Search

Power system operators are faced with the problem of unit commitment belonging to mixed integer programming, which becomes very complicated, as units become large-scale and highly constrained. Because unit commitment problem is a binary problem with commitment and de-commitment, a discrete/binary optimization algorithm with superior performance is required. This paper proposes a novel hybrid binary bat algorithm for unit commitment problem, which consists of two process. To begin with, the proposed binary bat algorithm is applied to determining the commitment schedule of unit commitment problem. Specifically, an improved crossover operator based on exponential-logic-modulo map is proposed to enhance the convergence and maintain the diversity of populations. To prevent the algorithm from falling into a local optimum, a local mutation strategy performs local perturbation. Chaotic map is responsible for updating some parameters to increase the performance of the proposed algorithm. Furthermore, Lambda-iteration method is adopted to solve economic load dispatch in continuous space. Constraint handling is performed using the heuristic constraint produce. The effectiveness of the proposed algorithm is verified by benchmark functions and test systems. Additionally, the simulation results are compared with other well-established heuristic and binary approaches. [ABSTRACT FROM AUTHOR]

In this paper, we study the knapsack problem with conflict pair constraints. After a thorough literature survey on the topic, our study focuses on the special case of bipartite conflict graphs. For complete bipartite (multipartite) conflict graphs, the problem is shown to be NP-hard but solvable in pseudo-polynomial time, and it admits an FPTAS. Extensions of these results to more general classes of graphs are also presented. Further, a class of integer programming models for the general knapsack problem with conflict pair constraints is presented, which generalizes and unifies the existing formulations. The strength of the LP relaxations of these formulations is analyzed, and we discuss different ways to tighten them. Experimental comparisons of these models are also presented to assess their relative strengths. This analysis disclosed various strong and weak points of different formulations of the problem and their relationships to different types of problem data. This information can be used in designing special purpose algorithms for KPCC involving a learning component. [ABSTRACT FROM AUTHOR]

Delay-sensitive task offloading in a device-to-device assisted mobile edge computing (D2D-MEC) system with energy harvesting devices is a critical challenge due to the dynamic load level at edge nodes and the variability in harvested energy. In this paper, we propose a joint dynamic task offloading and CPU frequency control scheme for delay-sensitive tasks in a D2D-MEC system, taking into account the intricacies of multi-slot tasks, characterized by diverse processing speeds and data transmission rates. Our methodology involves meticulous modeling of task arrival and service processes using queuing systems, coupled with the strategic utilization of D2D communication to alleviate edge server load and prevent network congestion effectively. Central to our solution is the formulation of average task delay optimization as a challenging nonlinear integer programming problem, requiring intelligent decision making regarding task offloading for each generated task at active mobile devices and CPU frequency adjustments at discrete time slots. To navigate the intricate landscape of the extensive discrete action space, we design an efficient multi-agent DRL learning algorithm named MAOC, which is based on MAPPO, to minimize the average task delay by dynamically determining task-offloading decisions and CPU frequencies. MAOC operates within a centralized training with decentralized execution (CTDE) framework, empowering individual mobile devices to make decisions autonomously based on their unique system states. Experimental results demonstrate its swift convergence and operational efficiency, and it outperforms other baseline algorithms. [ABSTRACT FROM AUTHOR]

The multi-objective integer programming problem often occurs in multi-criteria decision-making situations, where the decision variables are integers. In the present paper, we have discussed an algorithm for finding all efficient solutions of a multi-objective integer quadratic programming problem. The proposed algorithm is based on the aspect that efficient solutions of a multi-objective integer quadratic programming problem can be obtained by enumerating ranked solutions of an integer quadratic programming problem. For determining ranked solutions of an integer quadratic programming problem, we have constructed a related integer linear programming problem and from ranked solutions of this integer linear programming problem, ranked solutions of the original integer quadratic programming problem are generated. Theoretically, we have shown that the developed method generates the set of all efficient solutions in a finite number of steps, and numerically we have elaborated the working of our algorithm and compared our results with existing algorithms. Further, we have analyzed that the developed method is efficient for solving a multi-objective integer quadratic programming problem with a large number of constraints, variables and objectives. [ABSTRACT FROM AUTHOR]

To alleviate the congestion caused by the tidal traffic and to improve the operational performance of both directions in arterials, this paper proposes a coordinated control model for arterials with asymmetric traffic demands in both oversaturated and unsaturated directions. The model utilizes a three-step architecture: (1) A mixed-integer linear programming model is built to maximize the throughput according to the relationship between traffic supply and demand as well as the balance between inflow and outflow. (2) A quadratic programming model is constructed to minimize the vehicle delay in the oversaturated direction based on Lighthill-Whitham-Richards theory. (3) A mixed-integer linear programming model is built to maximize the variable bandwidth in the unsaturated direction by introducing the relaxation variable. Furthermore, a three-step algorithm is used to solve the model and obtain the optimal arterial signal timing. Finally, a simulation model is put forward to verify the coordinated model. The results indicate that the model meet the asymmetric traffic demand through optimizing the arterial throughput, reducing delay in the oversaturated direction and maximizing the green wave bandwidth in the unsaturated direction. [ABSTRACT FROM AUTHOR]

