arXiv subjects

Wei-Kun Chen

Publications and source records attributed to Wei-Kun Chen.

31 records · Page 2Linked to original sources

arXiv2023

Enabling Research through the SCIP Optimization Suite 8.0

The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. The focus of this paper is on the role of the SCIP Optimization Suite in supporting research. SCIP's main design principles are discussed, followed by a presentation of the latest performance improvements and developments in version 8.0, which serve both as examples of SCIP's application as a research tool and as a platform for further developments. Further, the paper gives an overview of interfaces to other programming and modeling languages, new features that expand the possibilities for user interaction with the framework, and the latest developments in several extensions built upon SCIP.

math.OC↗

arXiv2023

Towards Efficient Large-Scale Network Slicing: An LP Dynamic Rounding-and-Refinement Approach

In this paper, we propose an efficient algorithm for the network slicing problem which attempts to map multiple customized virtual network requests (also called services) to a common shared network infrastructure and allocate network resources to meet diverse service requirements. The problem has been formulated as a mixed integer linear programming (MILP) formulation in the literature. We first propose a novel linear programming (LP) relaxation of the MILP formulation. We show that compared with a natural LP relaxation of the MILP formulation, the novel LP relaxation is much more compact in terms of smaller numbers of variables and constraints, and much stronger in terms of providing a better LP bound, which makes it particularly suitable to be embedded in an LP relaxation based algorithm. Then we design an efficient two-stage LP dynamic rounding-and-refinement algorithm based on this novel LP relaxation. In the first stage, the proposed algorithm uses an LP dynamic rounding procedure to place the virtual network functions of all services into cloud nodes while taking traffic routing of all services into consideration; in the second stage, the proposed algorithm uses an iterative LP refinement procedure to obtain a solution for traffic routing of all services with their end-to-end delay constraints being satisfied. Compared with the existing algorithms which either have an exponential complexity or return a low-quality solution, our proposed algorithm achieves a better trade-off between the solution quality and the computational complexity. In particular, the worst-case complexity of our proposed algorithm is polynomial, which makes it suitable for solving large-scale problems. Numerical results demonstrate the effectiveness and efficiency of our proposed algorithm.

cs.IT↗

arXiv2023

Diversity Order Analysis for Quantized Constant Envelope Transmission

Quantized constant envelope (QCE) transmission is a popular and effective technique to reduce the hardware cost and improve the power efficiency of 5G and beyond systems equipped with large antenna arrays. It has been widely observed that the number of quantization levels has a substantial impact on the system performance. This paper aims to quantify the impact of the number of quantization levels on the system performance. Specifically, we consider a downlink single-user multiple-input-single-output (MISO) system with M-phase shift keying (PSK) constellation under the Rayleigh fading channel. We first derive a novel bound on the system symbol error probability (SEP). Based on the derived SEP bound, we characterize the achievable diversity order of the quantized matched filter (MF) precoding strategy. Our results show that full diversity order can be achieved when the number of quantization levels L is greater than the PSK constellation order M, i.e., L>M, only half diversity order is achievable when L=M, and the achievable diversity order is 0 when L<M. Simulation results verify our theoretical analysis.

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arXiv2022

A Cut-and-solve Algorithm for Virtual Machine Consolidation Problem

The virtual machine consolidation problem (VMCP) attempts to determine which servers to be activated, how to allocate virtual machines (VMs) to the activated servers, and how to migrate VMs among servers such that the summation of activated, allocation, and migration costs is minimized subject to the resource constraints of the servers and other practical constraints. In this paper, we first propose a new mixed integer linear programming (MILP) formulation for the VMCP. We show that compared with existing formulations, the proposed formulation is much more compact in terms of smaller numbers of variables or constraints, which makes it suitable for solving large-scale problems. We then develop a cut-and-solve (C&S) algorithm, a tree search algorithm to efficiently solve the VMCP to optimality. The proposed C&S algorithm is based on a novel relaxation of the VMCP that provides a stronger lower bound than the natural continuous relaxation of the VMCP, making a smaller search tree. By extensive computational experiments, we show that (i) the proposed formulation significantly outperforms existing formulations in terms of solution efficiency; and (ii) compared with standard MILP solvers, the proposed C&S algorithm is much more efficient.

cs.DS↗

arXiv2022

Optimal QoS-Aware Network Slicing for Service-Oriented Networks with Flexible Routing

