Joe Naoum-Sawaya

Adaptive approach for QoS support in IEEE 802.11e wireless LAN

the IEEE 802.11e standard has been introduced recently for providing quality of service (QoS) capabilities in the emerging wireless local area networks. This standard introduces a contention window based enhanced distributed channel access (EDCA) technique that provides a prioritized traffic to guarantee the minimum bandwidth needed for time critical applications. However, the EDCA technique resets statically the contention window of the mobile station after each successful transmission. This static behavior does not adapt to the network state hence reduces the network usage and results in bad performance and poor link utilization whenever the demand for link utilization increases. This paper proposes a new adaptive differentiation technique for IEEE 802.11e wireless local area networks that takes into account the network state before resetting the contention window. The performance of the proposed technique is evaluated compared to the original differentiation techniques of the IEEE 802.11a and IEEE 802.11e standards. Preliminary results show that the proposed adaptive technique enhances the channel utilization and increases throughput.

A Lagrangian decomposition approach for the pump scheduling problem in water networks

Dynamic pricing has become a common form of electricity tariff, where the price of electricity varies in real time based on the realized electricity supply and demand. Hence, optimizing industrial operations to benefit from periods with low electricity prices is vital to maximizing the benefits of dynamic pricing. In the case of water networks, energy consumed by pumping is a substantial cost for water utilities, and optimizing pump schedules to accommodate for the changing price of energy while ensuring a continuous supply of water is essential. In this paper, a Mixed-Integer Non-linear Programming (MINLP) formulation of the optimal pump scheduling problem is presented. Due to the non-linearities, the typical size of water networks, and the discretization of the planning horizon, the problem is not solvable within reasonable time using standard optimization software. We present a Lagrangian decomposition approach that exploits the structure of the problem leading to smaller problems that are solved independently. The Lagrangian decomposition is coupled with a simulation-based, improved limited discrepancy search algorithm that is capable of finding high quality feasible solutions. The proposed approach finds solutions with guaranteed upper and lower bounds. These solutions are compared to those found by a mixed-integer linear programming approach, which uses a piecewise-linearization of the non-linear constraints to find a global optimal solution of the relaxation. Numerical testing is conducted on two real water networks and the results illustrate the significant costs savings due to optimizing pump schedules.

An interior-point Benders based branch-and-cut algorithm for mixed integer programs

We present an interior-point branch-and-cut algorithm for structured integer programs based on Benders decomposition and the analytic center cutting plane method (ACCPM). We show that the ACCPM based Benders cuts are both pareto-optimal and valid for any node of the branch-and-bound tree. The valid cuts are added to a pool of cuts that is used to warm-start the solution of the nodes after branching. The algorithm is tested on two classes of problems: the capacitated facility location problem and the multicommodity capacitated fixed charge network design problem. For the capacitated facility location problem, the proposed approach was on average 2.5 times faster than Benders-branch-and-cut and 11 times faster than classical Benders decomposition. For the multicommodity capacitated fixed charge network design problem, the proposed approach was 4 times faster than Benders-branch-and-cut while classical Benders decomposition failed to solve the majority of the tested instances.

A Branch-and-Price Algorithm for the Bin Packing Problem with Conflicts

We provide a branch-and-price algorithm for the bin packing problem with conflicts, a variant of the classical bin packing problem that has major applications in scheduling and resource allocation. The proposed algorithm benefits from a number of special features that greatly contribute to its efficiency. First, we use a branching rule that matches the conflicting constraints, preserving the structure of the subproblems after branching. Second, maximal clique valid inequalities are generated based on the conflicting constraints and are added to the subproblems. The algorithm is tested on a standard set of problems and is compared to a recently proposed approach. Numerical results indicate its efficiency and stability.

Simulation-optimization approaches for water pump scheduling and pipe replacement problems

Network operation and rehabilitation are major concerns for water utilities due to their impact on providing a reliable and efficient service. Solving the optimization problems that arise in water networks is challenging mainly due to the nonlinearities inherent in the physics and the often binary nature of decisions. In this paper, we consider the operational problem of pump scheduling and the design problem of leaky pipe replacement. New approaches for these problems based on simulation-optimization are proposed as solution methodologies. For the pump scheduling problem, a novel decomposition technique uses solutions from a simulation-based sub-problem to guide the search. For the leaky pipe replacement problem a knapsack-based heuristic is applied. The proposed solution algorithms are tested and detailed results for two networks from the literature are provided.