Shared parking can fully utilize idle parking resources and alleviate parking conflicts. However, existing operational strategies suffer from low utilization of parking resources and neglect of parker preferences. This paper focuses on how to solve the problem of matching many-to-one in the shared parking process considering the benefits of parkers and parking lots. Given this, a stable matching mechanism is proposed based on the improved deferred-acceptance algorithm. Meanwhile, we develop a parking space rental and allocation model for multiple parking lots. A series of factors were considered in the model, such as the profits of the parking lot, the potential loss due to refusal of parking requests and rented spaces, and the walking distance to the destination of parkers. Parking requests are assigned to specific parking lots considering the preferences of the parkers, and then the allocation of shared parking spaces is achieved through the proposed matching mechanism. In numerical examples, we compare the proposed allocation method with the other two allocation methods. The results indicate that compared with the other two allocation methods, the proposed matching mechanism could achieve optimal allocation of parking spaces and a stable match between shared parking and parkers, which verifies the superiority of our method. [ABSTRACT FROM AUTHOR]

In this paper, a stochastic multi-objective structure is introduced in joint energy and reserve market to allow energy generation companies participating in the short-term hydro-thermal self-scheduling with uncertainties. To solve this problem, an antlion optimization (ALO) algorithm is used. In addition, uncertainties including energy price, spinning and non-spinning reserve prices, output power of the wind, photovoltaic and small hydro units are mentioned. In this study, two methods are used to generate stochastic multi-objective scenarios, namely lattice monte-carlo simulation and roulette wheel mechanism (RWM). After that, the main purpose of the study is described, i.e. making GENCOs able to achieve the maximum profit and the minimum emission by using a multi-objective function considering a stochastic process. To reach this aim, the mixed integer programming (MIP) which includes a set of multi stage deterministic scenarios is employed. However, some special cases should be introduced in the formulation structure of the presented scheduling regarding hydrothermal units to make the SMO-HTSS problem with wind, photovoltaic and small hydro units similar to the real time modeling. Since optimal solutions are produced in this method, one can allude to the application of the є-constraint. Nevertheless, in order to select one of the most appropriate solutions among Pareto solutions obtained, the utilization of fuzzy method has been presented. In the end, as shown in this paper, the ALO algorithm is limited to the є-constraint; some tests are carried out on an IEEE 118-bus test system to verify the accuracy and validity of the proposed method. [ABSTRACT FROM AUTHOR]

This paper deals with the school timetabling problem. The problem was formulated as encountered in a typical Greek high school. A local version of the particle swarm optimization algorithm was developed and applied to the problem at hand. Results on well-established benchmark instances showed that the proposed algorithm achieved the proven optima provided from an integer programming method presented in earlier research. In almost all cases, the current algorithm beat the integer programming method, either concerning the lower bound yielded or the execution time needed. [ABSTRACT FROM AUTHOR]

This paper focuses on seru scheduling problems considering the sequence-dependent setup time in seru production system, which is a new-type manufacturing system originated in Japanese production practice recently that can better adapt to the fluctuate market demand. A mixed integer programming (MIP) model with the objective of minimizing the sum of the makespan and the total weighted tardiness is constructed for the seru scheduling problem. The branch-and-bound (B&B) algorithm with two main steps is designed subsequently, where the first step solves the assignment of products to serus, while the second step solves the scheduling optimization in each seru. Finally, the computational experiments and comparative analysis with CPLEX 12.8 are made, and the report of results verifies that the effectiveness and practicability of the proposed MIP and B&B algorithm. [ABSTRACT FROM AUTHOR]

In real-life scenarios, both the vertex weight and edge weight in a network are hard to define exactly. We can incorporate the fuzziness into a network to handle this type of uncertain situation. Here, we use triangular fuzzy number to describe the vertex weight and edge weight of a fuzzy network G. In this paper, we consider weighted k-domination problem in fuzzy network. The weighted k-domination (WKD) problem is to find a k dominating set D which minimizes the cost f (D) : = ∑u∈Dw (u) + ∑v∈V\D min {∑u∈Sw (uv) |S ⊆ N (v) ∩ D, |S| = k}. First, we put forward an integer linear programming model with a polynomial number of constrains for the WKD problem. If G is a cycle, we design a dynamic algorithm to determine its exact weighted 2-domination number. If G is a tree, we give a label algorithm to determine its exact weighted 2-domination number. Combining a primal-dual method and a greedy method, we put forward an approximation algorithm for general fuzzy network on the WKD problem. Finally, we describe an application of the WKD problem to police camp problem. [ABSTRACT FROM AUTHOR]

This paper deals with simultaneous scheduling of machines, automated guided vehicles (AGVs) and tools in a multi-machine flexible manufacturing system (FMS) considering the transfer times of jobs to minimize makespan (MSN). Only one copy of each type of tools is made available due to economic restrictions, and the tools are stored in a central tool magazine (CTM) that shares with and serves for several machines. Jobs and tools among machines are carried by AGVs and tool transporter (TT). This simultaneous scheduling problem is highly complex in nature as it involves job operations sequencing on machines, allocation of tools and AGVs to job operations and associated trip operations including the times of dead heading trip and loaded trip of AGVs. This paper presents a nonlinear mixed integer programming (MIP) formulation to model the combined scheduling of machines, AGVs and tools and a flower pollination algorithm (FPA) built on the flowers' pollination process for solving this simultaneous scheduling problem. The results indicate the proposed FPA is superior in terms of final solution quality, efficiency, convergence rate and robustness. [ABSTRACT FROM AUTHOR]

