Exact Integer Linear Programming Research Articles

Security-aware 5G RAN slice mapping with tiered isolation in physical-layer secured metro-aggregation elastic optical networks using heuristic-assisted DRL

The optical transport network (OTN) encryption technology is attractive to solve the physical-layer security in services for the light-path provision process. This paper mainly explores the security-aware 5G radio access network (RAN) slice mapping problem with the tiered isolation (TI) policy, which decides the solution for aggregating service into the physical-layer secured metro-aggregation elastic optical networks (MA-EONs). We first introduce the physical-layer secured OTNs and illustrate their differences from the traditional optical networks. Then, we formulate the 5G RAN slice mapping problem in physical-layer secured MA-EONs as an exact integer linear programming (ILP) model to minimize the average cost (AC), which consists of the number of utilized processing pools (PPs)/general-purpose processors (GPPs)/virtual machines (VMs), and maximum frequency slot index (MFSI) on the light-paths, meanwhile satisfying the given slice’s latency, isolation, and security requirements. After that, to overcome the non-scalability problem of the ILP model, a heuristic-assisted deep reinforcement learning (HA-DRL) algorithm is proposed to obtain a near-optimal solution for large-scale network scenarios, where the classical shortest path algorithm is employed in the DRL to shrink the size of the exploration space and accelerate the convergence process. Finally, we evaluate the proposed ILP model and HA-DRL algorithm through extensive simulations. Simulation results indicate that our proposed HA-DRL method can find approximate solutions to the ILP model in the small-scale network scenario. Furthermore, the HA-DRL method can also achieve higher resource efficiency compared with benchmark heuristic first-fit algorithms in the large-scale network scenario. In comparison to the first-fit algorithm benchmark, the proposed HA-DRL can achieve up to 9.4% AC reduction in large-scale network scenarios.

Multi-robot task allocation in disaster response: Addressing dynamic tasks with deadlines and robots with range and payload constraints

This paper tackles a class of multi-robot task allocation (MRTA) problems called “Single-Task Robots and Single-Robot Tasks” or SR–ST problems, subject to the following additional characteristics: tasks with deadlines, tasks that are generated during the mission, and robots with range and payload constraints (thus requiring multiple tours per robot). While these characteristics are typical of various disaster response and commercial applications, there is a lack of online MRTA solutions to address them. To solve this class of complex MRTA problems, an efficient online method (which is also suitable for decentralized deployment) is developed based on the construction and weighted matching of bipartite graphs. An exact integer linear programming (ILP) formulation of this class of MRTA problems is also developed, the solution of which serves both as an offline MRTA approach and as a provably optimal benchmark against which the online method is compared. The new methods are applied to a flood response problem where multiple unmanned aerial vehicles must respond to victims spread out over a large area. The results show that the new online algorithm closely trails the offline ILP method in terms of task completion performance, while being >103 times more computationally efficient compared to the ILP method. Dedicated case studies provide further insights into the favorable scalability of the online method with an increasing number of UAVs — offering up to 46% higher task completion compared to a random walk baseline in huge 1000-task problems. Lastly, application to a slightly different class of SR–ST problems and comparison of the ensuing results with that of corresponding state-of-the-art methods demonstrate the potential wider applicability of the proposed online MRTA method.

A Fast Heuristic for Gateway Location in Wireless Backhaul of 5G Ultra-Dense Networks

In 5G ultra-dense networks, a distributed wireless backhaul is an attractive solution for forwarding traffic to the core. The macro-cell coverage area is divided into many small cells. A few of these cells are designated as gateways and are linked to the core by high-capacity fiber optic links. Each small cell is associated with one gateway and all small cells forward their traffic to their respective gateway through multi-hop mesh networks. We investigate the gateway location problem and show that finding near-optimal gateway locations improves the backhaul network capacity. An exact p-median integer linear program is formulated for comparison with our novel K-GA heuristic that combines a Genetic Algorithm (GA) with K-means clustering to find near-optimal gateway locations. We compare the performance of K-GA with six other approaches in terms of average number of hops and backhaul network capacity at different node densities through extensive Monte Carlo simulations. All approaches are tested in various user distribution scenarios, including uniform distribution, bivariate Gaussian distribution, and cluster distribution. In all cases, K-GA provides near-optimal results, achieving average number of hops and backhaul network capacity within 2% of optimal while saving an average of 95% of the execution time.

