I. Kuban Altınel

Binary integer programming formulation and heuristics for differentiated coverage in heterogeneous sensor networks

Coverage is a fundamental task in sensor networks. We consider the minimum cost point coverage problem and formulate a binary integer linear programming model for effective sensor placement on a grid-structured sensor field when there are multiple types of sensors with varying sensing quality and price. The formulation is general and can be adapted to handle situations where sensing is perfect, imperfect or uncertain, and the coverage requirements are differentiated. Unfortunately, the new model suffers from the intractability of the binary integer programming formulations. We therefore suggest approximation algorithms and heuristics. Computational results indicate that the heuristic based on Lagrangean relaxation outperforms the others in terms of solution quality.

Competitive facility location problem with attractiveness adjustment of the follower: A bilevel programming model and its solution

We are concerned with a problem in which a firm or franchise enters a market by locating new facilities where there are existing facilities belonging to a competitor. The firm aims at finding the location and attractiveness of each facility to be opened so as to maximize its profit. The competitor, on the other hand, can react by adjusting the attractiveness of its existing facilities with the objective of maximizing its own profit. The demand is assumed to be aggregated at certain points in the plane and the facilities of the firm can be located at predetermined candidate sites. We employ Huffs gravity-based rule in modeling the behavior of the customers where the fraction of customers at a demand point that visit a certain facility is proportional to the facility attractiveness and inversely proportional to the distance between the facility site and demand point. We formulate a bilevel mixed-integer nonlinear programming model where the firm entering the market is the leader and the competitor is the follower. In order to find the optimal solution of this model, we convert it into an equivalent one-level mixed-integer nonlinear program so that it can be solved by global optimization methods. Apart from reporting computational results obtained on a set of randomly generated instances, we also compute the benefit the leader firm derives from anticipating the competitors reaction of adjusting the attractiveness levels of its facilities. The results on the test instances indicate that the benefit is 58.33% on the average.

Wireless sensor network lifetime maximization by optimal sensor deployment, activity scheduling, data routing and sink mobility

The longevity of Wireless Sensor Networks (WSNs) is a crucial concern that significantly influences their applicability in a specific context. Most of the related literature focuses on communication protocols aiming to reduce the energy consumption which would eventually lead to longer network lifetimes. On the other hand, a limited number of studies concentrate on providing a unifying frame to investigate the integrated effect of the important WSN design decisions such as sensor places, activity schedules, data routes, trajectory of the mobile sink(s), along with the tactical level decisions including the data propagation protocols. However, a monolithic mathematical optimization model with a practically applicable, efficient, and accurate solution method is still missing. In this study, we first provide a mathematical model which integrates WSN design decisions on sensor places, activity schedules, data routes, trajectory of the mobile sink(s) and then present two heuristic methods for the solution of the model. We demonstrate the efficiency and accuracy of the heuristics on several randomly generated problem instances on the basis of extensive numerical experiments.

Efficient integer programming formulations for optimum sink location and routing in heterogeneous wireless sensor networks

Sensors spend most of their limited battery energy on communicating the collected environmental information to sinks. Therefore, the determination of the optimal sink locations and sensor-to-sink information flow routes becomes important for the survivability of sensor networks. In this work, we address these important design issues using an integrated approach and propose new mixed-integer linear programming models to determine the optimal sink locations and information flow paths between sensors and sinks when sensor locations are given. The first group of proposed models is energy-aware and tries to minimize total routing energy, whereas the second group is financially driven with the objective of minimizing total cost. We do not only report computational results providing information on the solution efficiency of the new formulations, and the accuracy of their linear programming relaxations, but also propose and test new heuristics and lower bounding approaches for the most efficient formulation.

Optimal berth allocation and time-invariant quay crane assignment in container terminals

Due to the dramatic increase in the world’s container traffic, the efficient management of operations in seaport container terminals has become a crucial issue. In this work, we focus on the integrated planning of the following problems faced at container terminals: berth allocation, quay crane assignment (number), and quay crane assignment (specific). First, we formulate a new binary integer linear program for the integrated solution of the berth allocation and quay crane assignment (number) problems called BACAP. Then we extend it by incorporating the quay crane assignment (specific) problem as well, which is named BACASP. Computational experiments performed on problem instances of various sizes indicate that the model for BACAP is very efficient and even large instances up to 60 vessels can be solved to optimality. Unfortunately, this is not the case for BACASP. Therefore, to be able to solve large instances, we present a necessary and sufficient condition for generating an optimal solution of BACASP from an optimal solution of BACAP using a post-processing algorithm. In case this condition is not satisfied, we make use of a cutting plane algorithm which solves BACAP repeatedly by adding cuts generated from the optimal solutions until the aforementioned condition holds. This method proves to be viable and enables us to solve large BACASP instances as well. To the best of our knowledge, these are the largest instances that can be solved to optimality for this difficult problem, which makes our work applicable to realistic problems.

