11,555 research outputs found
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
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
Fitness sharing and niching methods revisited
Interest in multimodal optimization function is expanding rapidly since real-world optimization problems often require the location of multiple optima in the search space. In this context, fitness sharing has been used widely to maintain population diversity and permit the investigation of many peaks in the feasible domain. This paper reviews various strategies of sharing and proposes new recombination schemes to improve its efficiency. Some empirical results are presented for high and a limited number of fitness function evaluations. Finally, the study
compares the sharing method with other niching techniques
On the Runtime of Randomized Local Search and Simple Evolutionary Algorithms for Dynamic Makespan Scheduling
Evolutionary algorithms have been frequently used for dynamic optimization
problems. With this paper, we contribute to the theoretical understanding of
this research area. We present the first computational complexity analysis of
evolutionary algorithms for a dynamic variant of a classical combinatorial
optimization problem, namely makespan scheduling. We study the model of a
strong adversary which is allowed to change one job at regular intervals.
Furthermore, we investigate the setting of random changes. Our results show
that randomized local search and a simple evolutionary algorithm are very
effective in dynamically tracking changes made to the problem instance.Comment: Conference version appears at IJCAI 201
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