On Neighborhood Tree Search

We consider the neighborhood tree induced by alternating the use of different neighborhood structures within a local search descent. We investigate the issue of designing a search strategy operating at the neighborhood tree level by exploring different paths of the tree in a heuristic way. We show that allowing the search to 'backtrack' to a previously visited solution and resuming the iterative variable neighborhood descent by 'pruning' the already explored neighborhood branches leads to the design of effective and efficient search heuristics. We describe this idea by discussing its basic design components within a generic algorithmic scheme and we propose some simple and intuitive strategies to guide the search when traversing the neighborhood tree. We conduct a thorough experimental analysis of this approach by considering two different problem domains, namely, the Total Weighted Tardiness Problem (SMTWTP), and the more sophisticated Location Routing Problem (LRP). We show that independently of the considered domain, the approach is highly competitive. In particular, we show that using different branching and backtracking strategies when exploring the neighborhood tree allows us to achieve different trade-offs in terms of solution quality and computing cost.Comment: Genetic and Evolutionary Computation Conference (GECCO'12) (2012

Studying Solutions of the p-Median Problem for the Location of Public Bike Stations

The use of bicycles as a means of transport is becoming more and more popular today, especially in urban areas, to avoid the disadvantages of individual car traffic. In fact, city managers react to this trend and actively promote the use of bicycles by providing a network of bicycles for public use and stations where they can be stored. Establishing such a network involves the task of finding best locations for stations, which is, however, not a trivial task. In this work, we examine models to determine the best location of bike stations so that citizens will travel the shortest distance possible to one of them. Based on real data from the city of Malaga, we formulate our problem as a p-median problem and solve it with a variable neighborhood search algorithm that was automatically configured with irace. We compare the locations proposed by the algorithm with the real ones used currently by the city council. We also study where new locations should be placed if the network grows.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech. This research was partially funded by the University of Málaga, Andalucı́a Tech, the Spanish MINECO and FEDER projects: TIN2014- 57341-R, TIN2016-81766-REDT, and TIN2017-88213-R. C. Cintrano is supported by a FPI grant (BES-2015-074805) from Spanish MINECO

On the use of biased-randomized algorithms for solving non-smooth optimization problems

Soft constraints are quite common in real-life applications. For example, in freight transportation, the fleet size can be enlarged by outsourcing part of the distribution service and some deliveries to customers can be postponed as well; in inventory management, it is possible to consider stock-outs generated by unexpected demands; and in manufacturing processes and project management, it is frequent that some deadlines cannot be met due to delays in critical steps of the supply chain. However, capacity-, size-, and time-related limitations are included in many optimization problems as hard constraints, while it would be usually more realistic to consider them as soft ones, i.e., they can be violated to some extent by incurring a penalty cost. Most of the times, this penalty cost will be nonlinear and even noncontinuous, which might transform the objective function into a non-smooth one. Despite its many practical applications, non-smooth optimization problems are quite challenging, especially when the underlying optimization problem is NP-hard in nature. In this paper, we propose the use of biased-randomized algorithms as an effective methodology to cope with NP-hard and non-smooth optimization problems in many practical applications. Biased-randomized algorithms extend constructive heuristics by introducing a nonuniform randomization pattern into them. Hence, they can be used to explore promising areas of the solution space without the limitations of gradient-based approaches, which assume the existence of smooth objective functions. Moreover, biased-randomized algorithms can be easily parallelized, thus employing short computing times while exploring a large number of promising regions. This paper discusses these concepts in detail, reviews existing work in different application areas, and highlights current trends and open research lines

Scalable Verification of Markov Decision Processes

Markov decision processes (MDP) are useful to model concurrent process optimisation problems, but verifying them with numerical methods is often intractable. Existing approximative approaches do not scale well and are limited to memoryless schedulers. Here we present the basis of scalable verification for MDPSs, using an O(1) memory representation of history-dependent schedulers. We thus facilitate scalable learning techniques and the use of massively parallel verification.Comment: V4: FMDS version, 12 pages, 4 figure