Electronic Notes in Discrete Mathematics最新文献

One of the main problems being faced at the time of performing data clustering consists in the deteremination of the best clustering method together with defining the ideal amount (k) of groups in which these data should be separated. In this paper, a preliminary approximation of a clustering recommender method is presented which, starting from a set of standardized data, suggests the best clustering strategy and also proposes an advisable k value. For this aim, the algorithm considers four indices for evaluating the final structure of clusters: Dunn, Silhouette, Widest Gap and Entropy. The prototype is implemented as a Genetic Algorithm in which individuals are possible configurations of the methods and their parameters. In this first prototype, the algorithm suggests between four partitioning methods namely K-means, PAM, CLARA and, Fanny. Also, the best set of parameters to execute the suggested method is obtained. The prototype was developed in an R environment, and its findings could be corroborated as consistent when compared with a combination of results provided by other methods with similar objectives. The idea of this prototype is to serve as the initial basis for a more complex framework that also incorporates the reduction of matrices with vast numbers of rows.

This paper addresses the k-traveling repairman problem with profits under uncertain travel times, a new vehicle routing problem aimed at visiting a subset of customers in order to collect a revenue, defined as decreasing function of the uncertain arrival times. We adopt a risk-averse approach, enabling the decision maker to manage and control risk, and develop a mean-risk model in which only the first and the second moment of the travel times distribution are required to be known. We propose an adaptive local search heuristic in which, in each iteration, a Greedy Randomized Adaptive Search Procedure is used to generate the initial solution. The effectiveness of the solution approach is shown by the computational experiments performed on a set of instances.

This work addresses a two-level discrete decision problem, a so-called Stackelberg strategic game in a Subset Sum setting. One of the players, the leader $L$, may alter the weights of some items, and a second player, the follower $F$, selects a solution in order to utilize a bounded resource in the best possible way. Finally, the leader receives a payoff which only depends on those items of its subset L that were included in the overall solution A, chosen by the follower. Complexity results and solution algorithms are presented for different variants of the leader problem.

In this paper, we study the deterministic single-reservoir Hydro Unit Commitment Problem. Under some hypotheses, we present a time expanded graph representation for the problem, where, at each time step, nodes correspond to discrete operational points, and arcs refer to possible state changes. We show that our problem reduces to a Constrained Shortest Path Problem, propose and compare different approaches to solve the HUCP, based on mixed integer linear or dynamic programming.

Bonus-Malus systems are widely used in the insurance business. For the operation of such systems transition rules and premium scales need to established. Optimization of these systems usually means the calculation of appropriate premium scales while treating transition rules external parameters. In this paper, on the contrary, we show how optimal transition rules can be determined for a given set of premium scales. To this end, integer programming (IP) is used as a basic tool. Numerical examples are also presented to demonstrate the viability of our approach.

The Yield Management System (YMS) described in this article has been developed by IBM for Trenitalia, main Italian and 3rd European railway undertaking, with 24 Million passengers and more than 260 High Speed Trains (“Frecce”) offered per day on average in 2017 first half, delivering good results in a period of raising competition. The YMS forecasts the unconstrained demand, using an additive method with an emphasis and a multiplicative correction, to account for censored data, allowing a capacity allocation optimization per Origin-Destination (O&D), and fare cluster. The system has been implemented gradually to most trains “Frecce” at Trenitalia, and since 2005 it has forecasted and optimized approximatively 4 Million model instances: nearly 120 Billion train-date-class-O&D-fare decisions.

Urban waste collection is an important problem in modern cities, where efficient techniques are demanded to reduce large budgetary expenses, and avoid environmental and social problems. This article presents two state-of-the-art multiobjective evolutionary algorithms to solve a variant of the urban waste collection problem considering priorities and the conflicting goals of minimizing the total distance while maximizing the Quality of Service. The main results for real scenarios in Montevideo, Uruguay, show that accurate trade-off solutions outperformed greedy approaches, including the current routing methodology applied by local authorities. The competitiveness of the evolutionary algorithms was also confirmed when solving a prototype scenario using dynamic information.

The goal in topological network design is to build a minimum-cost topology meeting specific real-life constraints. There is a cost-robustness trade-off under single and multiple failures.

Previous works in the field suggest that a backbone composed by a two-node-connected toplogy provides savings with respect to elementary cycles. Consequently, we introduce the Two-Node Connected Star Problem with Steiner Nodes (2NCSP-SN). The goal is to design a minimum-cost topology, where the backbone is two-node connected, the access network is connected in a star topology or by direct links to the backbone, and optional nodes (called Steiner nodes) could be included in the solution. The 2NCSP-SN belongs to the class of NP-Hard problems. This promotes the development of heuristics and approximation algorithms.

An approximation algorithm of factor 4α for the 2NCSP-SN is introduced, being $\alpha \ge 1/2$ the cost-ratio between backbone and access links. This is a generalization of the well-known factor 2 for the design of minimum-cost two-connected spanning networks (if we fix $\alpha =1/2$). Finally, an exact Integer Linear Programming (ILP) formulation is proposed in order to highlight the effectiveness of the approximation algorithm. The results confirm a small gap between the globally optimum solution and the topology offered by our approximation algorithm when the ratio α is close to 1/2.

Feature selection applied to QSAR (Quantitative Structure-Activity Relationship) modeling is a challenging combinatorial optimization problem due to the high dimensionality of the chemical space associated with molecules and the complexity of the physicochemical properties usually studied in Cheminformatics. This derives commonly in classification models with a large number of variables, decreasing the generalization and interpretability of these classifiers. In this paper, a novel strategy based on biclustering analysis is proposed for addressing this problem. The new method is applied as a post-processing step for feature selection outputs generated by consensus feature selection methods. The approach was evaluated using datasets oriented to ready biodegradation prediction of chemical compounds. These preliminary results show that biclustering can help to identify features with low class-discrimination power, which it is useful for reducing the complexity of QSAR models without losing prediction accuracy.

Multiple criteria decision analysis methods are incorporated into network flow problems as the arc weight. Each individual arc in the network consequently has a value or utility between 0 and 1, and the objective is thus to find the path with longest average value or maximum average cost flow. These problems are NP-hard for general graphs. For directed acyclic graphs (DAG), we develop a dynamic programming based algorithm to solve the average longest path problem in O(nm) and a heuristic to approximate the average longest path problem in O(m). These methods are then used successively to approximate the average maximum cost flow.