In this paper, we consider the network slicing problem which attempts to map multiple customized virtual network requests (also called services) to a common shared network infrastructure and allocate network resources to meet diverse quality of service (QoS) requirements. We first propose a mixed integer nonlinear program (MINLP) formulation for this problem that optimizes the network resource consumption while jointly considers QoS requirements, flow routing, and resource budget constraints. In particular, the proposed formulation is able to flexibly route the traffic flow of the services on multiple paths and provide end-to-end (E2E) delay and reliability guarantees for all services. Due to the intrinsic nonlinearity, the MINLP formulation is computationally difficult to solve. To overcome this difficulty, we then propose a mixed integer linear program (MILP) formulation and show that the two formulations and their continuous relaxations are equivalent. Different from the continuous relaxation of the MINLP formulation which is a nonconvex nonlinear programming problem, the continuous relaxation of the MILP formulation is a polynomial time solvable linear programming problem, which makes the MILP formulation much more computationally solvable. Numerical results demonstrate the effectiveness and efficiency of the proposed formulations over existing ones.

cs.IT↗

arXiv2021

The SCIP Optimization Suite 8.0

The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. This paper discusses enhancements and extensions contained in version 8.0 of the SCIP Optimization Suite. Major updates in SCIP include improvements in symmetry handling and decomposition algorithms, new cutting planes, a new plugin type for cut selection, and a complete rework of the way nonlinear constraints are handled. Additionally, SCIP 8.0 now supports interfaces for Julia as well as Matlab. Further, UG now includes a unified framework to parallelize all solvers, a utility to analyze computational experiments has been added to GCG, dual solutions can be postsolved by PaPILO, new heuristics and presolving methods were added to SCIP-SDP, and additional problem classes and major performance improvements are available in SCIP-Jack.

math.OC↗

arXiv2021

Optimal Network Slicing for Service-Oriented Networks with Flexible Routing and Guaranteed E2E Latency

Network function virtualization is a promising technology to simultaneously support multiple services with diverse characteristics and requirements in the 5G and beyond networks. In particular, each service consists of a predetermined sequence of functions, called service function chain (SFC), running on a cloud environment. To make different service slices work properly in harmony, it is crucial to appropriately select the cloud nodes to deploy the functions in the SFC and flexibly route the flow of the services such that these functions are processed in the order defined in the corresponding SFC, the end-to-end (E2E) latency constraints of all services are guaranteed, and all cloud and communication resource budget constraints are respected. In this paper, we first propose a new mixed binary linear program (MBLP) formulation of the above network slicing problem that optimizes the system energy efficiency while jointly considers the E2E latency requirement, resource budget, flow routing, and functional instantiation. Then, we develop another MBLP formulation and show that the two formulations are equivalent in the sense that they share the same optimal solution. However, since the numbers of variables and constraints in the second problem formulation are significantly smaller than those in the first one, solving the second problem formulation is more computationally efficient especially when the dimension of the corresponding network is large. Numerical results demonstrate the advantage of the proposed formulations compared with the existing ones.

cs.NI↗

arXiv2021

An Efficient Quadratic Programming Relaxation Based Algorithm for Large-Scale MIMO Detection

Multiple-input multiple-output (MIMO) detection is a fundamental problem in wireless communications and it is strongly NP-hard in general. Massive MIMO has been recognized as a key technology in the fifth generation (5G) and beyond communication networks, which on one hand can significantly improve the communication performance, and on the other hand poses new challenges of solving the corresponding optimization problems due to the large problem size. While various efficient algorithms such as semidefinite relaxation (SDR) based approaches have been proposed for solving the small-scale MIMO detection problem, they are not suitable to solve the large-scale MIMO detection problem due to their high computational complexities. In this paper, we propose an efficient sparse quadratic programming (SQP) relaxation based algorithm for solving the large-scale MIMO detection problem. In particular, we first reformulate the MIMO detection problem as an SQP problem. By dropping the sparse constraint, the resulting relaxation problem shares the same global minimizer with the SQP problem. In sharp contrast to the SDRs for the MIMO detection problem, our relaxation does not contain any (positive semidefinite) matrix variable and the numbers of variables and constraints in our relaxation are significantly less than those in the SDRs, which makes it particularly suitable for the large-scale problem. Then we propose a projected Newton based quadratic penalty method to solve the relaxation problem, which is guaranteed to converge to the vector of transmitted signals under reasonable conditions. By extensive numerical experiments, when applied to solve large-scale problems, the proposed algorithm achieves better detection performance than a recently proposed generalized power method.

math.OC↗

arXiv2021

An efficient linear programming rounding-and-refinement algorithm for large-scale network slicing problem