A Novel Genetic Algorithm-Based Methodology for Large-Scale Fixed Charge Plus Routing Network Design Problem With Efficient Operators

In this paper, we present a novel approach that addresses the problem of large-scale network topology design and routing. There are research works that used exact methodologies based on Integer Linear Programming (ILP) models to develop potential solutions for this problem. However, this problem is computationally NP-hard, thus solving it is hugely demanding on computational power for large-scale networks, and in many cases, it is not even possible to generate a solution with a reasonable optimality gap. This paper presents a hybrid algorithm based on the Genetic Algorithm with efficiently designed genetic operators. This algorithm aims to design the topology of large-scale networks and generate a routing configuration for a set of predefined traffic demands on the networks while keeping the total cost of design and routing at a minimum. The results have been compared to an exact ILP model, a relaxed ILP model, and a customized GA as benchmarks for validation purposes. These comparisons showed that the proposed algorithm significantly outperforms the ILP solutions in all of the large-scale network configurations that were used as case studies.

Exact integer linear programming solvers outperform simulated annealing for solving conservation planning problems.

The resources available for conserving biodiversity are limited, and so protected areas need to be established in places that will achieve objectives for minimal cost. Two of the main algorithms for solving systematic conservation planning problems are Simulated Annealing (SA) and exact integer linear programing (EILP) solvers. Using a case study in BC, Canada, we compare the cost-effectiveness and processing times of SA used in Marxan versus EILP using both commercial and open-source algorithms. Plans for expanding protected area systems based on EILP algorithms were 12–30% cheaper than plans using SA, due to EILP’s ability to find optimal solutions as opposed to approximations. The best EILP solver we examined was on average 1,071 times faster than the SA algorithm tested. The performance advantages of EILP solvers were also observed when we aimed for spatially compact solutions by including a boundary penalty. One practical advantage of using EILP over SA is that the analysis does not require calibration, saving even more time. Given the performance of EILP solvers, they can be used to generate conservation plans in real-time during stakeholder meetings and can facilitate rapid sensitivity analysis, and contribute to a more transparent, inclusive, and defensible decision-making process.

Complexity and heuristics for the weighted max cut‐clique problem

AbstractIn market basket analysis (MBA), the goal is to understand human behavior to maximize sales. A clear behavior is buying correlated items. As a consequence, the determination of a set of items with a high correlation with others is a valuable tool for MBA. In this work, we address a combinatorial optimization problem with valuable applications to MBA, especially in marketing and product placement. The focus will be on the combinatorial problem and not on specific applications. For any given undirected graph (where the nodes are items and the edges represent correlation), we aim to find the clique such that the number of edges shared between and is maximized. This problem is known in the literature as the max cut‐clique (MCC) problem. We can generalize this problem by considering the weights associated with each edge. In this context, we are interested in finding the clique such that the weighted sum associated with each edge shared between and is maximized. The weighted version of the MCC problem is known as the maximum edge‐weight neighborhood clique (MEWNC) problem. The main contributions of this paper are threefold. First, the computational complexity of both the MCC and MEWNC problems is established. Specifically, we prove that the MCC and MEWNC problems belong to the class of ‐complete problems. Second, an exact integer linear programming (ILP) formulation for the MEWNC problem is proposed. Third, a full greedy randomized adaptive search procedure/variable neighborhood descent methodology enriched with a tabu search is here developed, where the main components are novel neighborhood structures and a restricted candidate list that trade greediness for randomization in a multistart fashion. A dynamic tabu list considers a bounding technique based on the previous analysis. Finally, a fair comparison between our hybrid algorithm and a globally optimal solution using the ILP formulation confirms that a globally optimal solution is found by our heuristic for graphs with hundreds of nodes, but it is more efficient than the exact solution in terms of time and memory requirements.

