Evolving test instances of the Hamiltonian completion problem

Predicting and comparing algorithm performance on graph instances is challenging for multiple reasons. First, there is usually no standard set of instances to benchmark performance. Second, using existing graph generators results in a restricted spectrum of difficulty and the resulting graphs are usually not diverse enough to draw sound conclusions. That is why recent work proposes a new methodology to generate a diverse set of instances by using an evolutionary algorithm. We can then analyze the resulting graphs and get key insights into which attributes are most related to algorithm performance. We can also fill observed gaps in the instance space in order to generate graphs with previously unseen combinations of features. This methodology is applied to the instance space of the Hamiltonian completion problem using two different solvers, namely the Concorde TSP Solver and a multi-start local search algorithm.Comment: 12 pages, 12 figures, minor revisions in section

Feature-Based Diversity Optimization for Problem Instance Classification

Understanding the behaviour of heuristic search methods is a challenge. This even holds for simple local search methods such as 2-OPT for the Traveling Salesperson problem. In this paper, we present a general framework that is able to construct a diverse set of instances that are hard or easy for a given search heuristic. Such a diverse set is obtained by using an evolutionary algorithm for constructing hard or easy instances that are diverse with respect to different features of the underlying problem. Examining the constructed instance sets, we show that many combinations of two or three features give a good classification of the TSP instances in terms of whether they are hard to be solved by 2-OPT.Comment: 20 pages, 18 figure

Phase transitions in project scheduling.

The analysis of the complexity of combinatorial optimization problems has led to the distinction between problems which are solvable in a polynomially bounded amount of time (classified in P) and problems which are not (classified in NP). This implies that the problems in NP are hard to solve whereas the problems in P are not. However, this analysis is based on worst-case scenarios. The fact that a decision problem is shown to be NP-complete or the fact that an optimization problem is shown to be NP-hard implies that, in the worst case, solving it is very hard. Recent computational results obtained with a well known NP-hard problem, namely the resource-constrained project scheduling problem, indicate that many instances are actually easy to solve. These results are in line with those recently obtained by researchers in the area of artificial intelligence, which show that many NP-complete problemsexhibit so-called phase transitions, resulting in a sudden and dramatic change of computational complexity based on one or more order parameters that are characteristic of the system as a whole. In this paper we provide evidence for the existence of phase transitions in various resource-constrained project scheduling problems. We discuss the use of network complexity measures and resource parameters as potential order parameters. We show that while the network complexity measures seem to reveal continuous easy-hard or hard-easy phase-transitions, the resource parameters exhibit an easy-hard-easy transition behaviour.Networks; Problems; Scheduling; Algorithms;

Tour recommendation for groups

Consider a group of people who are visiting a major touristic city, such as NY, Paris, or Rome. It is reasonable to assume that each member of the group has his or her own interests or preferences about places to visit, which in general may differ from those of other members. Still, people almost always want to hang out together and so the following question naturally arises: What is the best tour that the group could perform together in the city? This problem underpins several challenges, ranging from understanding people’s expected attitudes towards potential points of interest, to modeling and providing good and viable solutions. Formulating this problem is challenging because of multiple competing objectives. For example, making the entire group as happy as possible in general conflicts with the objective that no member becomes disappointed. In this paper, we address the algorithmic implications of the above problem, by providing various formulations that take into account the overall group as well as the individual satisfaction and the length of the tour. We then study the computational complexity of these formulations, we provide effective and efficient practical algorithms, and, finally, we evaluate them on datasets constructed from real city data

Fine-grained Search Space Classification for Hard Enumeration Variants of Subset Problems

We propose a simple, powerful, and flexible machine learning framework for (i) reducing the search space of computationally difficult enumeration variants of subset problems and (ii) augmenting existing state-of-the-art solvers with informative cues arising from the input distribution. We instantiate our framework for the problem of listing all maximum cliques in a graph, a central problem in network analysis, data mining, and computational biology. We demonstrate the practicality of our approach on real-world networks with millions of vertices and edges by not only retaining all optimal solutions, but also aggressively pruning the input instance size resulting in several fold speedups of state-of-the-art algorithms. Finally, we explore the limits of scalability and robustness of our proposed framework, suggesting that supervised learning is viable for tackling NP-hard problems in practice.Comment: AAAI 201