We introduce a compact formulation for the fixed-destination multi-depot asymmetric travelling salesman problem (FD-mATSP). It consists of m salesmen distributed among D depots who depart from and return to their respective origins after visiting a set of customers. The proposed model exploits the multi-depot aspect of the problem by labelling the arcs to identify the nodes that belong to the same tour. Our experimental investigation shows that the proposed-two index formulation is versatile and effective in modelling new variations of the FD-mATSP compared with existing formulations. We demonstrate this by applying it for the solution of two important extensions of the FD-mATSP that arise in logistics and manufacturing environments.

This paper investigates the problem of partitioning a complete weighted graph into complete subgraphs, each having the same number of vertices, with the objective of minimizing the sum of edge weights of the resulting subgraphs. This NP-complete problem arises in many applications such as assignment and scheduling-related group partitioning problems and micro-aggregation techniques. In this paper, we present a mathematical programming model and propose a complementary column generation approach to solve the resulting model. A dual based lower bounding feature is also introduced to curtail the notorious tailing-off effects often induced when using column generation methods. Computational results are presented for a wide range of test problems.

The daily crew pairing problem (DCPP) seeks to generate a set of minimal-cost pairings that covers all the planned daily flights while complying with a variety of labor regulations, safety rules, and policies of the airline. The DCPP is a highly complex and large-scale optimization problem that is often modeled using a set-partitioning formulation and then solved via advanced optimization techniques (i.e., specialized column generation or branch-and-price algorithms). To complement this approach, we present a novel compact polynomial-sized nonlinear formulation for the DCPP, which is then linearized and lifted using the reformulation-linearization technique (RLT). Moreover, we propose two enhancement strategies to further improve the computational performance of the proposed formulation. The experimental results show that the compact formulation can be solved efficiently by commercial software without complicated algorithmic implementations, thus facilitating its use in the airline industry.

This paper presents an optimization based mathematical modelling approach for a single source single destination crude oil facility location transshipment problem. We began by formulating a mixed-integer nonlinear programming model and use a rolling horizon heuristic to find an optimal location for a storage facility within a restricted continuous region. We next design a hybrid two-stage algorithm that combines judicious facility locations resulting from the proposed model into a previously developed column generation approach. The results indicate that improved overall operational costs can be achieved by strategically determining cost-effective locations of the transshipment facility.

We address the robust weekly aircraft routing and retiming problem, which requires determining weekly schedules for a heterogeneous fleet that maximizes the aircraft on time performance, minimizes the total delay, and minimizes the number of delayed passengers. The fleet is required to serve a set of flights having known departure time windows while satisfying maintenance constraints. All flights are subject to random delays that may propagate through the network. We propose to solve this problem using a hybrid optimization-simulation approach based on a novel mixed-integer nonlinear programming model for the robust weekly aircraft maintenance routing problem. For this model, we provide an equivalent mixed-integer linear programming formulation that can be solved using a commercial solver. Furthermore, we describe a Monte-Carlo-based procedure for sequentially adjusting the flight departure times. We perform an extensive computational study using instances obtained from a major international airline, having up to 3387 flights and 164 aircraft, which demonstrates the efficacy of the proposed approach. Using the simulation software SimAir to assess the robustness of the solutions produced by our approach in comparison with that for the original solutions implemented by the airline, we found that on-time performance was improved by 9.8-16.0%, cumulative delay was reduced by 25.4-33.1%, and the number of delayed passengers was reduced by 8.2-51.6%. (C) 2017 Elsevier Ltd. All rights reserved.

We present an algorithm to solve single and multiple asymmetric traveling salesmen problems (ATSP and mATSP) by generating violated subtour elimination constraints from specific integer solutions. Computational results for the ATSP reveal that the proposed approach is able to solve 29 out of 33 well-known instances taken from the literature (involving between 100 and 1001 cities) to optimality within an hour of CPU time. Furthermore, the proposed approach is demonstrated to outperform any of the most effective state-of-the-art exact algorithms available in the literature when applied to solve the given ATSP instances via their equivalently transformed symmetric TSP representations. For the mATSP, the proposed approach is able to solve 27 out of 36 instances derived from the ATSP library involving up to 1001 cities to optimality within an hour of CPU time and also outperforms the direct solution by CPLEX, one of the three most effective formulations reported in the literature for this class of problems. The proposed approach is easy to implement and can be used to solve ATSP and mATSP as stand-alone models or can be applied in contexts where they appear as sub-models within some application settings.

This paper presents a column generation-based modelling and solution approach for a teaching assistant workload scheduling problem that arises at academic institutions. A typical weekly workload schedule involves teaching deficiency classes, instructing problem-solving tutorial sessions, and allocating help-hours for students. For this purpose, a mixed-integer programming model that selects valid combinations of weekly schedules from the set of all feasible schedules is formulated. Due to the overwhelming number of variables in this model, an effective column generation procedure is developed. To illustrate the proof-of-concept along with modelling and algorithmic constructs, a case study related to the Department of Mathematics at Kuwait University is addressed. Computational results based on real data indicate that the generated schedules using the proposed model and solution procedure yield improved weekly workloads for teaching assistants in terms of fairness, and achieve enhanced satisfaction levels among assistants, as compared to schedules obtained using ad-hoc manual approaches.