The joint replenishment problem has been extensively studied and the joint replenishment strategy has been adopted by a large variety of retailers in recent years. However, the joint replenishment problem under minimum order quantity and other constraints does not receive sufficient attention. This paper analyzes a retailing supply chain involving a supplier that provides quantity discount schedules and limits the order quantity. The order quantity constraints include minimum order requirements for each item and as to the total quantity; additionally, the latter cannot exceed the transport capacity constraint. These are common constraints in the retail industry today and create greater complexity and difficulty in the retailer's decision-making. To analyze the problem, an integer nonlinear programming model is set up to maximize retailers' profit with all practical constraints. A two-layer efficient algorithm named the Marginal and Cumulative Profit-Based Algorithm (MCPB) is then proposed to find whether to order and the optimal order quantity for each item. The results of computational experiments show that the proposed algorithm can find near-optimal solutions to the problem efficiently and is a reference for retailers to solve practical joint replenishment problems. [ABSTRACT FROM AUTHOR]

The exact solution of the NP-hard (nondeterministic polynomial-time hard) maximum cut problem is important in many applications across, for example, physics, chemistry, neuroscience, and circuit layout—which is also due to its equivalence to the unconstrained binary quadratic optimization problem. Leading solution methods are based on linear or semidefinite programming and require the separation of the so-called odd-cycle inequalities. In their groundbreaking research, F. Barahona and A. R. Mahjoub have given an informal description of a polynomial-time algorithm for this problem. As pointed out recently, however, additional effort is necessary to guarantee that the inequalities obtained correspond to facets of the cut polytope. In this paper, we shed more light on a so enhanced separation procedure and investigate experimentally how it performs in comparison with an ideal setting where one could even employ the sparsest, most violated, or geometrically most promising facet-defining odd-cycle inequalities. Summary of Contribution: This paper aims at a better capability to solve binary quadratic optimization or maximum cut problems and their various applications using integer programming techniques. To this end, the paper describes enhancements to a well-known algorithm for the central separation problem arising in this context; it is demonstrated experimentally that these enhancements are worthwhile from a computational point of view. The linear relaxations of the aforementioned problems are typically solved using fewer iterations and cutting planes than with a nonenhanced approach. It is also shown that the enhanced procedure is only slightly inferior to an ideal, enumerative, and, in practice, intractable global cutting-plane selection. [ABSTRACT FROM AUTHOR]

We address a dynamic covering location problem of an unmanned aerial vehicle base station (UAV-BS), in which the location sequence of a single UAV-BS in a wireless communication network is determined to satisfy data demand arising from ground users. This problem is especially relevant in the context of smart grid and disaster relief. The vertical movement ability of the UAV-BS and nonconvex covering functions in wireless communication restrict utilizing classical planar covering location approaches. Therefore, we develop new formulations to this emerging problem for a finite time horizon to maximize the total coverage. In particular, we develop a mixed-integer nonlinear programming formulation that is nonconvex in nature and propose a Lagrangean decomposition algorithm (LDA) to solve this formulation. Because of the high complexity of the problem, the LDA is still unable to find good local solutions to large-scale problems. Therefore, we develop a continuum approximation (CA) model and show that CA would be a promising approach in terms of both computational time and solution accuracy. Our numerical study also shows that the CA model can be a remedy to build efficient initial solutions for exact solution algorithms. Summary of Contribution: This paper addresses a facet of mixed integer nonlinear programming formulations. Dynamic facility location problems (DFLPs) arise in a wide range of applications. However, classical DFLPs typically focus on the two-dimensional spaces. Emerging technologies in wireless communication and some other promising application areas, such as smart grids, have brought new location problems that cannot be solved with classical approaches. For practical reasons, many research attempts to solve this new problem, especially by researchers whose primary research area is not OR, have seemed far from analyzing the characteristics of the formulations. Rather, solution-oriented greedy heuristics have been proposed. This paper has two main objectives: (i) to close the gap between practical and theoretical sides of this new problem with the help of current knowledge that OR possesses to solve facility location problems and (ii) to support the findings with an exhaustive computational study to show how these findings can be applied to practice. [ABSTRACT FROM AUTHOR]

Large-scale natural disaster or malicious attacks could cause serious damages to the communication network in smart grids. If the damaged network cannot be recovered timely, greater threat will be brought to the secure and stable operation of smart grids. In this paper, a link importance-based network recovery method for large-scale failures in smart grids has been proposed. Firstly, the link importance for the network can be obtained according to the link importance for the service type and the importance of the service type for the network; secondly, a network recovery model, which is 0–1 integer programming, has been established to recover more important communication services with limited recovery resources; finally, we propose a heuristic algorithm to solve the problem and reduce the computational expenditure. The simulation experiments are carried out to evaluate the performance of the proposed algorithm. The simulation results illustrate that our network recovery method is applicable to the large-scale failures and the link which carries the high-priority service can be first recovered in this paper, thus which further ensures the safe and stable operation of smart grids. [ABSTRACT FROM AUTHOR]

As pairwise ranking becomes broadly employed for elections, sports competitions, recommendation, information retrieval and so on, attackers have strong motivation and incentives to manipulate or disrupt the ranking list. They could inject malicious comparisons into the training data to fool the target ranking algorithm. Such a technique is called “poisoning attack” in regression and classification tasks. In this paper, to the best of our knowledge, we initiate the first systematic investigation of data poisoning attack on the pairwise ranking algorithms, which can be generally formalized as the dynamic and static games between the ranker and the attacker, and can be modeled as certain kinds of integer programming problems mathematically. To break the computational hurdle of the underlying integer programming problems, we reformulate them into the distributionally robust optimization (DRO) problems, which are computational tractable. Based on such DRO formulations, we propose two efficient poisoning attack algorithms and establish the associated theoretical guarantees including the existence of Nash equilibrium and the generalization ability bounds. The effectiveness of the suggested poisoning attack strategies is demonstrated by a series of toy simulations and several real data experiments. These experimental results show that the proposed methods can significantly reduce the performance of the ranker in the sense that the correlation between the true ranking list and the aggregated results with toxic data can be decreased dramatically. [ABSTRACT FROM AUTHOR]

