arXiv subjects

Wei-Kun Chen

Publications and source records attributed to Wei-Kun Chen.

At least 19 recordsLinked to original sources

arXiv2026

Enhancing Presolve in Mixed Integer Programming by Combining Probing and Dual Fixing

Probing and dual fixing are two powerful presolve techniques in mixed integer programming (MIP) solvers. Probing tentatively sets some binary variables to 0 or 1, applies linear constraint based domain propagation techniques to derive better variable bounds, and extracts useful information such as stronger variable implications and better global variable bounds. Dual fixing attempts to fix variables to lower or upper bounds while ensuring that at least one optimal solution is retained, as long as the problem was feasible. In this paper, we investigate how to combine the two approaches in MIP solvers to achieve a better performance. In particular, we first embed dual fixing into the probing framework, deriving more useful variables' implications for enhancing the capability of probing. Then, we develop an improved dual fixing technique where more variable fixings can be applied, and use the probing framework to detect the reductions. Computational results on the MIPLIB 2017 benchmark instances demonstrate the potential of the two proposed techniques in combining probing and dual fixing on the open-source MIP solver HiGHS.

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arXiv2026

Exploiting Variable Implications in Presolve for Mixed Integer Programming

Presolve for mixed integer programming (MIP) problems aims to eliminate redundant information, strengthen the formulation, and extract useful structural information for the subsequent branch-and-cut process. An important type of such structural information is the variable implications (VIs), which describe how a bound on a variable depends on a bound of a binary variable. In this paper, we develop two new presolve techniques that exploit VIs to derive reductions for MIP problems. The first technique, called VI aggregation, aggregates multiple VIs into a single inequality by using implications between a variable and a set of binary variables that form a clique. This aggregation can reduce the number of constraints and tighten the linear programming relaxation. The second technique, called VI-aware linear constraint propagation (LCP), builds on the standard LCP but incorporates VIs associated with the variable being tightened to derive more reductions and can derive tighter variable bounds. We show that although VI information is additionally considered, the tightest lower or upper bound of a variable can still be derived in linear time. Moreover, compared with a state-of-the-art approach in the literature, the proposed VI-aware LCP can derive tighter variable bounds. Computational results on MIPLIB 2017 benchmark instances demonstrate the effectiveness of VI aggregation and VI-aware LCP in improving the performance of the open-source MIP solver HiGHS. In particular, using the two proposed presolve techniques, a reduction of 4% in solving time and 6% in node number on HiGHS can be achieved.

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arXiv2026

Towards large-scale probabilistic set covering problems: an efficient Benders decomposition approach

In this paper, we investigate the probabilistic set covering problem (PSCP) in which the right-hand side is a binary random vector and the covering constraint is required to be satisfied with a prespecified probability. We consider the case with a finite discrete distribution of the random vector, which usually arises in the context of the sample average approximation approach. We develop an effective Benders decomposition (BD) algorithm for solving large-scale PSCPs, which enjoys two key advantages: (i) the number of variables in the underlying Benders reformulation is independent of the scenario size; and (ii) the Benders cuts can be separated by an efficient combinatorial algorithm. For the special case that random vector is a combination of several independent random blocks/subvectors, we explicitly take this kind of block structure into consideration and develop a more efficient BD algorithm. Moreover, to further speed up the two proposed BD algorithms, we develop a class of strong valid inequalities, which are guaranteed to be facet-defining for the polytope induced by the probabilistic constraint. Numerical results on instances with up to one million scenarios demonstrate the effectiveness of the proposed BD algorithms over a black-box mixed integer programming solver's branch-and-cut and automatic BD algorithms and a state-of-the-art algorithm in the literature.