Mathematical formulations for large scale check-in counter allocation problem

Strategic planning of check-in counter allocation with a focus on passenger waiting time is essential for airport operators to accommodate airline departures. This article proposes novel exact integer linear programming formulations for implementing first-in-first-out queue discipline, controlling waiting time and determining variable counter allocation with adjacency constraints for real world problems. Exact formulations in the existing literature handle small problems but do not address queue discipline and explicit control of waiting time. With our formulations, we solved live problems huge in size compared to those reported in the literature. The solutions are very efficient with passenger waiting times well below the international norms and high counter utilization.

Computing the spark: mixed-integer programming for the (vector) matroid girth problem

We investigate the NP-hard problem of computing the spark of a matrix (i.e., the smallest number of linearly dependent columns), a key parameter in compressed sensing and sparse signal recovery. To that end, we identify polynomially solvable special cases, gather upper and lower bounding procedures, and propose several exact (mixed-)integer programming models and linear programming heuristics. In particular, we develop a branch and cut scheme to determine the girth of a matroid, focussing on the vector matroid case, for which the girth is precisely the spark of the representation matrix. Extensive numerical experiments demonstrate the effectiveness of our specialized algorithms compared to general-purpose black-box solvers applied to several mixed-integer programming models.

New heuristics for the RCPSP with multiple overlapping modes

Activity overlapping in project management and concurrent engineering allows a downstream activity to start before the end of its upstream activity based on some preliminary information and feedback. Because the preliminary information can be issued at multiple stages during an upstream activity’s execution, the downstream activity may have multiple overlapping modes. Project scheduling with activity overlapping has a wide range of applications in manufacturing, R&D, construction and professional service industries. An optimal overlapping plan may help project manager accelerate project progress effectively with improved rate of investment. In this research, we study a resource-constrained project scheduling problem with multiple overlapping modes, which is NP-hard. To obtain high-quality near-optimal solutions, we formulate it as a dynamic program (DP), and develop a rollout policy based approximate dynamic programming (ADP) algorithm to obtain near-optimal policy efficiently. Our rollout policy sequentially improves over a priority-rule base policy. A rollout procedure based on pre-processing of overlapping options is also devised which we call pre-rollout. The pre-rollout improves over the rollout in some instances with moderately more computational time. A comprehensive experiment is performed on the PSPLIB benchmark instances. Computational results show that our rollout policy and the pre-rollout procedure significantly outperform the exact integer linear programming (ILP) solutions in both solution quality and computational time for medium and large instances.

Scratchpad-Memory Management for Multi-Threaded Applications on Many-Core Architectures

Contemporary many-core architectures, such as Adapteva Epiphany and Sunway TaihuLight, employ per-core software-controlled Scratchpad Memory (SPM) rather than caches for better performance-per-watt and predictability. In these architectures, a core is allowed to access its own SPM as well as remote SPMs through the Network-On-Chip (NoC). However, the compiler/programmer is required to explicitly manage the movement of data between SPMs and off-chip memory. Utilizing SPMs for multi-threaded applications is even more challenging, as the shared variables across the threads need to be placed appropriately. Accessing variables from remote SPMs with higher access latency further complicates this problem as certain links in the NoC may be heavily contended by multiple threads. Therefore, certain variables may need to be replicated in multiple SPMs to reduce the contention delay and/or the overall access time. We present Coordinated Data Management (CDM), a compile-time framework that automatically identifies shared/private variables and places them with replication (if necessary) to suitable on-chip or off-chip memory, taking NoC contention into consideration. We develop both an exact Integer Linear Programming (ILP) formulation as well as an iterative, scalable algorithm for placing the data variables in multi-threaded applications on many-core SPMs. Experimental evaluation on the Parallella hardware platform confirms that our allocation strategy reduces the overall execution time and energy consumption by 1.84× and 1.83× , respectively, when compared to the existing approaches.

