The Group Theoretic Approach and Decomposition for Integer Linear Programming

Using cutting planes in an interactive reference point approach for multiobjective integer linear programming problems

This paper presents a distributed server allocation model with preventive start-time optimization against a single server failure. The presented model preventively determines the assignment of servers to users under each failure pattern to minimize the largest maximum delay among all failure patterns. We formulate the proposed model as an integer linear programming (ILP) problem. We prove the NP-completeness of the considered problem. As the number of users and that of servers increase, the size of ILP problem increases; the computation time to solve the ILP problem becomes excessively large. We develop a heuristic approach that applies simulated annealing and the ILP approach in a hybrid manner to obtain the solution. Numerical results reveal that the developed heuristic approach reduces the computation time by 26% compared to the ILP approach while increasing the largest maximum delay by just 3.4% in average. It reduces the largest maximum delay compared with the start-time optimization model; it avoids the instability caused by the unnecessary disconnection permitted by the run-time optimization model.

As millimeter wave (mmWave) technology becomes more integrated into today's communication infrastructure, its application to mobile scenarios has attracted considerable interests. In particular, mmWave technology is one of the leading candidates in Vehicle-to-Everything (V2X) community to address the ever-rising data exchange demand from vehicles. However, the inherent directionality of the technology poses challenges to peer discovery and transmission scheduling in typical V2X scenarios, causing significant loss of network capacity. To mitigate this issue, we propose a novel sub-6 GHz V2X-assisted synchronous mmWave communication scheduler in this paper. The sub-6 GHz channel serves as control channel for mmWave scheduling. The scheduler carefully considers data importance and freshness in determining communication schedule, such that network utility across mmWave links is maximized. We formulate the scheduling problem into an integer linear programming (ILP) problem. However, ILP problem is NP-hard and has exponential computational complexity for the worst cases. We then develop a scheduling algorithm, maximum weight matching based iterative algorithm (MWMIA), that operates in polynomial time with performance guarantees for the NP-hard ILP, by leveraging structural properties of link conflicts. Comparative simulation studies verify the effectiveness of our scheduler against other solutions.

A suggested algorithm to solve triangular fuzzy rough integer linear programming (TFRILP) problems with α-level is introduced in this paper in order to find rough value optimal solutions and decision rough integer variables, where all parameters and decision variables in the constraints and the objective function are triangular fuzzy rough numbers. In real-life situations, the parameters of a linear programming problem model may not be defined precisely, because of the current market globalization and some other uncontrollable factors. In order to solve this problem, a proper methodology is adopted to solve the TFRILP problems by the slice-sum method with the branch-and-bound technique, through which two fuzzy integers linear programming (FILP) problems with triangular fuzzy interval coefficients and variables were constructed. One of these problems is an FILP problem, where all of its coefficients are the upper approximation interval and represent rather satisfactory solutions; the other is an FILP problem, where all of its coefficients are the lower approximation interval and represent completely satisfactory solutions. Moreover, α-level at α = 0.5 is adopted to find some other rough value optimal solutions and decision rough integer variables. Integer programming is used, since a lot of the linear programming problems require that the decision variables be integers. In addition, the motivation behind this study is to enable the decision makers to make the right decision considering the proposed solutions, while dealing with the uncertain and imprecise data. A flowchart is also provided to illustrate the problem-solving steps. Finally, two numerical examples are given to clarify the obtained results.

Data-parallel applications generate a mix of coflows with and without deadlines. Deadline coflows are mission-critical and must be completed within deadlines, while the non-deadline coflows desire to be completed as soon as possible. Scheduling such mix-coflows is an important problem in modern datacenters. However, existing solutions only focus on one of the two types of coflows: they either solely concentrate on meeting the deadlines of deadline-aware coflows or reducing the coflow completion times (CCTs) of non-deadline coflows. In this article, we study the problem of optimizing deadline and non-deadline coflows simultaneously. To this end, we present a new optimization framework, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">mixCoflow</i> , to schedule deadline coflows to minimize and balance their bandwidth footprint, such that non-deadline coflows can be scheduled as early as possible. Specifically, we develop the mathematical model and formulate the scheduling problem for deadline coflows as a lexicographical min-max integer linear programming (ILP) problem. Through rigorous theoretical analysis, this ILP problem has been proved to be equivalent to a linear programming (LP) problem that can be solved with standard LP solvers. By solving this LP, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">mixCoflow</i> is able to balance the bandwidth footprint of deadline coflows while guaranteeing their deadlines. As a result, non-deadline coflows can be scheduled as soon as possible whenever they arrive. To demonstrate the effectiveness of our work, we have conducted extensive simulations based on a widely used Facebook data trace. The simulation results verify that <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">mixCoflow</i> can achieve significant improvement on the average CCT of non-deadline coflows, at no expense of increasing the deadline miss rates of deadline coflows, when compared to the state-of-art solutions.