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arXiv2026

Exploiting Overlap Information in Chance-constrained Program with Random Right-hand Side

We consider the chance-constrained program (CCP) with random right-hand side under a finite discrete distribution. It is known that the standard mixed integer linear programming (MILP) reformulation of the CCP is generally difficult to solve by general-purpose solvers as the branch-and-cut search trees are enormously large, partly due to the weak linear programming relaxation. In this paper, we identify another reason for this phenomenon: the intersection of the feasible regions of the subproblems in the search tree could be nonempty, leading to a wasteful duplication of effort in exploring the uninteresting overlap in the search tree. To address the newly identified challenge and enhance the capability of the MILP-based approach in solving CCPs, we first show that the overlap in the search tree can be completely removed by a family of valid nonlinear if-then constraints, and then propose two practical approaches to tackle the highly nonlinear if-then constraints. In particular, we use the concept of dominance relations between different scenarios of the random variables, and propose a novel branching, called dominance-based branching, which is able to create a valid partition of the problem with a much smaller overlap than the classic variable branching. Moreover, we develop overlap-oriented node pruning and variable fixing techniques, applied at each node of the search tree, to remove more overlaps in the search tree. Computational results demonstrate the effectiveness of the proposed dominance-based branching with the overlap-oriented node pruning and variable fixing techniques in reducing the search tree size and improving the overall solution efficiency.

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arXiv2026

On strong valid inequalities for a class of mixed-integer nonlinear sets with box constraints

In this paper, we investigate the mixed-integer nonlinear set with box constraints $X = \{(w,x)\in R\times Z^n:w\leq f(a^Tx),0\leq x\leq μ\}$, where $f$ is a univariate concave function, $a\in R^n$, and $μ\in Z^n_{++}$. This set arises as a substructure in many mixed-integer nonlinear optimization models and encompasses, as special cases, several previously investigated mixed-integer sets, namely the submodular maximization set, the mixed-integer knapsack set, and the mixed-integer polyhedral conic set. We present the first comprehensive polyhedral study of conv($X$). In particular, we derive a class of seed inequalities for a two-dimensional restriction of $X$, obtained by fixing all but one of the $x$ variables to their bounds in $X$, and develop two lifting procedures to obtain strong valid inequalities for conv($X$). In the first lifting procedure, we derive a subadditive approximation for the exact lifting function of the seed inequalities, and lift all fixed variables in a single phase. In the second lifting procedure, we first lift variables fixed at their lower bounds before those at their upper bounds (and vice versa), using subadditive exact and approximation lifting functions, respectively. The derived single- and two-phase lifted inequalities are shown to be facet-defining for conv($X$) under mild conditions. Moreover, for the aforementioned special cases of conv($X$), we show that the proposed lifted inequalities can either unify existing strong valid inequalities or yield new facet-defining inequalities. Finally, extensive computational experiments on expected utility maximization and weapon-target assignment problems demonstrate that the proposed lifted inequalities can substantially strengthen the continuous relaxations and significantly improve the overall computational performance of branch-and-cut algorithms.

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arXiv2026

Polyhedral results for two classes of submodular sets with GUB constraints

In this paper, we investigate the polyhedral structure of two submodular sets with generalized upper bound (GUB) constraints, which arise as important substructures in various real-world applications. We derive a class of strong valid inequalities for the two sets using sequential lifting techniques. The proposed lifted inequalities are facet-defining for the convex hulls of two sets and are stronger than the well-known extended polymatroid inequalities (EPIs). We provide a more compact characterization of these inequalities and show that each of them can be computed in linear time. Moreover, the proposed lifted inequalities, together with bound and GUB constraints, can completely characterize the convex hulls of the two sets, and can be separated using a combinatorial polynomial-time algorithm. Finally, computational results on probabilistic covering location and multiple probabilistic knapsack problems demonstrate the superiority of the proposed lifted inequalities over the EPIs within a branch-and-cut framework.

