Rigorous Performance Analysis of State-of-the-Art TSP Heuristic Solvers

Understanding why some problems are better solved by one algorithm rather than another is still an open problem, and the symmetric Travelling Salesperson Problem (TSP) is no exception. We apply three state-of-the-art heuristic solvers to a large set of TSP instances of varying structure and size, identifying which heuristics solve specific instances to optimality faster than others. The first two solvers considered are variants of the multi-trial Helsgaun's Lin-Kernighan Heuristic (a form of iterated local search), with each utilising a different form of Partition Crossover; the third solver is a genetic algorithm (GA) using Edge Assembly Crossover. Our results show that the GA with Edge Assembly Crossover is the best solver, shown to significantly outperform the other algorithms in 73% of the instances analysed. A comprehensive set of features for all instances is also extracted, and decision trees are used to identify main features which could best inform algorithm selection. The most prominent features identified a high proportion of instances where the GA with Edge Assembly Crossover performed significantly better when solving to optimality

Metaheuristics “In the Large”

Many people have generously given their time to the various activities of the MitL initiative. Particular gratitude is due to Adam Barwell, John A. Clark, Patrick De Causmaecker, Emma Hart, Zoltan A. Kocsis, Ben Kovitz, Krzysztof Krawiec, John McCall, Nelishia Pillay, Kevin Sim, Jim Smith, Thomas Stutzle, Eric Taillard and Stefan Wagner. J. Swan acknowledges the support of UK EPSRC grant EP/J017515/1 and the EU H2020 SAFIRE Factories project. P. GarciaSanchez and J. J. Merelo acknowledges the support of TIN201785727-C4-2-P by the Spanish Ministry of Economy and Competitiveness. M. Wagner acknowledges the support of the Australian Research Council grants DE160100850 and DP200102364.Following decades of sustained improvement, metaheuristics are one of the great success stories of opti- mization research. However, in order for research in metaheuristics to avoid fragmentation and a lack of reproducibility, there is a pressing need for stronger scientific and computational infrastructure to sup- port the development, analysis and comparison of new approaches. To this end, we present the vision and progress of the Metaheuristics “In the Large”project. The conceptual underpinnings of the project are: truly extensible algorithm templates that support reuse without modification, white box problem descriptions that provide generic support for the injection of domain specific knowledge, and remotely accessible frameworks, components and problems that will enhance reproducibility and accelerate the field’s progress. We argue that, via such principled choice of infrastructure support, the field can pur- sue a higher level of scientific enquiry. We describe our vision and report on progress, showing how the adoption of common protocols for all metaheuristics can help liberate the potential of the field, easing the exploration of the design space of metaheuristics.UK Research & Innovation (UKRI)Engineering & Physical Sciences Research Council (EPSRC) EP/J017515/1EU H2020 SAFIRE Factories projectSpanish Ministry of Economy and Competitiveness TIN201785727-C4-2-PAustralian Research Council DE160100850 DP20010236

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

Evolving comprehensible and scalable solvers using CGP for solving some real-world inspired problems

My original contribution to knowledge is the application of Cartesian Genetic Programming to design some scalable and human-understandable metaheuristics automatically; those find some suitable solutions for real-world NP-hard and discrete problems. This technique is thought to possess the ability to raise the generality of a problem-solving process, allowing some supervised machine learning tasks and being able to evolve non-deterministic algorithms. \\ Two extensions of Cartesian Genetic Programming are presented. Iterative My original contribution to knowledge is the application of Cartesian Genetic Programming to design some scalable and human-understandable metaheuristics automatically; those find some suitable solutions for real-world NP-hard and discrete problems. This technique is thought to possess the ability to raise the generality of a problem-solving process, allowing some supervised machine learning tasks and being able to evolve non-deterministic algorithms. \\ Two extensions of Cartesian Genetic Programming are presented. Iterative Cartesian Genetic Programming can encode loops and nested loop with their termination criteria, making susceptible to evolutionary modification the whole programming construct. This newly developed extension and its application to metaheuristics are demonstrated to discover effective solvers for NP-hard and discrete problems. This thesis also extends Cartesian Genetic Programming and Iterative Cartesian Genetic Programming to adapt a hyper-heuristic reproductive operator at the same time of exploring the automatic design space. It is demonstrated the exploration of an automated design space can be improved when specific types of active and non-active genes are mutated. \\ A series of rigorous empirical investigations demonstrate that lowering the comprehension barrier of automatically designed algorithms can help communicating and identifying an effective and ineffective pattern of primitives. The complete evolution of loops and nested loops without imposing a hard limit on the number of recursive calls is shown to broaden the automatic design space. Finally, it is argued the capability of a learning objective function to assess the scalable potential of a generated algorithm can be beneficial to a generative hyper-heuristic