A mathematical formulation of the loop pipelining problem

This paper presents a mathematical model for the loop pipelining problem that considers several parameters for optimization and supports any combination of resource and timing constraints. The unrolling degree of the loop is one of the variables explored by the model. By using Farey’s series, an optimal exploration of the unrolling degree is performed and optimal solutions not considered by other methods are obtained. Finding an optimal schedule that minimizes resource and register requirements is solved by using an Integer linear programming (ILP) model. A novel paradigm called branch and prune is proposed to eficiently converge towards the optimal schedule and prune the search tree for integer solutions, thus drastically reducing the running time. This is the first formulation that combines the unrolling degree of the loop with timing and resource constraints in a mathematical model that guarantees optimal solutions.Peer ReviewedPostprint (author's final draft

Spectrum Sharing in mmWave Cellular Networks via Cell Association, Coordination, and Beamforming

This paper investigates the extent to which spectrum sharing in mmWave networks with multiple cellular operators is a viable alternative to traditional dedicated spectrum allocation. Specifically, we develop a general mathematical framework by which to characterize the performance gain that can be obtained when spectrum sharing is used, as a function of the underlying beamforming, operator coordination, bandwidth, and infrastructure sharing scenarios. The framework is based on joint beamforming and cell association optimization, with the objective of maximizing the long-term throughput of the users. Our asymptotic and non-asymptotic performance analyses reveal five key points: (1) spectrum sharing with light on-demand intra- and inter-operator coordination is feasible, especially at higher mmWave frequencies (for example, 73 GHz), (2) directional communications at the user equipment substantially alleviate the potential disadvantages of spectrum sharing (such as higher multiuser interference), (3) large numbers of antenna elements can reduce the need for coordination and simplify the implementation of spectrum sharing, (4) while inter-operator coordination can be neglected in the large-antenna regime, intra-operator coordination can still bring gains by balancing the network load, and (5) critical control signals among base stations, operators, and user equipment should be protected from the adverse effects of spectrum sharing, for example by means of exclusive resource allocation. The results of this paper, and their extensions obtained by relaxing some ideal assumptions, can provide important insights for future standardization and spectrum policy.Comment: 15 pages. To appear in IEEE JSAC Special Issue on Spectrum Sharing and Aggregation for Future Wireless Network

Cyclic transfers in school timetabling

In this paper we propose a neighbourhood structure based on sequential/cyclic moves and a cyclic transfer algorithm for the high school timetabling problem. This method enables execution of complex moves for improving an existing solution, while dealing with the challenge of exploring the neighbourhood efficiently. An improvement graph is used in which certain negative cycles correspond to the neighbours; these cycles are explored using a recursive method. We address the problem of applying large neighbourhood structure methods on problems where the cost function is not exactly the sum of independent cost functions, as it is in the set partitioning problem. For computational experiments we use four real world data sets for high school timetabling in the Netherlands and England.We present results of the cyclic transfer algorithm with different settings on these data sets. The costs decrease by 8–28% if we use the cyclic transfers for local optimization compared to our initial solutions. The quality of the best initial solutions are comparable to the solutions found in practice by timetablers

Industrial and Tramp Ship Routing Problems: Closing the Gap for Real-Scale Instances

Recent studies in maritime logistics have introduced a general ship routing problem and a benchmark suite based on real shipping segments, considering pickups and deliveries, cargo selection, ship-dependent starting locations, travel times and costs, time windows, and incompatibility constraints, among other features. Together, these characteristics pose considerable challenges for exact and heuristic methods, and some cases with as few as 18 cargoes remain unsolved. To face this challenge, we propose an exact branch-and-price (B&P) algorithm and a hybrid metaheuristic. Our exact method generates elementary routes, but exploits decremental state-space relaxation to speed up column generation, heuristic strong branching, as well as advanced preprocessing and route enumeration techniques. Our metaheuristic is a sophisticated extension of the unified hybrid genetic search. It exploits a set-partitioning phase and uses problem-tailored variation operators to efficiently handle all the problem characteristics. As shown in our experimental analyses, the B&P optimally solves 239/240 existing instances within one hour. Scalability experiments on even larger problems demonstrate that it can optimally solve problems with around 60 ships and 200 cargoes (i.e., 400 pickup and delivery services) and find optimality gaps below 1.04% on the largest cases with up to 260 cargoes. The hybrid metaheuristic outperforms all previous heuristics and produces near-optimal solutions within minutes. These results are noteworthy, since these instances are comparable in size with the largest problems routinely solved by shipping companies

Cyclic transfers in school timetabling

In this paper we propose a neighbourhood structure based\ud on sequential/cyclic moves and a Cyclic Transfer algorithm for the high school timetabling problem. This method enables execution of complex moves for improving an existing solution, while dealing with the challenge of exploring the neighbourhood efficiently. An improvement graph is used in which certain negative cycles correspond to the neighbours; these cycles are explored using a recursive method. We address the problem of applying large neighbourhood structure methods on problems where the cost function is not exactly the sum of independent cost functions, as it is in the set partitioning problem. For computational experiments we use four real world datasets for high school timetabling in the Netherlands and England. We present results of the cyclic transfer algorithm with different settings on these datasets. The costs decrease by 8% to 28% if we use the cyclic transfers for local optimization compared to our initial solutions. The quality of the best initial solutions are comparable to the solutions found in practice by timetablers

Minimizing weighted total earliness, total tardiness and setup costs

The paper considers a (static) portfolio system that satisfies adding-up contraints and the gross substitution theorem. The paper shows the relationship of the two conditions to the weak dominant diagonal property of the matrix of interest rate elasticities. This enables to investigate the impact of simultaneous changes in interest rates on the asset demands.