In long-distance gas transmission pipelines, there are many booster compressor stations consisting of parallel compressors that provide pressure for the delivery of natural gas. So, it is economically important to optimize the operation of the booster compressor station. The booster compressor station optimization problem is a typical mixed integer nonlinear programming (MINLP) problem, and solving it accurately and stably is a challenge. In this paper, we propose an improved salp swarm algorithm based on good point set, adaptive population division and adaptive inertia weight (GASSA) to solve this problem. In GASSA, three improvement strategies are utilized to enhance the global search capability of the algorithm and help the algorithm jump out of the local optimum. We also propose a constraint handling approach. By using semi-continuous variables, we directly describe the on or off state of the compressor instead of using auxiliary binary variables to reduce the number of variables and the difficulty of solving. The effectiveness of GASSA is firstly verified using eight standard benchmark functions, and the results show that GASSA has better performance than other selected algorithms. Then, GASSA is applied to optimize the booster compressor station load distribution model and compared with some well-known meta-heuristic algorithms. The results show that GASSA outperforms other algorithms in terms of accuracy and reliability. [ABSTRACT FROM AUTHOR]

A graph is said to be two connected if between every pair of nodes there are at least two node-disjoint paths. Given weights on the edges of the graph, the two connected subgraph problem is to find a two connected spanning subgraph of G whose weight is minimum. This problem has many applications in telecommunications. In this paper we consider a new variant of this problem with additional disjunctive constraints (called also conflict constraints) related to the survivability of telecommunication networks. This can be called the Disjunctive Two-Connected Subgraph Problem (DTCSP). First, we give an extended formulation for the problem whose variables are the cycles of the graph. Then, we use a column generation algorithm to solve its linear relaxation, and further show that the pricing reduces to finding a specific cycle in the graph which can be formulated as an integer programming problem. We also describe several valid inequalities for the polytope. Moreover, we study the related separation problems and devise separation routines for these inequalities. Using this, we devise a Branch-and-Cut-and-Price algorithm for the problem along with an extensive experimental study. [ABSTRACT FROM AUTHOR]

Multi-objective programming problem often contains numerous efficient solutions, which confuses the decision-maker. To assist in selecting the most desirable solution, optimizing a function over the efficient set becomes crucial. In this paper, we present a novel method for optimizing a general quadratic function over the efficient set of a multi-objective integer linear programming problem. To solve this problem, a ranking approach and efficiency test is utilized. The proposed methodology obtains a globally optimal solution by systematically scanning ranked solutions of an integer quadratic programming problem until the efficiency condition is satisfied. For generating ranked solutions, we construct a related integer linear programming problem. Then, ranked solutions of the integer linear programming problem are used for enumerating ranked solutions of the integer quadratic programming problem. The convergence of our algorithm is established theoretically, and its steps are illustrated using a numerical example. Aparticular case of the proposed method for optimizing a linear function over the efficient set of a multi-objective integer linear programming problem is also discussed. Further, extensive computational results demonstrate the effectiveness of our method for solving problems with large number of constraints, variables, and objective functions. Moreover, comparative analysis shows that the developed algorithm came out to be computationally more efficient as compared to the existing state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

We introduce and motivate several variants of the bin packing problem where bins are assigned to time slots, and minimum and maximum lags are required between some pairs of items. We suggest two integer programming formulations for the general problem: a compact one and a stronger formulation with an exponential number of variables and constraints. We propose a branch-cut-and-price approach that exploits the latter formulation. For this purpose, we devise separation algorithms based on a mathematical characterization of feasible assignments for two important special cases of the problem: when the number of possible bins available at each period is infinite and when this number is limited to one and time lags are nonnegative. Computational experiments are reported for instances inspired from a real-case application of chemical treatment planning in vineyards, as well as for literature instances for special cases of the problem. The experimental results show the efficiency of our branch-cut-and-price approach, as it outperforms the compact formulation on newly proposed instances and is able to obtain improved lower and upper bounds for literature instances. Summary of Contribution: The paper considers a new variant of the bin packing problem, which is one of the most important problems in operations research. A motivation for introducing this variant is given, as well as a real-life application. We present a novel and original exact branch-cut-and-price algorithm for the problem. We implement this algorithm, and we present the results of extensive computational experiments. The results show a very good performance of our algorithm. We give several research directions that can be followed by subsequent researchers to extend our contribution to more complex and generic problems. [ABSTRACT FROM AUTHOR]

