The Team Orienteering Problem with Time Windows: An LP-based Granular Variable Neighborhood Search

The Team Orienteering Problem (TOP) is a known NP-hard problem that typically arises in vehicle routing and production scheduling contexts. In this paper we introduce a new solution method to solve the TOP with hard Time Window constraints (TOPTW). We propose a Variable Neighborhood Search (VNS) procedure based on the idea of exploring, most of the time, granular instead of complete neighborhoods in order to improve the algorithm’s efficiency without loosing effectiveness. The method provides a general way to deal with granularity for those routing problems based on profits and complicated by time constraints. Extensive computational results are reported on standard benchmark instances. Performance of the proposed algorithm is compared to optimal solution values, when available, or to best known solution values obtained by state-of-the-art algorithms. The method comes out to be, on average, quite effective allowing to improve the best know values for 25 test instances.     

Bayesian variable selection in generalized linear models using a combination of stochastic optimization methods

In this paper the usage of a stochastic optimization algorithm as a model search tool is proposed for the Bayesian variable selection problem in generalized linear models. Combining aspects of three well known stochastic optimization algorithms, namely, simulated annealing, genetic algorithm and tabu search, a powerful model search algorithm is produced. After choosing suitable priors, the posterior model probability is used as a criterion function for the algorithm; in cases when it is not analytically tractable Laplace approximation is used. The proposed algorithm is illustrated on normal linear and logistic regression models, for simulated and real-life examples, and it is shown that, with a very low computational cost, it achieves improved performance when compared with popular MCMC algorithms, such as the MCMC model composition, as well as with “vanilla” versions of simulated annealing, genetic algorithm and tabu search.     

The eye and the fist: Optimizing search and interdiction

Interdiction operations involving search, identification, and interception of suspected objects are of great interest and high operational importance to military and naval forces as well as nation’s coast guards and border patrols. The interdiction scenario discussed in this paper includes an area of interest with multiple neutral and hostile objects moving through this area, and an interdiction force, consisting of an airborne sensor and an intercepting surface vessel or ground vehicle, whose objectives are to search, identify, track, and intercept hostile objects within a given time frame. The main contributions of this paper are addressing both airborne sensor and surface vessel simultaneously, developing a stochastic dynamic-programming model for optimizing their employment, and deriving operational insight. In addition, the search and identification process of the airborne sensor addresses both physical (appearance) and behavioral (movement pattern) signatures of a potentially hostile object. As the model is computationally intractable for real-world scenarios, we propose a simple heuristic policy, which is shown, using a bounding technique, to be quite effective. Based on a numerical case study of maritime interdiction operations, which includes several representative scenarios, we show that the expected number of intercepted hostile objects, following the heuristic decision policy, is at least 60% of the number of hostile objects intercepted following an optimal decision policy.     

Tabu search heuristics for the order batching problem in manual order picking systems

In a manual order picking system, order pickers walk or ride through a distribution warehouse in order to collect items requested by (internal or external) customers. In order to perform these operations efficiently, it is usually required that customer orders be combined into (more substantial) picking orders that are limited in size. The order batching problem considered in this paper deals with the question of how a given set of customer orders should be combined into picking orders such that the total length of all picker tours necessary for all of the requested items to be collected is minimized. For the solution of this problem the authors suggest two approaches based on the tabu search principle. The first is a (classic) tabu search (TS), and the second is the attribute-based hill climber (ABHC). In a series of extensive numerical experiments, these approaches are benchmarked against other solution methods put forward in the current literature. It is demonstrated that the proposed methods are superior to the existing methods and provide solutions which may allow distribution warehouses to operate more efficiently.     

City-courier routing and scheduling problems

This research seeks to propose innovative routing and scheduling strategies to help city couriers reduce operating costs and enhance service level. The strategies are realized by constructing a new type of routing and scheduling problem. The problem directly takes into account the inherent physical and operating constraints associated with riding in city distribution networks, which makes the problem involve multiple objectives and visiting specified nodes and arcs. Through network transformations, this study first formulates the city-courier routing and scheduling problem as a multi-objective multiple traveling salesman problem with strict time windows (MOMTSPSTW) that is NP-hard and new to the literature, and then proposes a multi-objective Scatter Search framework that seeks to find the set of Pareto-optimal solutions to the problem. Various new and improved sub-procedures are embedded in the solution framework. This is followed by an empirical study that shows and analyzes the results of applying the proposed method to a real-life city-courier routing and scheduling problem.     

An evolutionary approach for bandwidth multicoloring problems

In this paper we consider some generalizations of the vertex coloring problem, where distance constraints are imposed between adjacent vertices (bandwidth coloring problem) and each vertex has to be colored with more than one color (bandwidth multicoloring problem). We propose an evolutionary metaheuristic approach for the first problem, combining an effective tabu search algorithm with population management procedures. The approach can be applied to the second problem as well, after a simple transformation. Computational results on instances from the literature show that the overall algorithm is able to produce high quality solutions in a reasonable amount of time, outperforming the most effective algorithms proposed for the bandwidth coloring problem, and improving the best known solution of many instances of the bandwidth multicoloring problem.     

Bifurcation analysis on a discrete-time tabu learning model

In this paper, we consider a discrete-time tabu learning single neuron model. After investigating the stability of the given system, we demonstrate that Pichfork bifurcation, Flip bifurcation and Neimark–Sacker bifurcation will occur when the bifurcation parameter exceed a critical value, respectively. A formula is given for determining the direction and stability of Neimark–Sacker bifurcation by applying the normal form theory and the center manifold theorem. Some numerical simulations for justifying the theoretical results are also provided.     

Fast heuristics for the Steiner tree problem with revenues,budget and hop constraints

This article describes and compares three heuristics for a variant of the Steiner tree problem with revenues, which includes budget and hop constraints. First, a greedy method which obtains good approximations in short computational times is proposed. This initial solution is then improved by means of a destroy-and-repair method or a tabu search algorithm. Computational results compare the three methods in terms of accuracy and speed.     

Single- and multi-objective defensive location problems on a network

This paper considers a new optimal location problem, called defensive location problem (DLP). In the DLPs, a decision maker locates defensive facilities in order to prevent her/his enemies from reaching an important site, called a core; for example, “a government of a country locates self-defense bases in order to prevent her/his aggressors from reaching the capital of the country.” It is assumed that the region where the decision maker locates her/his defensive facilities is represented as a network and the core is a vertex in the network, and that the facility locater and her/his enemy are an upper and a lower level of decision maker, respectively. Then the DLPs are formulated as bilevel 0-1 programming problems to find Stackelberg solutions. In order to solve the DLPs efficiently, a solving algorithm for the DLPs based upon tabu search methods is proposed. The efficiency of the proposed solving methods is shown by applying to examples of the DLPs. Moreover, the DLPs are extended to multi-objective DLPs that the decision maker needs to defend several cores simultaneously. Such DLPs are formulated as multi-objective programming problems. In order to find a satisfying solution of the decision maker for the multi-objective DLP, an interactive fuzzy satisfying method is proposed, and the results of applying the method to examples of the multi-objective DLPs are shown.