Balanced connected task allocations for multi-robot systems: An exact flow-based integer program and an approximate tree-based genetic algorithm

Task allocation for a multi-robot system is often imposed with various constraints to promote efficiency and avoid unwanted consequences. This study focuses on the min-max balanced connected q-partition problem (BCPq) that seeks the early completion time of a multi-robot system while satisfying mission constraints. In the problem, each environmental region is modeled as a weighted node of a graph and the graph is to be partitioned into a predefined number, q, of disjoint node sets, such that nodes in each set are connected and the largest “sum of the set” is as small as possible. The problem is NP-hard in general cases, and has a brute-force search space exponential to the number of nodes. BCPq arises in many fields besides robotics. To date, existing work has mainly been conducted on special versions of the problem, such as small q or special types of graphs. In this study, we propose two approaches for the general case: one is exact and suitable for graphs of less than 200 nodes, while the other is approximate and can handle graphs with up to 3000 nodes. Specifically, this study presents the first exact mixed integer linear program (MILP) in the literature that can partition an arbitrary graph into a given arbitrary number of components. The MILP is based on a flow model and can solve graphs with 100 more nodes than the existing MILP that can only tackle 2-partition in the q=2 case. The study also presents an approximate genetic algorithm (GA) based on tree partition and tree evolution. It is the first GA that can handle BCPq (q ≥ 2) problems. On graphs of less than 500 nodes and 2-partition, the GA achieved all the optima in 20 runs. On q ≤ 12, this GA also can achieve results close to the optima after a few individuals were evolved, i.e., a gap smaller than 3% of the ideal average value. Moreover, the GA is scalable to q as the consumed time is nearly stable, independent of q.

An Approximation Algorithm for the Two-Node-Connected Star Problem with Steiner Nodes

The goal in topological network design is to build a minimum-cost topology meeting specific real-life constraints. There is a cost-robustness trade-off under single and multiple failures.Previous works in the field suggest that a backbone composed by a two-node-connected toplogy provides savings with respect to elementary cycles. Consequently, we introduce the Two-Node Connected Star Problem with Steiner Nodes (2NCSP-SN). The goal is to design a minimum-cost topology, where the backbone is two-node connected, the access network is connected in a star topology or by direct links to the backbone, and optional nodes (called Steiner nodes) could be included in the solution. The 2NCSP-SN belongs to the class of NP-Hard problems. This promotes the development of heuristics and approximation algorithms.An approximation algorithm of factor 4α for the 2NCSP-SN is introduced, being α≥1/2 the cost-ratio between backbone and access links. This is a generalization of the well-known factor 2 for the design of minimum-cost two-connected spanning networks (if we fix α=1/2). Finally, an exact Integer Linear Programming (ILP) formulation is proposed in order to highlight the effectiveness of the approximation algorithm. The results confirm a small gap between the globally optimum solution and the topology offered by our approximation algorithm when the ratio α is close to 1/2.

Finding local genome rearrangements

BackgroundThe double cut and join (DCJ) model of genome rearrangement is well studied due to its mathematical simplicity and power to account for the many events that transform gene order. These studies have mostly been devoted to the understanding of minimum length scenarios transforming one genome into another. In this paper we search instead for rearrangement scenarios that minimize the number of rearrangements whose breakpoints are unlikely due to some biological criteria. One such criterion has recently become accessible due to the advent of the Hi-C experiment, facilitating the study of 3D spacial distance between breakpoint regions.ResultsWe establish a link between the minimum number of unlikely rearrangements required by a scenario and the problem of finding a maximum edge-disjoint cycle packing on a certain transformed version of the adjacency graph. This link leads to a 3/2-approximation as well as an exact integer linear programming formulation for our problem, which we prove to be NP-complete. We also present experimental results on fruit flies, showing that Hi-C data is informative when used as a criterion for rearrangements.ConclusionsA new variant of the weighted DCJ distance problem is addressed that ignores scenario length in its objective function. A solution to this problem provides a lower bound on the number of unlikely moves necessary when transforming one gene order into another. This lower bound aids in the study of rearrangement scenarios with respect to chromatin structure, and could eventually be used in the design of a fixed parameter algorithm with a more general objective function.