Alternative LP and SOCP Hierarchies for ACOPF Problems

The alternating current optimal power flow (ACOPF) problem optimizes the generation and the distribution of electric energy taking into account the active and the reactive power generation limits, demand requirements, bus voltage limits, and network flow limits. The ACOPF problem can be formulated as a nonconvex polynomial program that is generally difficult to solve due to the nonlinear power flow constraints. A recently proposed approach to globally solve the ACOPF problem is through the formulation of a hierarchy of semidefinite programs that are computationally challenging to solve for large-scale problems. In this paper, we explore a solution approach that alleviates this computational burden by using hierarchies of linear and second order cone programs and by exploiting the network structure of the transmission grid. Furthermore, we show that the first level of the second order cone hierarchy is equivalent to solving the conic dual of the approximation that was recently proposed in the literature, which provides the optimal solution of the ACOPF problem for special network topologies.

High dimensional data classification and feature selection using support vector machines

In many big-data systems, large amounts of information are recorded and stored for analytics purposes. Often however, this vast amount of information does not offer additional benefits for optimal decision making, but may rather be complicating and too costly for collection, storage, and processing. For instance, tumor classification using high-throughput microarray data is challenging due to the presence of a large number of noisy features that do not contribute to the reduction of classification errors. For such problems, the general aim is to find a limited number of genes that highly differentiate among the classes. Thus in this paper, we address a specific class of machine learning, namely the problem of feature selection within support vector machine classification that deals with finding an accurate binary classifier that uses a minimal number of features. We introduce a new approach based on iteratively adjusting a bound on the l1-norm of the classifier vector in order to force the number of selected features to converge towards the desired maximum limit. We analyze two real-life classification problems with high dimensional features. The first case is the medical diagnosis of tumors based on microarray data where we present a generic approach for cancer classification based on gene expression. The second case deals with sentiment classification of on-line reviews from Amazon, Yelp, and IMDb. The results show that the proposed classification and feature selection approach is simple, computationally tractable, and achieves low error rates which are key for the construction of advanced decision-support systems.

An interior point cutting plane heuristic for mixed integer programming

We explore the use of interior point methods in finding feasible solutions to mixed integer programming. As integer solutions are typically in the interior, we use the analytic center cutting plane method to search for integer feasible points within the interior of the feasible set. The algorithm searches along two line segments that connect the weighted analytic center and two extreme points of the linear programming relaxation. Candidate points are rounded and tested for feasibility. Cuts aimed to improve the objective function and restore feasibility are then added to displace the weighted analytic center until a feasible integer solution is found. The algorithm is composed of three phases. In the first, points along the two line segments are rounded gradually to find integer feasible solutions. Then in an attempt to improve the quality of the solutions, the cut related to the bound constraint is updated and a new weighted analytic center is found. Upon failing to find a feasible integer solution, a second phase is started where cuts related to the violated feasibility constraints are added. As a last resort, the algorithm solves a minimum distance problem in a third phase. The heuristic is tested on a set of problems from MIPLIB and CORAL. The algorithm finds good quality feasible solutions in the first two phases and never requires the third phase.

Approximating the ACOPF problem with a hierarchy of SOCP problems

Semidefinite programming (SDP) relaxations for the Alternating Current Optimal Power Flow (ACOPF) problem have been shown to be tight for well studied problem instances. However, due to the computational demands of SDP, it becomes difficult to use SDP relaxations to approximate large-scale instances of the ACOPF problem. Recently, computationally cheaper second-order cone relaxations have been proposed for the ACOPF problem that are tight for networks with a simple topology. In this paper, we exploit recent results in polynomial optimization to construct a hierarchy of second-order cone relaxations that provide increasingly better approximations for ACOPF problems. We show that in comparison with proposed related SDP hierarchies, the second-order cone hierarchies provide good approximations to the ACOPF problems for larger scale networks. We illustrate this with numerical examples on well studied instances of the ACOPF problem.

Controlled predatory pricing in a multiperiod Stackelberg game: an MPEC approach

We analyze a multiperiod oligopolistic market where each period is a Stackelberg game between a leader firm and multiple follower firms. The leader chooses his production level first, taking into account the reaction of the followers. Then, the follower firms decide their production levels after observing the leader’s decision. The difference between the proposed model and other models discussed in literature is that the leader firm has the power to force the follower firms out of business by preventing them from achieving a target sales level in a given time period. The leader firm has an incentive to lower the market prices possibly lower than the Stackelberg equilibrium in order to push the followers to sell less and eventually go out of business. Intentionally lowering the market prices to force competitors to fail is known as predatory pricing, and is illegal under antitrust laws since it negatively affects consumer welfare. In this work, we show that there exists a predatory pricing strategy where the market price is above the average cost and consumer welfare is preserved. We develop a mixed integer nonlinear problem (MINLP) that models the multiperiod Stackelberg game. The MINLP problem is transformed to a mixed integer linear problem (MILP) by using binary variables and piecewise linearization. A cutting plane algorithm is used to solve the resulting MILP. The results show that firms can engage in predatory pricing even if the average market price is forced to remain higher than the average cost. Furthermore, we show that in order to protect the consumers, antitrust laws can control predatory pricing by setting rules on consumer welfare.