261 research outputs found
Parameterized Complexity Analysis of Randomized Search Heuristics
This chapter compiles a number of results that apply the theory of
parameterized algorithmics to the running-time analysis of randomized search
heuristics such as evolutionary algorithms. The parameterized approach
articulates the running time of algorithms solving combinatorial problems in
finer detail than traditional approaches from classical complexity theory. We
outline the main results and proof techniques for a collection of randomized
search heuristics tasked to solve NP-hard combinatorial optimization problems
such as finding a minimum vertex cover in a graph, finding a maximum leaf
spanning tree in a graph, and the traveling salesperson problem.Comment: This is a preliminary version of a chapter in the book "Theory of
Evolutionary Computation: Recent Developments in Discrete Optimization",
edited by Benjamin Doerr and Frank Neumann, published by Springe
A Parameterized 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. With this paper, we start the
runtime analysis of evolutionary algorithms for bi-level optimisation problems.
We examine two NP-hard problems, the generalised minimum spanning tree problem
(GMST), and the generalised travelling salesman problem (GTSP) 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) EA working with the spanning nodes
representation is not a fixed-parameter evolutionary algorithm for the problem,
whereas the global structure representation enables to solve the problem in
fixed-parameter time. 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 salesman problem, we analyse the problem with
respect to the number of clusters in the problem instance. Our results show
that a (1+1) EA working with the global structure representation is a
fixed-parameter evolutionary algorithm for the problem
Evolving Diverse Sets of Tours for the Travelling Salesperson Problem
Evolving diverse sets of high quality solutions has gained increasing
interest in the evolutionary computation literature in recent years. With this
paper, we contribute to this area of research by examining evolutionary
diversity optimisation approaches for the classical Traveling Salesperson
Problem (TSP). We study the impact of using different diversity measures for a
given set of tours and the ability of evolutionary algorithms to obtain a
diverse set of high quality solutions when adopting these measures. Our studies
show that a large variety of diverse high quality tours can be achieved by
using our approaches. Furthermore, we compare our approaches in terms of
theoretical properties and the final set of tours obtained by the evolutionary
diversity optimisation algorithm.Comment: 11 pages, 3 tables, 3 figures, to be published in GECCO '2
Expected Fitness Gains of Randomized Search Heuristics for the Traveling Salesperson Problem.
Randomized search heuristics are frequently applied to NP-hard combinatorial optimization problems. The runtime analysis of randomized search heuristics has contributed tremendously to their theoretical understanding. Recently, randomized search heuristics have been examined regarding their achievable progress within a fixed time budget. We follow this approach and present a fixed budget analysis for an NP-hard combinatorial optimization problem. We consider the well-known Traveling Salesperson problem (TSP) and analyze the fitness increase that randomized search heuristics are able to achieve within a given fixed time budget. In particular, we analyze Manhattan and Euclidean TSP instances and Randomized Local Search (RLS), (1 + 1) EA and (1 + λ) EA algorithms for the TSP in a smoothed complexity setting and derive the lower bounds of the expected fitness gain for a specified number of generations
On the Impact of Operators and Populations within Evolutionary Algorithms for the Dynamic Weighted Traveling Salesperson Problem
Evolutionary algorithms have been shown to obtain good solutions for complex
optimization problems in static and dynamic environments. It is important to
understand the behaviour of evolutionary algorithms for complex optimization
problems that also involve dynamic and/or stochastic components in a systematic
way in order to further increase their applicability to real-world problems. We
investigate the node weighted traveling salesperson problem (W-TSP), which
provides an abstraction of a wide range of weighted TSP problems, in dynamic
settings. In the dynamic setting of the problem, items that have to be
collected as part of a TSP tour change over time. We first present a dynamic
setup for the dynamic W-TSP parameterized by different types of changes that
are applied to the set of items to be collected when traversing the tour. Our
first experimental investigations study the impact of such changes on resulting
optimized tours in order to provide structural insights of optimization
solutions. Afterwards, we investigate simple mutation-based evolutionary
algorithms and study the impact of the mutation operators and the use of
populations with dealing with the dynamic changes to the node weights of the
problem
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