In this paper, we consider the network slicing problem which attempts to map multiple customized virtual network requests (also called services) to a common shared network infrastructure and allocate network resources to meet diverse service requirements, and propose an efficient two-stage algorithm for solving this NP-hard problem. In the first stage, the proposed algorithm uses an iterative linear programming (LP) rounding procedure to place the virtual network functions of all services into cloud nodes while taking traffic routing of all services into consideration; in the second stage, the proposed algorithm uses an iterative LP refinement procedure to obtain a solution for traffic routing of all services with their end-to-end delay constraints being satisfied. Compared with the existing algorithms which either have an exponential complexity or return a low-quality solution, our proposed algorithm achieves a better trade-off between solution quality and computational complexity. In particular, the worst-case complexity of our proposed algorithm is polynomial, which makes it suitable for solving large-scale problems. Numerical results demonstrate the effectiveness and efficiency of our proposed algorithm.

cs.NI↗

arXiv2020

An exact separation algorithm for unsplittable flow capacitated network design arc-set polyhedron

In this paper, we concentrate on generating cutting planes for the unsplittable capacitated network design problem. We use the unsplittable flow arc-set polyhedron of the considered problem as a substructure and generate cutting planes by solving the separation problem over it. To relieve the computational burden, we show that, in some special cases, a closed form of the separation problem can be derived. For the general case, a brute-force algorithm, called exact separation algorithm, is employed in solving the separation problem of the considered polyhedron such that the constructed inequality guarantees to be facet-defining. Furthermore, a new technique is presented to accelerate the exact separation algorithm, which significantly decreases the number of iterations in the algorithm. Finally, a comprehensive computational study on the unsplittable capacitated network design problem is presented to demonstrate the effectiveness of the proposed algorithm.

math.OC↗

arXiv2020

Network Slicing for Service-Oriented Networks with Flexible Routing and Guaranteed E2E Latency

Network function virtualization is a promising technology to simultaneously support multiple services with diverse characteristics and requirements in the fifth generation and beyond networks. In practice, each service consists of a predetermined sequence of functions, called service function chain (SFC), running on a cloud environment. To make different service slices work properly in harmony, it is crucial to select the cloud nodes to deploy the functions in the SFC and flexibly route the flow of the services such that these functions are processed in sequence, the end-to-end (E2E) latency constraints of all services are guaranteed, and all resource constraints are respected. In this paper, we propose a new (mixed binary linear program) formulation of the above network slicing problem that optimizes the system energy efficiency while jointly considers the resource budget, functional instantiation, flow routing, and E2E latency requirement. Numerical results show the advantage of the proposed formulation compared to the existing ones.

cs.NI↗

arXiv2019

Combinatorial separation algorithms for the continuous knapsack polyhedra with divisible capacities

It is important to design separation algorithms of low computational complexity in mixed integer programming. We study the separation problems of the two continuous knapsack polyhedra with divisible capacities. The two polyhedra are the convex hulls of the sets which consist of $ n $ nonnegative integer variables, one unbounded continuous, $ m $ bounded continuous variables, and one linear constraint in either $ \geq $ or $ \leq $ form where the coefficients of integer variables are integer and divisible. Wolsey and Yaman (Math Program 156: 1--20, 2016) have shown that the polyhedra can be described by adding the two closely related families of partition inequalities. However, no combinatorial separation algorithm is known yet for the polyhedra. In this paper, for each polyhedron, we provide a combinatorial separation algorithm with the complexity of $ \mathcal{O}(nm+m\log m ) $. In particular, we solve the separation problem for the continuous $ \geq $-knapsack polyhedron by presenting a polynomial-time separation algorithm for the family of $ \geq $-partition inequalities. For the continuous $ \leq $-knapsack polyhedron, we derive the complemented partition inequalities, which dominate the $ \leq $-partition inequalities. The continuous $ \leq $-knapsack polyhedron is completely described with the addition of the proposed inequalities. We again show that the family of the proposed inequalities can be separated in polynomial time.

math.OC↗

arXiv2019

On the complexity of sequentially lifting cover inequalities for the knapsack polytope

The well-known sequentially lifted cover inequality is widely employed in solving mixed integer programs. However, it is still an open question whether a sequentially lifted cover inequality can be computed in polynomial time for a given minimal cover (Gu, Nemhauser, and Savelsbergh, INFORMS J. Comput., 26: 117--123, 1999). We show that this problem is NP-hard, thus giving a negative answer to the question.

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