Edge Elimination in TSP Instances

The Traveling Salesman Problem is one of the best studied NP-hard problems in combinatorial optimization. Powerful methods have been developed over the last 60 years to find optimum solutions to large TSP instances. The largest TSP instance so far that has been solved optimally has 85,900 vertices. Its solution required more than 136 years of total CPU time using the branch-and-cut based Concorde TSP code [1]. In this paper we present graph theoretic results that allow to prove that some edges of a TSP instance cannot occur in any optimum TSP tour. Based on these results we propose a combinatorial algorithm to identify such edges. The runtime of the main part of our algorithm is $O(n^2 \log n)$ for an n-vertex TSP instance. By combining our approach with the Concorde TSP solver we are able to solve a large TSPLIB instance more than 11 times faster than Concorde alone

EARL: Joint Entity and Relation Linking for Question Answering over Knowledge Graphs

Many question answering systems over knowledge graphs rely on entity and relation linking components in order to connect the natural language input to the underlying knowledge graph. Traditionally, entity linking and relation linking have been performed either as dependent sequential tasks or as independent parallel tasks. In this paper, we propose a framework called EARL, which performs entity linking and relation linking as a joint task. EARL implements two different solution strategies for which we provide a comparative analysis in this paper: The first strategy is a formalisation of the joint entity and relation linking tasks as an instance of the Generalised Travelling Salesman Problem (GTSP). In order to be computationally feasible, we employ approximate GTSP solvers. The second strategy uses machine learning in order to exploit the connection density between nodes in the knowledge graph. It relies on three base features and re-ranking steps in order to predict entities and relations. We compare the strategies and evaluate them on a dataset with 5000 questions. Both strategies significantly outperform the current state-of-the-art approaches for entity and relation linking.Comment: International Semantic Web Conference 201

Tunnelling Crossover Networks for the Asymmetric TSP

Local optima networks are a compact representation of fitness landscapes that can be used for analysis and visualisation. This paper provides the first analysis of the Asymmetric Travelling Salesman Problem using local optima networks. These are generated by sampling the search space by recording the progress of an existing evolutionary algorithm based on the Generalised Asymmetric Partition Crossover. They are compared to networks sampled through the Chained Lin-Kernighan heuristic across 25 instances. Structural differences and similarities are identified, as well as examples where crossover smooths the landscape

Generating test case chains for reactive systems

Testing of reactive systems is challenging because long input sequences are often needed to drive them into a state to test a desired feature. This is particularly problematic in on-target testing, where a system is tested in its real-life application environment and the amount of time required for resetting is high. This article presents an approach to discovering a test case chain—a single software execution that covers a group of test goals and minimizes overall test execution time. Our technique targets the scenario in which test goals for the requirements are given as safety properties. We give conditions for the existence and minimality of a single test case chain and minimize the number of test case chains if a single test case chain is infeasible. We report experimental results with our ChainCover tool for C code generated from Simulink models and compare it to state-of-the-art test suite generators

Ownership and control in a competitive industry

We study a differentiated product market in which an investor initially owns a controlling stake in one of two competing firms and may acquire a non-controlling or a controlling stake in a competitor, either directly using her own assets, or indirectly via the controlled firm. While industry profits are maximized within a symmetric two product monopoly, the investor attains this only in exceptional cases. Instead, she sometimes acquires a noncontrolling stake. Or she invests asymmetrically rather than pursuing a full takeover if she acquires a controlling one. Generally, she invests indirectly if she only wants to affect the product market outcome, and directly if acquiring shares is profitable per se. --differentiated products,separation of ownership and control,private benefits of control

An Iterated Local Search Approach for Finding Provably Good Solutions for Very Large TSP Instances

Abstract. Meta-heuristics usually lack any kind of performance guar-antee and therefore one cannot be certain whether the resulting solutions are (near) optimum solutions or not without relying on additional algo-rithms for providing lower bounds (in case of minimization). In this paper, we present a highly effective hybrid evolutionary local search algorithm based on the iterated Lin-Kernighan heuristic combined with a lower bound heuristic utilizing 1-trees. Since both upper and lower bounds are improved over time, the gap between the two bounds is minimized by means of effective heuristics. In experiments, we show that the proposed approach is capable of finding short tours with a gap of 0.8 % or less for TSP instances up to 10 million cities. Hence, to the best of our knowledge, we present the first evolutionary algorithm and meta-heuristic in general that delivers provably good solutions and is highly scalable with the problem size. We show that our approach outperforms all existing heuristics for very large TSP instances.

Improving a branch-and-bound approach for the degree-constrained minimum spanning tree problem with LKH

The degree-constrained minimum spanning tree problem, which involves finding a minimum spanning tree of a given graph with upper bounds on the vertex degrees, has found multiple applications in several domains. In this paper, we propose a novel CP approach to tackle this problem where we extend a recent branch-and-bound approach with an adaptation of the LKH local search heuristic to deal with trees instead of tours. Every time a solution is found, it is locally optimised by our new heuristic, thus yielding a tightened cut. Our experimental evaluation shows that this significantly speeds up the branch-and-bound search and hence closes the performance gap to the state-of-the-art bottom-up CP approach