The Weapon-Target Assignment (WTA) problem aims to assign a set of weapons to a number of assets (targets), such that the expected value of survived targets is minimized. The WTA problem is a nonlinear combinatorial optimization problem known to be NP-hard. This paper applies several existing techniques to linearize the WTA problem. One linearization technique (Camm et al. in Oper Res 50(6):946–955, 2002) approximates the nonlinear terms of the WTA problem via convex piecewise linear functions and provides heuristic solutions to the WTA problem. Such approximation problems are, though, relatively easy to solve from the computational point of view even for large-scale problem instances. Another approach proposed by O'Hanley et al. (Eur J Oper Res 230(1):63–75, 2013) linearizes the WTA problem exactly at the expense of incorporating a significant number of additional variables and constraints, which makes many large-scale problem instances intractable. Motivated by the results of computational experiments with these existing solution approaches, a specialized new exact solution approach is developed, which is called branch-and-adjust. The proposed solution approach involves the compact piecewise linear convex under-approximation of the WTA objective function and solves the WTA problem exactly. The algorithm builds on top of any existing branch-and-cut or branch-and-bound algorithm and can be implemented using the tools provided by state-of-the-art mixed integer linear programming solvers. Numerical experiments demonstrate that the proposed specialized algorithm is capable of handling very large scale problem instances with up to 1500 weapons and 1000 targets, obtaining solutions with optimality gaps of up to 2.0 % within 2 h of computational runtime. [ABSTRACT FROM AUTHOR]

Inverse optimization—determining parameters of an optimization problem that render a given solution optimal—has received increasing attention in recent years. Although significant inverse optimization literature exists for convex optimization problems, there have been few advances for discrete problems, despite the ubiquity of applications that fundamentally rely on discrete decision making. In this paper, we present a new set of theoretical insights and algorithms for the general class of inverse mixed integer linear optimization problems. Specifically, a general characterization of optimality conditions is established and leveraged to design new cutting plane solution algorithms. Through an extensive set of computational experiments, we show that our methods provide substantial improvements over existing methods in solving the largest and most difficult instances to date. [ABSTRACT FROM AUTHOR]

A new notion of anonymity was recently introduced at PODC 2017, namely, anonymity on the names of the registers that define the shared memory. As an example, a shared register named A by a process p and a shared register named B by another process q may correspond to the very same shared register X , while the same name C may correspond to different shared registers for p and q. Considering an asynchronous n -process anonymous shared memory system, this paper is concerned with the de-anonymization of the memory, i.e., at the end of the execution of a de-anonymization algorithm, the processes must agree on the same name for each shared register, and different shared registers must have different names. To this end, the paper first addresses leader election in an anonymous memory system. Let n be the number of processes and m the size of the anonymous memory (total number of anonymous registers). It is first shown that there is no election algorithm when the number of anonymous registers is a multiple of n. Then, assuming m = α n + β , where α is a positive integer, three election algorithms are presented, which consider the cases β = 1 , β = n − 1 , and β ∈ M (n) , where the set M (n) characterizes the values for which mutual exclusion can be solved despite memory anonymity. Once election is solved, a general (and simple) de-anonymization algorithm is presented, which takes as a subroutine any memory anonymous leader election algorithm. Hence, any instance of this algorithm works for the values of m required by the selected underlying election algorithm. As the underlying election algorithms, the de-anonymization algorithm is symmetric in the sense that process identities can only be compared for equality. [ABSTRACT FROM AUTHOR]

The resources in the edge cloud are numerous and complex, and elastic scaling services can make efficient use of these resources. However, the elastic scaling services need to suspend the user's application tasks forcibly when carrying out resource redistribution, which brings a poor sense of experience to the user. In view of the above problems, a dynamic elastic scaling model based on load prediction is proposed, which improves resource utilization and reduces scaling costs without affecting user experience. The model is divided into two parts. In terms of load prediction, on the one hand, according to the historical features and current trends of the load, the load prediction model based on the improved cloud model is used to predict the load demand at the next moment. On the other hand, the correlation between CPU and memory is considered. In terms of elastic scaling, integer programming algorithm is proposed to expand and release the corresponding resources with the minimum cost of horizontal scaling (HS) and vertical scaling (VS). In order to verify the superiority of elastic scaling model based on load prediction, corresponding comparative experiments are conducted, which show that the proposed model can improve the accuracy of load prediction and resource utilization with low scaling costs. Especially, the cost of elastic scaling proposed by this paper is lower than horizontal and vertical scaling. Compared with HS, the elastic scaling method proposed in this paper reduces the cost by 14%. Compared with VS, this method reduces the cost by 11%. [ABSTRACT FROM AUTHOR]

Batch processing machine (BPM) scheduling problem is a NP hard problem for it includes machine allocation, job grouping, and batch scheduling. In this paper, to address the BPM scheduling problem with unrelated parallel machine, a multiobjective algorithm based on multipopulation coevolution is proposed to minimize the total energy consumption and the completion time simultaneously. Firstly, the mixed integer programming model of the problem is established, and four heuristic decoding rules are proposed. Secondly, to improve the diversity and convergence of the algorithm, the population is divided into two populations: each of the populations evolves independently by using different decoding rules, and the two populations will communicate through a common external archive set every certain number of generations. Thirdly, an initialization strategy and a variable neighborhood search algorithm (VNS) are proposed to improve the overall performance of the algorithm. Finally, in order to evaluate the proposed algorithm, a large number of comparative experiments with the state-of-the-art multiobjective algorithms are carried out, and the experimental results proved the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In the bin-packing problem with minimum color fragmentation (BPPMCF), we are given a fixed number of bins and a collection of items, each associated with a size and a color, and the goal is to avoid color fragmentation by packing items with the same color within as few bins as possible. This problem emerges in areas as diverse as surgical scheduling and group event seating. We present several optimization models for the BPPMCF, including baseline integer programming formulations, alternative integer programming formulations based on two recursive decomposition strategies that utilize decision diagrams, and a branch-and-price algorithm. Using the results from an extensive computational evaluation on synthetic instances, we train a decision tree model that predicts which algorithm should be chosen to solve a given instance of the problem based on a collection of derived features. Our insights are validated through experiments on the aforementioned applications on real-world data. Summary of Contribution: In this paper, we investigate a colored variant of the bin-packing problem. We present and evaluate several exact mixed-integer programming formulations to solve the problem, including models that explore recursive decomposition strategies based on decision diagrams and a set partitioning model that we solve using branch and price. Our results show that the computational performance of the algorithms depends on features of the input data, such as the average number of items per bin. Our algorithms and featured applications suggest that the problem is of practical relevance and that instances of reasonable size can be solved efficiently. [ABSTRACT FROM AUTHOR]