Ranking in quadratic integer programming problems

In elastic optical networks (EONs), a major obstacle to using the spectrum resources efficiently is the spectrum fragmentation. In the literature, several defragmentation approaches have been presented. For 1+1 path protection, conventional defragmentation approaches consider designated primary and backup paths. This exposes the spectrum to fragmentations induced by the primary lightpaths, which are not to be disturbed in order to achieve hitless defragmentation. This paper proposes a defragmentation scheme using path exchanging in 1+1 path protected EONs. We exchange the path function of the 1+1 protection with the primary toggling to the backup state, while the backup becomes the primary. This allows both lightpaths to be reallocated during the defragmentation process, while they work as backup, offering hitless defragmentation. Considering path exchanging, we define a static spectrum reallocation optimization problem that minimizes the spectrum fragmentation while limiting the number of path exchanging and reallocation operations. We then formulate the problem as an integer linear programming (ILP) problem. We prove that a decision version of the defined static reallocation problem is NP-complete. We present a spectrum defragmentation process for dynamic traffic, and introduce a heuristic algorithm for the case that the ILP problem is not tractable. The simulation results show that the proposed scheme outperforms the conventional one and improves the total admissible traffic up to 10%.

Recently, space-division multiplexing (SDM) has been incorporated with elastic optical networks (EONs) to enhance the fiber capability, which forms space-division multiplexing-based elastic optical networks (SDM-EONs). During transmission of optical signals through multi-core fibers, inter-core crosstalk (XT) and intra-core physical layer impairments (PLIs) arise, which deteriorate the signal quality. Existing models typically handle inter-core XT and intra-core PLIs separately and set a single XT threshold for each modulation format, which results in an unacceptable lightpath due to the degradation of signal quality or leads to inefficient spectrum utilization. This paper proposes a routing, modulation, spectrum, and core allocation (RMSCA) model for SDM-EONs to consider inter-core XT and intra-core PLIs jointly. For each modulation format, it sets different XT thresholds and transmission reaches according to inter-core XT and intra-core PLIs. An optimization problem is formulated as an integer linear programming (ILP) problem. We prove that the RMSCA decision problem is NP-complete. We introduce a heuristic algorithm when the ILP problem is not tractable. Numerical results demonstrate that, by setting several XT limits for each modulation format, the proposed model increases spectrum efficiency compared to a benchmark model based on the literature.

Network Function Virtualization (NFV) is a paradigm that virtualizes traditional network functions and instantiates Virtual Network Functions (VNFs) as software instances separate from hardware appliances. Service Chaining (SC), seen as one of the major NFV use cases, provides customized services to users by concatenating VNFs. A VNF placement model for SC that relaxes the visit order constraints of requested VNFs has been considered. Relaxing the VNF visit order constraints reduces the number of VNFs which need to be placed in the network. However, since the model does not permit any loop within an SC path, the efficiency of utilization of computation resources deteriorates in some topologies. This paper proposes a VNF placement model for SC which minimizes the cost for placing VNFs and utilizing link capacity while allowing both relaxation of VNF visit order constraints and configuration of SC paths including loops. The proposed model determines routes of requested SC paths, which can have loops, by introducing a logical layered network generated from an original physical network. This model is formulated as an Integer Linear Programming (ILP) problem. A heuristic algorithm is introduced for the case that the ILP problem is not tractable. Simulation results show that the proposed model provides SC paths with smaller cost compared to the conventional model.