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arXiv2025

An efficient branch-and-cut algorithm for the multiple probabilistic covering location problem

In this paper, we consider the multiple probabilistic covering location problem (MPCLP), which attempts to open a fixed number of facilities to maximize the total covered customer demand under a joint probabilistic coverage setting. We present a new mixed integer nonlinear programming (MINLP) formulation, and develop an efficient linear programming (LP) based branch-and-cut (B&C) algorithm where submodular and outer-approximation inequalities are used to replace the nonlinear constraints and are separated at the nodes of the search tree. One key advantage of the proposed B&C algorithm is that the number of variables in the underlying formulation grows only linearly with the number of customers and facility locations and is one-order of magnitude smaller than that in the underlying formulation of a state-of-the-art B&C algorithm in the literature. Moreover, we propose two new families of strong valid inequalities, called enhanced outer-approximation and lifted subadditive inequalities, to strengthen the LP relaxation and speed up the convergence of the proposed B&C algorithm. In extensive computational experiments on a testbed of 240 benchmark MPCLP instances, we show that, thanks to the small problem size and the strong LP relaxation of the underlying formulation, the proposed B&C algorithm significantly outperforms a state-of-the-art B&C algorithm in terms of running time, number of nodes in the search tree, and number of solved instances. In particular, using the proposed B&C algorithm, we are able to provide optimal solutions for 57 previously unsolved benchmark instances within a time limit of one hour.

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arXiv2025

An efficient branch-and-cut approach for the sequential competitive facility location problem under partially binary rule

We investigate the sequential competitive facility location problem (SCFLP) under partially binary rule where two companies sequentially open a limited number of facilities to maximize their market shares, requiring customers to patronize, for each company, the facility with the highest utility. The SCFLP is a bilevel mixed integer nonlinear programming (MINLP) problem and can be rewritten as a single-level MINLP problem, where each nonlinear constraint corresponds to a hypograph of a multiple ratio function characterizing the leader's market share for a fixed follower's location choice. By establishing the submodularity of the multiple ratio functions, we characterize the mixed 0-1 set induced by each hypograph using submodular inequalities and extend a state-of-the-art branch-and-cut (B&C) algorithm to the considered SCFLP. To address the challenge of poor linear programming (LP) relaxation of the underlying formulation, we develop two new mixed integer linear programming (MILP) formulations for the SCFLP as well as efficient B&C algorithms based on them. The first MILP formulation is based on a class of improved submodular inequalities, which include the classic submodular inequalities as special cases, and together with the trivial inequalities characterize the convex hull of the mixed 0-1 set. The second one is an extended formulation of the first one that provides the same LP relaxation bound. We also develop efficient algorithms for the separations of the exponential families of the inequalities in the MILP formulations. Extensive computational experiments show that the proposed B&C algorithms significantly outperform an adapted state-of-the-art B&C algorithm and a sophisticated heuristic algorithm in the literature. Moreover, the proposed B&C algorithms can find optimal solutions for SCFLP instances with up to 1000 customers and facilities within a two-hour time limit.

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arXiv2025

QoS-Aware and Routing-Flexible Network Slicing for Service-Oriented Networks

In this paper, we consider the network slicing (NS) problem which attempts to map multiple customized virtual network requests (also called services) to a common shared network infrastructure and manage network resources to meet diverse quality of service (QoS) requirements. We propose a mixed-integer nonlinear programming (MINLP) formulation for the considered NS problem that can flexibly route the traffic flow of the services on multiple paths and provide end-to-end delay and reliability guarantees for all services. To overcome the computational difficulty due to the intrinsic nonlinearity in the MINLP formulation, we transform the MINLP formulation into an equivalent mixed-integer linear programming (MILP) formulation and further show that their continuous relaxations are equivalent. In sharp contrast to 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 significantly facilitates the algorithmic design. Based on the newly proposed MILP formulation, we develop a customized column generation (cCG) algorithm for solving the NS problem. The proposed cCG algorithm is a decomposition-based algorithm and is particularly suitable for solving large-scale NS problems. Numerical results demonstrate the efficacy of the proposed formulations and the proposed cCG algorithm.