• We have carefully proofread the whole manuscript to fix minor typos. • Each algorithm has been correctly labeled as "Algorithm" • The experimental results and their corresponding explanations have been updated. This paper addresses a new multi-commodity unpaired pickup and delivery vehicle routing problem in which each vehicle is allowed to visit each customer more than once for both pickup and delivery of each commodity. It is a complex variant of the classical capacitated vehicle routing problem and comes from resource transfer among different plants in a distributed manufacturing environment. Notably, the pairing decisions of pickup and delivery for each commodity and the routing decisions among customers are interdependent, and they need to be made simultaneously and collaboratively. Firstly, a mixed integer programming model is developed, and then new valid inequalities are derived to improve the linear programming relaxation. Afterwards, a branch-and-cut algorithm is proposed by exploring different branching strategies and tailored separation algorithms. Computational results based on real-case instances from an automobile manufacturing company demonstrate that the costs are considerably reduced by considering the multiple visits compared to the single visit of each customer. In addition, our proposed branch-and-cut algorithm outperforms a manual solution method adopted by the company in practice and two solution methods in the literature. Furthermore, two adaptations of our branch-and-cut algorithm also perform better than two state-of-the-art algorithms in solving two closely-related problems in terms of solution quality and computation time. Sensitivity analyses with respect to vehicle capacity, vehicle duration, and vehicle speed are conducted to derive several valuable managerial insights. [ABSTRACT FROM AUTHOR]

Because of the COVID-19 pandemic, Chinese hospitals are increasing their efforts to control the number of patients to decrease cross-infection risks. In this paper, we investigate the flexible physician scheduling problem for emergency departments (EDs), considering the constraint of the maximum number of emergency patients in one time period. We model the ED service system as a time-varying queue with returns and formulate the physician scheduling problem as a mixed-integer programming model. To solve the scheduling problem effectively, we design a learning-based two-stage optimization algorithm. In the first stage, we solve the physician staffing problem, in which two effective acceleration strategies based on machine learning models are developed. In the second stage, we propose a branch-and-price algorithm to determine the physician scheduling plan. Numerical experiments based on real-life data show that the proposed two-stage algorithm can effectively solve our flexible physician scheduling problem, and the scheduling plan obtained by the proposed two-stage algorithm can significantly improve the physician schedule without involving more physicians. [ABSTRACT FROM AUTHOR]

Time-varying resource allocation allows users to define their own unique resource requirement plans during different time periods. This mode of allocation can increase the flexibility of resource usage and reduce resource usage costs for users. Moreover, combining this approach with an auction mechanism can enable resource providers to obtain greater social welfare and benefits; therefore, such resource allocation has become a hot topic in cloud computing. This paper addresses the problem of time-varying batch virtual machine (VM) allocation and pricing in the cloud. Specifically, (1) we propose a novel integer programming model for the time-varying batch VM allocation problem, and (2) we design two truthful auction mechanisms to solve the allocation and pricing problem in a competitive environment. The optimal mechanism includes a dynamic programming (DP)-based resource allocation algorithm and a Vickrey–Clarke–Groves (VCG)-based payment price algorithm. Meanwhile, we also design a greedy mechanism that includes a dominant-resource-based allocation algorithm and a dichotomy-based payment price algorithm. We prove the economic characteristics, including truthfulness and individual rationality, of the above two mechanisms. Furthermore, we prove the approximation ratio of the allocation algorithm in the greedy mechanism. Compared to state-of-the-art research, our approach is characterized by high social welfare, a high served user ratio and a short execution time. [ABSTRACT FROM AUTHOR]

The computing power of mobile devices is too limited to execute computation tasks fast. Mobile edge computing (MEC) allows mobile devices to offload tasks to near servers to reduce the completion time of the tasks (a.k.a makespan). The input data of some critical tasks should be encrypted before the offloading. Aiming at the security critical tasks in the MEC composed of multiple servers, this paper addresses to minimize the makespan by scheduling security-critical tasks. We provide the formulation of the problem which is generally an integer programming problem, and three effective composite heuristics CH1–CH3 are proposed to solve the problem. Task permutations are considered as solutions. We construct a greedy heuristic algorithm to calculate the value of the objective. These three composite heuristics consist of two phases: solution initialization and solution improvement. In the first phase, the solutions of all the proposed algorithms are generated by a task arrangement rule called Biggest data Task First (BTF), and then in the second phase, improved by three searching methods based on different neighborhoods including a insertion neighborhood, a swap neighborhood and a hybrid neighborhood, respectively. Experimental results show that CH1–CH3 outperform the well-known RoundRobin algorithm. Particularly, BTF is demonstrated to initialize highly qualified solutions, making contributions to the high effectiveness. Meanwhile, all the improvement methods are justified to be effective and the method based on the hybrid neighborhood achieves the best effectiveness. [ABSTRACT FROM AUTHOR]