A leader-follower game in competitive facility location

We address the problem of locating new facilities of a firm or franchise that enters a market where a competitor operates existing facilities. The goal of the new entrant firm is to decide the location and attractiveness of its new facilities that maximize its profit. The competitor can react by opening new facilities, closing existing ones, and adjusting the attractiveness levels of its existing facilities, with the aim of maximizing its own profit. The demand is assumed to be aggregated at certain points in the plane and the new facilities of both the firm and the competitor can be located at predetermined candidate sites. We employ the gravity-based rule in modeling the behavior of the customers where the probability that a customer visits a certain facility is proportional to the facility attractiveness and inversely proportional to the distance between the facility site and demand point. We formulate a bilevel mixed-integer nonlinear programming model where the firm entering the market is the leader and the competitor is the follower. We propose heuristics that combine tabu search with exact solution methods.

Lifetime Maximization in Wireless Sensor Networks Using a Mobile Sink with Nonzero Traveling Time

It is a known phenomenon that in a wireless sensor network, sensors communicating directly with a sink deplete their energy faster than the others. As a result, the so-called neighboring sensors can die, disconnecting some of the sinks from the rest of the network, even though most of the sensors are still fully functional. One possible remedy is to balance the relaying load of the sensors using mobile sinks and controlling their mobility, which has attracted the interest of researchers. In this work, we extend the relevant literature by introducing two new mathematical programming models. They intend to maximize the network lifetime through the controlled mobility of a sink with nonzero travel times with and without limiting the number of hops by which the data originating from the sensors reach the sink. Both models allow more than one tour of the sink during the network lifetime and determine the optimal sink route and sojourn times. Since the models are computationally difficult to solve, we propose efficient heuristics methods to compute near-optimal solutions. On the basis of the computational results performed on randomly generated problem instances, we can say that their performance is remarkable.

A location–allocation heuristic for the capacitated multi-facility Weber problem with probabilistic customer locations

The capacitated multi-facility Weber problem is concerned with locating m facilities in the Euclidean plane, and allocating their capacities to n customers at minimum total cost. The deterministic version of the problem, which assumes that customer locations and demands are known with certainty, is a non-convex optimization problem and difficult to solve. In this work, we focus on a probabilistic extension and consider the situation where the customer locations are randomly distributed according to a bivariate distribution. We first present a mathematical programming formulation, which is even more difficult than its deterministic version. We then propose an alternate location-allocation local search heuristic generalizing the ideas used originally for the deterministic problem. In its original form, the applicability of the heuristic depends on the calculation of the expected distances between the facilities and customers, which can be done for only very few distance and probability density function combinations. We therefore propose approximation methods which make the method applicable for any distance function and bivariate location distribution.

Efficient solution techniques for the integrated coverage, sink location and routing problem in wireless sensor networks

Sensors are tiny electronic devices having limited battery energy and capability for sensing, data processing and communicating. They can collectively behave to provide an effective wireless network that monitors a region and transmits the collected information to gateway nodes called sinks. Most of the applications require the operation of the network for long periods of times, which makes the efficient management of the available energy resources an important concern. There are three major issues in the design of sensor networks: sensor deployment or the coverage of the sensing area, sink location, and data routing. In this work, we consider these three design problems within a unified framework and develop two mixed-integer linear programming formulations. They are difficult to solve exactly. However, it is possible to compute good feasible solutions of the sink location and routing problems easily, when the sensors are deployed and their locations in the sensor field become known. Therefore, we propose a tabu search heuristic that tries to identify the best sensor locations satisfying the coverage requirements. The objective value corresponding to each set of sensor locations is calculated by solving the sink location and routing problem. Computational tests carried out on randomly generated test instances indicate that the proposed hybrid approach is both accurate and efficient.

Optimum component test plans for phased-mission systems

We consider the component testing problem of a system that has to perform a mission consisting of a sequence of stages. Once a stage is over, all failed components of the system are replaced before the next stage starts in order to improve its reliability. The components have exponential life distributions where the failure rates depend on the stage of the mission. We formulate the optimal component testing problem as a semi-infinite linear program. We present an algorithmic procedure to compute optimal test times based on the column generation technique and illustrate with numerical examples.