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arXiv2025

Presolving and cutting planes for the generalized maximal covering location problem

This paper considers the generalized maximal covering location problem (GMCLP) which establishes a fixed number of facilities to maximize the weighted sum of the covered customers, allowing customer weights to be positive or negative. Due to the huge number of linear constraints to model the covering relations between the candidate facility locations and customers, and particularly the poor linear programming (LP) relaxation, the GMCLP is extremely difficult to solve by state-of-the-art mixed integer programming (MIP) solvers. To improve the computational performance of MIP-based approaches for solving GMCLPs, we propose customized presolving and cutting plane techniques, which are isomorphic aggregation, dominance reduction, and two-customer inequalities. The isomorphic aggregation and dominance reduction can not only reduce the problem size but also strengthen the LP relaxation of the MIP formulation of the GMCLP. The two-customer inequalities can be embedded into a branch-and-cut framework to further strengthen the LP relaxation of the MIP formulation on the fly. By extensive computational experiments, we show that all three proposed techniques can substantially improve the capability of MIP solvers in solving GMCLPs. In particular, for a testbed of 40 instances with identical numbers of customers and candidate facility locations in the literature, the proposed techniques enable us to provide optimal solutions for 13 previously unsolved benchmark instances; for a testbed of 336 instances where the number of customers is much larger than the number of candidate facility locations, the proposed techniques can turn most of them from intractable to easily solvable.

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arXiv2025

Benders decomposition for the large-scale probabilistic set covering problem

In this paper, we consider a probabilistic set covering problem (PSCP) in which each 0-1 row of the constraint matrix is random with a finite discrete distribution, and the objective is to minimize the total cost of the selected columns such that each row is covered with a prespecified probability. We develop an effective decomposition algorithm for the PSCP based on the Benders reformulation of a standard mixed integer programming (MIP) formulation. The proposed Benders decomposition (BD) algorithm enjoys two key advantages: (i) the number of variables in the underlying Benders reformulation is equal to the number of columns but independent of the number of scenarios of the random data; and (ii) the Benders feasibility cuts can be separated by an efficient polynomial-time algorithm, which makes it particularly suitable for solving large-scale PSCPs. We enhance the BD algorithm by using initial cuts to strengthen the relaxed master problem, implementing an effective heuristic procedure to find high-quality feasible solutions, and adding mixed integer rounding enhanced Benders feasibility cuts to tighten the problem formulation. Numerical results demonstrate the efficiency of the proposed BD algorithm over a state-of-the-art MIP solver. Moreover, the proposed BD algorithm can efficiently identify optimal solutions for instances with up to 500 rows, 5000 columns, and 2000 scenarios of the random rows.

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arXiv2024

Distributed Recursion Revisited

The distributed recursion (DR) algorithm is an effective method for solving the pooling problem that arises in many applications. It is based on the well-known P-formulation of the pooling problem, which involves the flow and quality variables; and it can be seen as a variant of the successive linear programming (SLP) algorithm, where the linear programming (LP) approximation problem can be transformed from the LP approximation problem derived by using the first-order Taylor series expansion technique. In this paper, we first propose a new nonlinear programming (NLP) formulation for the pooling problem involving only the flow variables, and show that the DR algorithm can be seen as a direct application of the SLP algorithm to the newly proposed formulation. With this new useful theoretical insight, we then develop a new variant of DR algorithm, called penalty DR (PDR) algorithm, based on the proposed formulation. The proposed PDR algorithm is a penalty algorithm where violations of the (linearized) nonlinear constraints are penalized in the objective function of the LP approximation problem with the penalty terms increasing when the constraint violations tend to be large. Compared with the LP approximation problem in the classic DR algorithm, the LP approximation problem in the proposed PDR algorithm can return a solution with a better objective value, which makes it more suitable for finding high-quality solutions for the pooling problem. Numerical experiments on benchmark and randomly constructed instances show that the proposed PDR algorithm is more effective than the classic SLP and DR algorithms in terms of finding a better solution for the pooling problem.