A proper coloring of a given graph is an assignment of a positive integer number (color) to each vertex such that two adjacent vertices receive different colors. This paper studies the Minimum Sum Coloring Problem (MSCP), which asks for finding a proper coloring while minimizing the sum of the colors assigned to the vertices. We propose the first branch-and-price algorithm to solve the MSCP to proven optimality. The newly developed exact approach is based on an Integer Programming (IP) formulation with an exponential number of variables which is tackled by column generation. We present extensive computational experiments, on synthetic and benchmark DIMACS graphs from the literature, to compare the performance of our newly developed branch-and-price algorithm against three compact IP formulations. On synthetic graphs, our algorithm outperforms the compact formulations in terms of: (i) number of solved instances, (i i) running times and (i i i) exit gaps obtained when optimality is not achieved. For the DIMACS instances, our algorithm is competitive with the best compact formulation and provides very strong dual bounds. [ABSTRACT FROM AUTHOR]

For a simple, undirected, connected graph G , a function h : V (G) → { 0 , 1 , 2 , 3 } which satisfies the following conditions is called a total Roman {3}-dominating function (TR3DF) of G with weight h (V) = ∑ p ∈ V h (p) : (C1) For every vertex u ∈ V if h (u) = 0 , then u has m (m ≥ 1) neighbors such that whose sum is at least 3, and if h (u) = 1 , then u has n (n ≥ 1) neighbors such that whose sum is at least 2. (C2) The subgraph induced by the set of vertices labeled one, two or three has no isolated vertices. For a graph G , the smallest possible weight of a TR3DF of G denoted γ t { R 3 } (G) is known as the total Roman { 3 } -domination number of G. The problem of determining γ t { R 3 } (G) of a graph G is called minimum total Roman {3}-domination problem (MTR3DP). In this paper, we show that the problem of deciding if G has a TR3DF of weight at most l for chordal graphs is NP-complete. We also show that MTR3DP is polynomial time solvable for bounded treewidth graphs, chain graphs and threshold graphs. We design a 3 (ln (Δ − 0. 5) + 1. 5) -approximation algorithm for the MTR3DP and show that the same cannot have (1 − δ) ln | V | ratio approximation algorithm for any δ > 0 unless NP ⊆ DTIME (| V | O (log log | V |)). Next, we show that MTR3DP is APX-complete for graphs with Δ = 4. We also show that the domination and total Roman {3}-domination problems are not equivalent in computational complexity aspects. Finally, we present an integer linear programming formulation for MTR3DP. [ABSTRACT FROM AUTHOR]

This paper proposes a new mixed integer programming formulation and branch and cut (BC) algorithm to solve the dial-a-ride problem (DARP). The DARP is a route-planning problem where several vehicles must serve a set of customers, each of which has a pickup and delivery location, and includes time window and ride time constraints. We develop "restricted fragments," which are select segments of routes that can represent any DARP route. We show how to enumerate these restricted fragments and prove results on domination between them. The formulation we propose is solved with a BC algorithm, which includes new valid inequalities specific to our restricted fragment formulation. The algorithm is benchmarked on existing and new instances, solving nine existing instances to optimality for the first time. In comparison with current state-of-the-art methods, run times are reduced between one and two orders of magnitude on large instances. [ABSTRACT FROM AUTHOR]

With the penetration of Network Function Virtualization (NFV), network functions, traditionally deployed as proprietary physical equipment like firewalls, Network Address Translations (NATs), are gradually being implemented as software and deployed on standardized hardware. One of the crucial challenges in this paradigm is how to place the software implemented network functions to minimize the number of used physical servers. In this paper, we study the problem of how to optimally place Virtual Network Functions (VNFs) in networks where it is allowed to migrate already placed VNFs to decrease used servers. We first formulate the offline problem as an Integer Linear Programming (ILP) problem, and then propose a semi-online algorithm to solve the online variant of the problem. We name the proposed algorithm Semi-onlIne Vnf plAcement (SIVA). In particular, SIVA is based on a bin packing algorithm that solves online bin packing problem while taking care of migrations. According to our theoretical analysis, SIVA migrates at most λ VNFs each step, and it has Asymptotic Competitive Ratio (ACR) of 3/2 if k → ∞ , where λ = k · | N | , k is a tunable parameter, and | N | is the the number of supported VNF types. We conduct extensive numerical simulations to evaluate the performances of SIVA. The experiment results validate the theoretical analysis and show that SIVA outperforms the state-of-the-art algorithms by achieving near-optimal performance with minor VNF migrations. [ABSTRACT FROM AUTHOR]

In the present paper, an exact algorithm is proposed for maximizing a quadratic function over the efficient set of a multi-objective integer linear fractional programming problem. This method uses a branch and bound search in the decision space and a cutting plane which will significantly shorten the search. A sequence of quadratic programs are solved, the feasible region is iteratively partitioned with two branching constraints or reduced using a cutting plane. We establish theoretical results which prove the effectiveness of this exact method. For illustration, a numerical example and some computational experiments are reported. [ABSTRACT FROM AUTHOR]

