11 research outputs found
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
Exploratory Landscape Analysis for Mixed-Variable Problems
Exploratory landscape analysis and fitness landscape analysis in general have been pivotal in facilitating problem understanding, algorithm design and endeavors such as automated algorithm selection and configuration. These techniques have largely been limited to search spaces of a single domain. In this work, we provide the means to compute exploratory landscape features for mixed-variable problems where the decision space is a mixture of continuous, binary, integer, and categorical variables. This is achieved by utilizing existing encoding techniques originating from machine learning. We provide a comprehensive juxtaposition of the results based on these different techniques. To further highlight their merit for practical applications, we design and conduct an automated algorithm selection study based on a hyperparameter optimization benchmark suite. We derive a meaningful compartmentalization of these benchmark problems by clustering based on the used landscape features. The identified clusters mimic the behavior the used algorithms exhibit. Meaning, the different clusters have different best performing algorithms. Finally, our trained algorithm selector is able to close the gap between the single best and the virtual best solver by 57.5% over all benchmark problems
sunny-as2: Enhancing SUNNY for Algorithm Selection
SUNNY is an Algorithm Selection (AS) technique originally tailored for
Constraint Programming (CP). SUNNY enables to schedule, from a portfolio of
solvers, a subset of solvers to be run on a given CP problem. This approach has
proved to be effective for CP problems, and its parallel version won many gold
medals in the Open category of the MiniZinc Challenge -- the yearly
international competition for CP solvers. In 2015, the ASlib benchmarks were
released for comparing AS systems coming from disparate fields (e.g., ASP, QBF,
and SAT) and SUNNY was extended to deal with generic AS problems. This led to
the development of sunny-as2, an algorithm selector based on SUNNY for ASlib
scenarios. A preliminary version of sunny-as2 was submitted to the Open
Algorithm Selection Challenge (OASC) in 2017, where it turned out to be the
best approach for the runtime minimization of decision problems. In this work,
we present the technical advancements of sunny-as2, including: (i)
wrapper-based feature selection; (ii) a training approach combining feature
selection and neighbourhood size configuration; (iii) the application of nested
cross-validation. We show how sunny-as2 performance varies depending on the
considered AS scenarios, and we discuss its strengths and weaknesses. Finally,
we also show how sunny-as2 improves on its preliminary version submitted to
OASC
Leveraging TSP solver complementarity through machine learning
The Travelling Salesperson Problem (TSP) is one of the best-studied NP-hard problems. Over the years, many different solution approaches and solvers have been developed. For the first time, we directly compare five state-of-the-art inexact solvers-namely, LKH, EAX, restart variants of those, and MAOS-on a large set of well-known benchmark instances and demonstrate complementary performance, in that different instances may be solved most effectively by different algorithms. We leverage this complementarity to build an algorithm selector, which selects the best TSP solver on a per-instance basis and thus achieves significantly improved performance compared to the single best solver, representing an advance in the state of the art in solving the Euclidean TSP. Our in-depth analysis of the selectors provides insight into what drives this performance improvement.Pascal Kerschke, Lars Kotthoff, Jakob Bossek, Holger H. Hoos, Heike Trautman