Intensive research effort has been dedicated to tackle multi-hop network problems. Joint consideration across multiple layers is required to achieve optimal performance. The general trend in solving these problems is to develop strong mathematical programming formulations that are capable of providing near-optimal solutions to practical-sized problems. For the class of problems studied, we show that a traditionally formulated model turns out to be insufficient from a problem-solving perspective. When the size of the problem increases, even state-of-the-art optimizers cannot obtain an optimal solution because of running out of memory. In this work, we show that augmenting the model with suitable additional constraints and structure enables the optimizer to derive optimal solutions, or significantly reduce the optimality gap, which were previously elusive given available memory restrictions.

In this paper, we present a single-commodity flow-based formulation for the high-multiplicity asymmetric traveling salesman problem (HMATSP), which is an extension of the asymmetric traveling salesman problem (ATSP) wherein a city can be visited multiple times. We show that even though this formulation is not as tight as the best known formulation for the HMATSP, it is faster and easier to use for direct solution by CPLEX and can be used to model several variants or extensions of the HMATSP that have not been studied in the literature. Furthermore, we propose effective accelerated Benders algorithms that are demonstrated to solve instances of the HMATSP and its extensions, which are derived from the well-known ATSP libraries and involve up to 1001 cities, within an hour of CPU time. These are the largest-sized HMATSP instances solved to optimality in the literature.

We investigate the solution of the Second-Order Cone Quadratic Eigenvalue Complementarity Problem (SOCQEiCP), which has a solution under reasonable assumptions on the matrices included in its definition. A Nonlinear Programming Problem (NLP) formulation of the SOCQEiCP is introduced. A necessary and sufficient condition for a stationary point (SP) of NLP to be a solution of SOCQEiCP is established. This condition indicates that, in many cases, the computation of a single SP of NLP is sufficient for solving SOCQEiCP. In order to compute a global minimum of NLP for the general case, we develop an enumerative method based on the Reformulation-Linearization Technique and prove its convergence. For computational effectiveness, we also introduce a hybrid method that combines the enumerative algorithm and a semi-smooth Newton method. Computational experience on the solution of a set of test problems demonstrates the efficacy of the proposed hybrid method for solving SOCQEiCP.

Recently, a new MIMO degree-of-freedom (DoF) model was proposed to allocate DoF resources for spatial multiplexing (SM) and interference cancellation (IC) in a multi-hop network. Although this DoF model promises many benefits, it hinges upon a global node ordering to keep track of IC responsibilities among all the nodes. An open question about this model is whether its global ordering property can be achieved among the nodes in the network through distributed operations. In this paper, we explore this question by studying DoF scheduling in a multi-hop MIMO network, with the objective of maximizing the minimum throughput among a set of sessions. We propose an efficient DoF scheduling algorithm to solve it and show that our algorithm only requires local operations. We prove that the resulting DoF scheduling solution is globally feasible and show that there exists a corresponding feasible global node ordering for IC, albeit such global ordering is implicit. Simulation results show that the solution values obtained by our algorithm are relatively close to the upper bound values computed by CPLEX solver, thereby indicating that our algorithm is highly competitive.

The beam-forming property associated with directional antennas introduces some unique problems that do not exist for omni-directional antennas and therefore significantly increases the design space for routing algorithms. A problem that can be solved when omni-directional antennas are used may become Non-deterministic Polynomial-time hard (NP-hard) when directional antennas are used. In this chapter, we discuss some algorithmic challenges associated with directional antennas and then present an in-depth case study. In the case study, we consider a wireless ad hoc network where each node employs a single-beam directional antenna and is provisioned with limited energy. We are interested in an online routing algorithm for successive multicast communication requests with the aim of maximizing network lifetime. We provide some important theoretical understanding on various multicast problems and deduce that even an offline version of this problem is NP-hard. Then we develop a highly competitive online routing algorithm that takes network lifetime consideration directly into iterative calculations and show that this algorithm provides consistently better performance than the current state-of-the-art algorithm considering only remaining energy. The theoretical results and routing algorithm in this chapter offer some important insights on algorithm design for energy-constrained wireless ad hoc networks with directional antennas.