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arXiv2024

An Efficient Benders Decomposition Approach for Optimal Large-Scale Network Slicing

This paper considers the network slicing (NS) problem which attempts to map multiple customized virtual network requests to a common shared network infrastructure and allocate network resources to meet diverse service requirements. This paper proposes an efficient customized Benders decomposition algorithm for globally solving the large-scale NP-hard NS problem. The proposed algorithm decomposes the hard NS problem into two relatively easy function placement (FP) and traffic routing (TR) subproblems and iteratively solves them enabling the information feedback between each other, which makes it particularly suitable to solve large-scale problems. Specifically, the FP subproblem is to place service functions into cloud nodes in the network, and solving it can return a function placement strategy based on which the TR subproblem is defined; and the TR subproblem is to find paths connecting two nodes hosting two adjacent functions in the network, and solving it can either verify that the solution of the FP subproblem is an optimal solution of the original problem, or return a valid inequality to the FP subproblem that cuts off the current infeasible solution. The proposed algorithm is guaranteed to find the globally optimal solution of the NS problem. By taking the special structure of the NS problem into consideration, we successfully develop two families of valid inequalities that render the proposed algorithm converge much more quickly and thus much more efficient. Numerical results demonstrate that the proposed valid inequalities effectively accelerate the convergence of the decomposition algorithm, and the proposed algorithm significantly outperforms the existing algorithms in terms of both solution efficiency and quality.

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arXiv2024

One-Bit MIMO Detection: From Global Maximum-Likelihood Detector to Amplitude Retrieval Approach

As communication systems advance towards the future 6G era, the incorporation of large-scale antenna arrays in base stations (BSs) presents challenges such as increased hardware costs and energy consumption. To address these issues, the use of one-bit analog-to-digital converters (ADCs)/digital-to-analog converters (DACs) has gained significant attentions. This paper focuses on one-bit multiple-input multiple-output (MIMO) detection in an uplink multiuser transmission scenario where the BS employs one-bit ADCs. One-bit quantization retains only the sign information and loses the amplitude information, which poses a unique challenge in the corresponding detection problem. The maximum-likelihood (ML) formulation of one-bit MIMO detection has a challenging likelihood function that hinders the application of many high-performance detectors developed for classic MIMO detection (under high-resolution ADCs). While many approximate methods for the ML detection problem have been studied, it lacks an efficient global algorithm. This paper fills this gap by proposing an efficient branch-and-bound algorithm, which is guaranteed to find the global solution of the one-bit ML MIMO detection problem. Additionally, a new amplitude retrieval (AR) detection approach is developed, incorporating explicit amplitude variables into the problem formulation. The AR approach yields simpler objective functions that enable the development of efficient algorithms offering both global and approximate solutions. The paper also contributes to the computational complexity analysis of both ML and AR detection problems. Extensive simulations are conducted to demonstrate the effectiveness and efficiency of the proposed formulations and algorithms.

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arXiv2024

An efficient branch-and-cut approach for large-scale competitive facility location problems with limited choice rule

In the paper, we consider the competitive facility location problem with limited choice rule (CFLPLCR), which attempts to open a subset of facilities to maximize the net profit of a newcomer company, requiring customers to patronize only a limited number of opening facilities and an outside option. We propose an efficient branch-and-cut (B&C) approach for the CFLPLCR based on newly proposed mixed integer linear programming (MILP) formulations. Specifically, by establishing the submodularity of the probability function, we develop an MILP formulation for the CFLPLCR using the submodular inequalities. For the special case where each customer patronizes at most one open facility and the outside option, we show that the submodular inequalities can characterize the convex hull of the considered set and provide a compact MILP formulation. Moreover, for the general case, we strengthen the submodular inequalities by sequential lifting, resulting in a class of facet-defining inequalities. The proposed lifted submodular inequalities are shown to be stronger than the classic submodular inequalities, enabling to obtain another MILP formulation with a tighter linear programming (LP) relaxation. By extensive numerical experiments, we show that the proposed B&C approach outperforms the state-of-the-art generalized Benders decomposition approach by at least one order of magnitude. Furthermore, it enables to solve CFLPLCR instances with 10000 customers and 2000 facilities.