Controlled Islanding Solution for Large-Scale Power Systems

Intentional Controlled Islanding (ICI) has been proposed as a corrective measure of last resort to split the power system into several sustainable islands and prevent cascading outages. This paper proposes a novel ICI algorithm based on a linear programming (LP) formulation that directly determines an islanding solution with minimal power-flow disruption for any given number of islands, while ensuring that each island contains only coherent generators. In addition, the proposed algorithm enables operators to constrain any transmission line to be excluded from the solution, allows the control of the size of islands and ensures their connectivity. The basis of the proposed LP formulation is an exact mixed integer linear programming (MILP) formulation. A search space reduction procedure that generates additional constraints for reducing the search space of the MILP is also proposed. In most cases, these additional constraints are enough for the relaxed MILP formulation (LP formulation) to generate optimal solutions. Nonetheless, the proposed LP formulation is executed as a part of a recursive linearization procedure, which ensures that optimal solutions are always obtained. Multiple simulation results demonstrate the ability of the proposed LP ICI algorithm to meet the requirement of real-time controlled islanding in large-scale power systems.

Efficient Algorithms for Flexible Sweep Coverage in Crowdsensing

Sweep coverage is an important covering technique in mobile crowdsensing, in which users or participants are employed to periodically monitor a set of points of interest (POIs) each with a weight indicating the value of its information to be collected. Traditionally, each user proposes a route along which there is a set of POIs to be monitored. The task is to select a set of participants such that the total weight of the monitored POIs is maximized. However, in real applications, users should have the flexibility to offer several preferred routes. This arises our studied maximum sweep assignment problem with flexibility, where each participant proposes several routes, and the new task is to strategically assign each participant a route among their choices in which the way maximizes the total weight of the monitored POIs. In this paper, we first prove that the problem is ${\mathcal{ NP}}$ -complete and then devise two novel approximation algorithms with ratios 0.5 and 0.632. Experiments are also conducted to evaluate algorithms’ practical performance. The results demonstrate that the proposed approximate methods are significantly faster (with up to two orders of magnitude runtime reduction) than the exact integer linear programming solution. In addition, we theoretically study another flexible sweep coverage model in which it costs to hire each user, and the goal is to cover all POIs multiple times (for more complete and accurate information) while minimizing the total hiring cost.

Energy-Aware Provisioning in Optical Cloud Networks

Cloud computing has recently emerged as a dominant Internet service computing model due to its “pay-as-you-go” and “elastic service” features. Cloud computing systems are usually composed of distributed datacenters, which leverage virtualization technology to provide a scalable and reliable service. Optical networks are recognized as promising next-generation core networks for connecting these distributed datacenters due to their characteristics such as high bandwidth provisioning, low latency, low bit error rate, etc. However, concern about the ever-increasing energy consumption of cloud computing systems together with core networks has been raised due to high electricity bills as well as environmental pollution. In this paper, we study the Energy-aware Provisioning in Optical Cloud Networks (EPOCN) problem for both dynamic and static cases. When traffic requests arrive in an online fashion, we propose a polynomial-time energy-aware routing algorithm to solve the dynamic EPOCN problem. Simulations show that our energy-aware routing algorithm brings more energy savings in comparison to a shortest path-based routing algorithm and a traffic grooming algorithm. On the other hand, we show that the EPOCN problem in the static case (the traffic matrix is known in advance) is NP-hard. We further divide this problem into (1) the Energy-Aware Routing (EAR) problem in optical networks and (2) the Energy-efficient Server and Switch Allocation (ESSA) problem in datacenter networks. Considering these two (sub)problems are still NP-hard, we present an exact Integer Linear Program (ILP) and a heuristic to solve each problem. We also conduct simulations to compare the proposed ILPs and heuristics in terms of energy consumption and running time.

