methods. We also propose a way of integrating the various urban
transportation services by introducing a constraint on the speed variables that
takes into account the traffic volume caused across the different services.
Based on the formulation architecture, we introduce a (bilevel) problem where
assignment and routing are at the upper level and speed is at the lower level.
To address the challenge of dealing with routing problems on urban road
networks, we develop an algorithm that alternates between the
assignment-routing problem on an auxiliary complete graph and the speed
optimization problem on the original non-complete graph. The computational
experiments show the effectiveness of the proposed approach in determining
approximate Pareto fronts among the conflicting objectives
Modeling and Solving a Multi-Period Inventory Fulfilling and Routing Problem for Hazardous Materials
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