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arXiv2024

Quantized Constant-Envelope Waveform Design for Massive MIMO DFRC Systems

Both dual-functional radar-communication (DFRC) and massive multiple-input multiple-output (MIMO) have been recognized as enabling technologies for 6G wireless networks. This paper considers the advanced waveform design for hardware-efficient massive MIMO DFRC systems. Specifically, the transmit waveform is imposed with the quantized constant-envelope (QCE) constraint, which facilitates the employment of low-resolution digital-to-analog converters (DACs) and power-efficient amplifiers. The waveform design problem is formulated as the minimization of the mean square error (MSE) between the designed and desired beampatterns subject to the constructive interference (CI)-based communication quality of service (QoS) constraints and the QCE constraint. To solve the formulated problem, we first utilize the penalty technique to transform the discrete problem into an equivalent continuous penalty model. Then, we propose an inexact augmented Lagrangian method (ALM) algorithm for solving the penalty model. In particular, the ALM subproblem at each iteration is solved by a custom-built block successive upper-bound minimization (BSUM) algorithm, which admits closed-form updates, making the proposed inexact ALM algorithm computationally efficient. Simulation results demonstrate the superiority of the proposed approach over existing state-of-the-art ones. In addition, extensive simulations are conducted to examine the impact of various system parameters on the trade-off between communication and radar performances.

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arXiv2023

Efficient presolving methods for the influence maximization problem

We consider the influence maximization problem (IMP) which asks for identifying a limited number of key individuals to spread influence in a network such that the expected number of influenced individuals is maximized. The stochastic maximal covering location problem (SMCLP) formulation is a mixed integer programming formulation that effectively approximates the IMP by the Monte-Carlo sampling. For IMPs with a large-scale network or a large number of samplings, however, the SMCLP formulation cannot be efficiently solved by existing exact algorithms due to its large problem size. In this paper, we attempt to develop presolving methods to reduce the problem size and hence enhance the capability of employing exact algorithms in solving large-scale IMPs. In particular, we propose two effective presolving methods, called strongly connected nodes aggregation (SCNA) and isomorphic nodes aggregation (INA), respectively. The SCNA enables to build a new SMCLP formulation that is potentially much more compact than the existing one, and the INA further eliminates variables and constraints in the SMCLP formulation. A theoretical analysis on two special cases of the IMP is provided to demonstrate the strength of the SCNA and INA in reducing the problem size of the SMCLP formulation. We integrate the proposed presolving methods, SCNA and INA, into the Benders decomposition algorithm, which is recognized as one of the state-of-the-art exact algorithms for solving the IMP. We show that the proposed SCNA and INA provide the possibility to develop a much faster separation algorithm for the Benders cuts. Numerical results demonstrate that with the SCNA and INA, the Benders decomposition algorithm is much more effective in solving the IMP in terms of solution time.

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arXiv2023

An Efficient Global Algorithm for One-Bit Maximum-Likelihood MIMO Detection

There has been growing interest in implementing massive MIMO systems by one-bit analog-to-digital converters (ADCs), which have the benefit of reducing the power consumption and hardware complexity. One-bit MIMO detection arises in such a scenario. It aims to detect the multiuser signals from the one-bit quantized received signals in an uplink channel. In this paper, we consider one-bit maximum-likelihood (ML) MIMO detection in massive MIMO systems, which amounts to solving a large-scale nonlinear integer programming problem. We propose an efficient global algorithm for solving the one-bit ML MIMO detection problem. We first reformulate the problem as a mixed integer linear programming (MILP) problem that has a massive number of linear constraints. The massive number of linear constraints raises computational challenges. To solve the MILP problem efficiently, we custom build a light-weight branch-and-bound tree search algorithm, where the linear constraints are incrementally added during the tree search procedure and only small-size linear programming subproblems need to be solved at each iteration. We provide simulation results to demonstrate the efficiency of the proposed method.

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