In recent years, many resource allocation models have been developed to protect critical infrastructure by maximizing system resiliency or minimizing its vulnerability to disasters or disruptions. However, these are often computationally intensive and require simplifying assumptions and approximations. In this study, we develop a robust and representative, yet tractable, model for optimizing maintenance planning of generic network-structured systems (transportation, water, power, communication). The proposed modeling framework examines models that consider both linear and nonlinear objective functions and enhances their structure through suitable manipulations. Moreover, the designed models inherently capture the network topography and the stochastic nature of disruptions and can be applied to network-structured systems where performance is assessed based on network flow efficiency and mobility. The developed models are applied to the Istanbul highway system in order to assess their relative computational effectiveness and robustness using several test cases that consider single- and multiple-treatment types, and the problems are solved on the NEOS server using different available software. The results demonstrate that our models are capable of obtaining optimal solutions within a very short time. Furthermore, the linear model is shown to yield a good approximation to the nonlinear model (it determined solutions within 0.3% of optimality, on average). Managerial insights are provided in regard to the optimal policies obtained, which generally appear to favor selecting fewer links and applying a higher quality treatment to them.

This paper is concerned with a hospital staff scheduling problem wherein surgical operation times are stochastic. We formulate a complete recourse, scenario-based model for this problem, and develop a branch-and-cut (B&C) algorithm that is further hybridised with the Monte Carlo method (MCM). The proposed hybrid MCM-based approach is demonstrated to substantially reduce the required computational effort over a purely branch-and-cut methodology while producing near-optimal solutions having relatively small optimality gaps.

Cooperation has become an essential element in spectrum sharing between the primary and secondary networks. A new trend in cooperation is to allow the primary and secondary networks to cooperate on the node level for data forwarding. This new paradigm allows to pool network resources from both the primary and secondary networks and allows users in each network to access a much richer network infrastructure in a combined network. This paper offers an in-depth study of such node-level cooperation by explaining its optimal throughput curve-the maximum achievable throughput for both the primary and secondary users. We formulate the problem as a multicriteria optimization problem with the goal of maximizing the throughput of both the primary and secondary users. Through a novel approach based on weighted Chebyshev norm, we transform the multicriteria optimization problem into a single criteria optimization problem and find a sequence of Pareto-optimal points iteratively. Based on the Pareto-optimal points, we construct the throughput curve and show that it provides an e-approximation to the optimal curve. We prove some important properties of the optimal throughput curve. Through a case study, we show that the throughput region (the area under the throughput curve) under node-level cooperation is substantially larger than that when there is no node-level cooperation.

In this paper, we introduce a Reformulation-Linearization Technique-based open-source optimization software for solving polynomial programming problems (RLT-POS). We present algorithms and mechanisms that form the backbone of RLT-POS, including constraint filtering techniques, reduced RLT representations, and semidefinite cuts. When implemented individually, each model enhancement has been shown in previous papers to significantly improve the performance of the standard RLT procedure. However, the coordination between different model enhancement techniques becomes critical for an improved overall performance since special structures in the original formulation that work in favor of a particular technique might be lost after implementing some other model enhancement. More specifically, we discuss the coordination between (1) constraint elimination via filtering techniques and reduced RLT representations, and (2) semidefinite cuts for sparse problems. We present computational results using instances from the literature as well as randomly generated problems to demonstrate the improvement over a standard RLT implementation and to compare the performances of the software packages BARON, COUENNE, and SparsePOP with RLT-POS.

Distributed joint congestion control and routing optimization has received a significant amount of attention recently. To date, however, most of the existing schemes follow a key idea called the back-pressure algorithm. Despite having many salient features, the first-order subgradient nature of the back-pressure based schemes results in slow convergence and poor delay performance. To overcome these limitations, in this paper, we make a first attempt at developing a second-order joint congestion control and routing optimization framework that offers utility-optimality, queue-stability, fast convergence, and low delay. Our contributions in this paper are three-fold: i) we propose a new second-order joint congestion control and routing framework based on a primal-dual interior-point approach; ii) we establish utility-optimality and queue-stability of the proposed second-order method; and iii) we show how to implement the proposed second-order method in a distributed fashion.

In this chapter, we address the problem of optimally routing and sequencing a set of jobs over a network of flexible machines for the objective of minimizing the sum of completion times and the cost incurred, assuming stochastic job processing times. This problem is of particular interest for the production control in high investment, low volume manufacturing environments, such as pilot-fabrication of microelectromechanical systems (MEMS) devices. We model this problem as a two-stage stochastic program with recourse, where the first-stage decision variables are binary and the second-stage variables are continuous. This basic formulation lacks relatively complete recourse due to infeasibilities that are caused by the presence of re-entrant flows in the processing routes, and also because of potential deadlocks that result from the first-stage routing and sequencing decisions. We use the expected processing times of operations to enhance the formulation of the first-stage problem, resulting in good linear programming bounds and inducing feasibility for the second-stage problem. In addition, we develop valid inequalities for the first-stage problem to further tighten its formulation. Experimental results are presented to demonstrate the effectiveness of using these strategies within a decomposition algorithm (the L-shaped method) to solve the underlying stochastic program. In addition, we present heuristic methods to handle large-sized instances of this problem and provide related computational results.