This paper addresses the fault diagnosis problem in discrete event systems using backward conflict-free Petri nets, where two different transitions have no common output places. The notion of generalized markings is employed, where the number of tokens in a place can be negative. Based on the special structures of backward conflict-free Petri nets and the generalized marking corresponding to an observed transition sequence, an integer linear programming (ILP) problem is constructed where the numbers of unknown integer variables and constraints are independent of the length of the observed transition sequence. A diagnosis algorithm is proposed by associating two different objective functions with the ILP problem and solving it. The computational efficiency of the proposed algorithm depends on the net structure only, regardless of the length of an observed transition sequence.

An accelerated Benders decomposition approach for virtual base station formation in stochastic Cloud-RANs

Space-division multiplexing-based elastic optical networks (SDM-EONs) enhance the fiber capacity. Inter-core crosstalk (XT) and intra-core physical layer impairments (PLIs) occur in the multi-core fiber and degrade the optical signal. An existing model separately considers inter-core XT and intra-core PLIs, and sets a single XT threshold to each modulation format. This can lead to an unacceptable lightpath due to signal degradation or the occurrence of spectrum inefficiency. This paper proposes a routing, modulation, spectrum, and core allocation (RMSCA) model, which jointly considers inter-core XT and intra-core PLIs for SDM-EONs. The proposed model sets multiple XT thresholds for each modulation format based on inter-core XT and intra-core PLIs. We present an optimization problem and formulate it as an integer linear programming (ILP) problem. We introduce a heuristic algorithm for a network where the ILP problem is not tractable. Numerical results observe that the proposed model improves the spectrum efficiency by setting multiple XT thresholds to each modulation format.

The poor performance at cell-edge communication in most existed systems is a common and challenging problem. In terms of this issue, we propose a strategy of resource allocation based on Carrier Aggregation (CA) to improve cell-edge performance. This paper starts from the point of resource allocation, aiming to improve cell-edge performance through rational and effective resource allocation schemes inside cells. Taking throughput and fairness along with business factor which represents the amount of loads into account, we define a novel utility function referring the general idea of proportional fair scheme. We firstly propose a centralized scheme in which the optimization problem is a 0-1 Integer Linear Programming (ILP) problem. By relaxing the 0-1 ILP problem to a LP problem, we get the optimal solution. Considering the difficulty in communication among carriers in some existed communication systems along with the complexity of the centralized scheme, we subsequently propose a distributed scheme. At last, simulation results show that both schemes perform outstandingly.

Global routing is an essential part of VLSI physical design, and has been traditionally solved using sequential or concurrent methods. In the sequential techniques, routes are generated one at a time based on a predetermined ordering. These methods are very fast, but because of their sequential nature can result in sub-optimal solutions. Concurrent techniques attempt to solve the problem using global optimization techniques. These methods can provide a global view of the circuit's routing, but take a considerable amount of time. A global router based on concurrent techniques is presented. The proposed technique formulates the global routing problem as an integer linear programming (ILP) problem. This model combines the traditional wire length minimization model with channel capacity minimization to obtain more accurate routings. In addition, the characteristics of the trees generated by our global router are investigated. A tree pruning technique, based on the characteristics of the trees, is developed to reduce the size of the ILP problem, and consequently reduce the solution time. The results show an average of 58% improvement in solving time without any loss in the quality of the results.

This paper proposes a deterministic two-stage mixed integer linear programming (TSMILP) approach to solve the reserve constrained dynamic economic dispatch (DED) problem considering valve-point effect (VPE). In stage one, the nonsmooth cost function and the transmission loss are piecewise linearized and consequently the DED problem is formulated as a mixed integer linear programming (MILP) problem, which can be solved by commercial solvers. In stage two, based on the solution obtained in stage one, a range compression technique is proposed to make a further exploitation in the subspace of the whole solution domain. Due to the linear approximation of the transmission loss, the solution obtained in stage two dose not strictly satisfies the power balance constraint. Hence, a forward procedure is employed to eliminate the error. The simulation results on four test systems show that TSMILP makes satisfactory performances, in comparison with the existing methods.