Two‐node‐connected star problem

AbstractIn this study, a two‐node‐connected star problem (2NCSP) is introduced. We are given a simple graph and internal and external costs for each link of the graph. The goal is to find the minimum‐cost spanning subgraph, where the core is two‐node‐connected and the remaining external nodes are connected to the core. First, we show that the 2NCSP belongs to the class of NP‐hard computational problems. Therefore, a greedy randomized adaptive search procedure (GRASP) heuristic is developed, enriched with a variable neighborhood descent (VND). The neighborhood structures include exact integer linear programming models to find the best paths and two‐node‐connected replacements, as well as a shaking operation in order to prevent being trapped in a local minima. The ring star problem (RSP) represents a relevant model in network optimization, where the core is a ring instead of an arbitrary two‐node‐connected graph. We contrast our GRASP/VND methodology with a previous reference work on the RSP in order to highlight the effectiveness of our heuristic. The heuristic is competitive, and the best results produced for several instances so far are under study. In this study, a discussion of the results and trends for future work are provided.

Efficient modularity density heuristics for large graphs

Modularity density maximization is a community detection optimization problem which improves the resolution limit degeneracy of modularity maximization. This paper presents seven scalable heuristics for modularity density and compares them with literature results from exact mixed integer linear programming and GAOD, iMeme-Net, HAIN, and BMD-λ heuristics. The results are also compared with CNM and Louvain, which are scalable heuristics for modularity maximization. The results suggest that our seven heuristics are faster than GAOD, iMeme-Net, HAIN, and BMD-λ modularity density heuristics. Our experiments also show that some of our heuristics surpassed the objective function value reported by iMeme-Net, Hain, and BMD-λ for some real graphs. Our seven heuristics were tested with real graphs from the Stanford Large Network Dataset Collection and the experiments show that they are scalable. This feature was confirmed by an amortized complexity analysis which reveals average linear time for three of our heuristics. Hypothesis tests suggest that four proposed heuristics are state-of-the-art since they are scalable for hundreds of thousands of nodes for the modularity density problem, and they find the high objective value partitions for the largest instances. Ground truth experiments in artificial random graphs were performed and suggest that our heuristics lead to better cluster detection than both CNM and Louvain.

An exact extended formulation for the unrelated parallel machine total weighted completion time problem

The plethora of research on $$\mathcal {NP}$$NP-hard parallel machine scheduling problems is focused on heuristics due to the theoretically and practically challenging nature of these problems. Only a handful of exact approaches are available in the literature, and most of these suffer from scalability issues. Moreover, the majority of the papers on the subject are restricted to the identical parallel machine scheduling environment. In this context, the main contribution of this work is to recognize and prove that a particular preemptive relaxation for the problem of minimizing the total weighted completion time (TWCT) on a set of unrelated parallel machines naturally admits a non-preemptive optimal solution and gives rise to an exact mixed integer linear programming formulation of the problem. Furthermore, we exploit the structural properties of TWCT and attain a very fast and scalable exact Benders decomposition-based algorithm for solving this formulation. Computationally, our approach holds great promise and may even be embedded into iterative algorithms for more complex shop scheduling problems as instances with up to 1000 jobs and 8 machines are solved to optimality within a few seconds.

Finding Outbreak Trees in Networks with Limited Information

Real-time control of infectious disease outbreaks represents one of the greatest epidemiological challenges currently faced. In this paper we address the problem of identifying contagion patterns responsible for the spread of a disease in a network, which can be applied in real-time to evaluate an ongoing outbreak. We focus on the scenario where limited information, i.e. infection reports which may or may not include the actual source, is available during an ongoing outbreak and we seek the most likely infection tree that spans at least a set of known infected nodes. This problem can be represented using a maximum likelihood constrained Steiner tree model where the objective is to find a spanning tree with an assignment of integer nodes weights. We propose a novel formulation and solution method based on a two-step heuristic which (1) reduces the initial graph using a polynomial time algorithm designed to find feasible infection paths and (2) solves an exact mixed integer linear programming reformulation of the maximum likelihood model on the resulting subgraph. The proposed methodology can be applied to outbreaks which may evolve from multiple sources. Simulated contagion episodes are used to evaluate the performance of our solution method. Our results show that the approach is computationally efficient and is able to reconstruct a significant proportion of the outbreak, even in the context of low levels of information availability.