The maximum weighted stable set problem in claw-free graphs is a well-known generalization of the maximum weighted matching problem, and a classical problem in combinatorial optimization. In spite of the recent development of fast(er) combinatorial algorithms and some progresses in the characterization of the corresponding stable set polytope, the problem of "providing a decent linear description" for this polytope (Grötschel et al. in Geometric algorithms and combinatorial optimization, Springer, New York, 1988) is still open. The main contribution of this paper is to propose an algorithmic answer to that question by providing a polynomial-time and computationally attractive separation routine for the stable set polytope of claw-free graphs, that only requires a combinatorial decomposition algorithm, the solution of (moderate sized) compact linear programs, and Padberg and Rao's algorithm for separating over the matching polytope. In particular, it is a generalization of the latter and avoids the heavy computational burden of resorting to the ellipsoid method, on which the only poly-time separation routine known so far relied. Besides, our separation routine comes with a 'small' (but not polynomial) extended linear programming formulation and a procedure to derive a linear description of the stable set polytope of claw-free graphs in the original space. [ABSTRACT FROM AUTHOR]

A robot can determine its location by a set of fixed landmarks (consider the robot path is like a graph). By a signal from the robot, it can determine how far it from each among a set of fixed landmarks. We can formulate this problem such that the robot can always determine its location as the following: how to compute the minimum landmarks and where these landmarks should be placed. The metric dimension problem of a given graph can answer about the above two questions. The metric basis of the graph represents the set of landmarks and the metric dimension of the graph is equal to the cardinality of the landmarks. The determining of the metric dimension of an arbitrary graph is an NP-complete problem. In this paper we determine the metric dimension of new classes of networks with polynomial algorithms. In particular, the metric dimension of the triangular snake graph, the ladder graph Ln, Bk, the k-home chain graph Hk and the k-kite chain graph Kk are determined. We propose an exponential algorithm for finding the metric dimension of a given graph. We also introduce the results of computer calculations that determined the metric dimension of various classes of networks by using an approximate algorithm namely integer linear programming. Finally, a comparative analysis between the proposed approximate and exponential algorithms shows that the LINGO solver outperforms the proposed algorithm for huge graphs. [ABSTRACT FROM AUTHOR]

Abstract In this paper we consider a variant of the k -separator problem. Given a graph G = (V ∪ T , E) with V ∪ T the set of vertices, where T is a set of k terminals, the multi-terminal vertex separator problem consists in partitioning V ∪ T into k + 1 subsets { S , V 1 , ... , V k } such that there is no edge between two different subsets V i and V j , each V i contains exactly one terminal and the size of S is minimum. In this paper, we first show that the problem is NP-hard. Then we give two integer programming formulations for the problem. For one of these formulations, we investigate the related polyhedron and discuss its polyhedral structure. We describe some valid inequalities and characterize when these inequalities define facets. We also derive separation algorithms for these inequalities. Using these results, we develop a Branch-and-Cut algorithm for the problem, along with an extensive computational study. [ABSTRACT FROM AUTHOR]

This paper is concerned with the network selection for heterogeneous networks. Although many network selection approaches have been developed for heterogeneous networks, few of them explore the network selection problem for integrated cellular and drone-cell networks. Furthermore, most of the existing designs may be unsuitable for the integrated cellular and drone-cell networks owing to the high dynamic drone-cell-user association and the relatively limited drone-cell network capacity. In this paper, we investigate a network selection problem for the integrated cellular and drone-cell networks with a goal of maximizing a proportional fairness function of time average utilities across users under coarse correlated equilibrium constraints and minimum time average utility constraints. To mitigate this challenging problem, we first convert it into a non-linear integer programming (NLIP) problem based on our derived theoretical results. Next, we propose a repeated-stochastic-game-based efficient and fair network selection (RSG-EF) algorithm to alleviate the NLIP problem by leveraging a linear approximation mechanism. Simulation results show that the RSG-EF algorithm can achieve the highest total utility and a high level of fairness across users compared with three benchmark algorithms. [ABSTRACT FROM AUTHOR]

We are given a graph G = (V ∪ T , E) , with V ∪ T the set of vertices where T is a set of terminals and E the set of edges. The multi-terminal vertex separator problem consists in finding a subset of vertices S ⊆ V of minimum size intersecting all paths between every pair of terminals. In this paper we present three extended linear integer programming formulations for the multi-terminal vertex separator problem and we develop Branch-and-Price and Branch-and-Cut-and-Price algorithms. For each formulation we present the pricing problem, the branching scheme and the computation of the dual bound used during the column generation phase. Computational results are reported comparing the performance of the formulations on a set of instances. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of mixed integer programming problems (MIPs) whose objective functions are DC functions, that is, functions representable in terms of a difference of two convex functions. These MIPs contain a very wide class of computationally difficult non-convex MIPs since the DC functions have powerful expressability. Recently, Maehara, Marumo, and Mutota provided a continuous reformulation without integrality gaps for discrete DC programs having only integral variables. They also presented a new algorithm to solve the reformulated problem. Our aim is to extend their results to MIPs and give two specific algorithms to solve them. First, we propose an algorithm based on DCA originally proposed by Pham Dinh and Le Thi, where convex MIPs are solved iteratively. Next, to handle non-smooth functions efficiently, we incorporate a smoothing technique into the first method. We show that sequences generated by the two methods converge to stationary points under some mild assumptions. [ABSTRACT FROM AUTHOR]

Focusing on the balanced use of production capacity in the formulation of master production schedule (MPS), this paper sets up a single-product, multi-stage, multi-objective MPS model based on balanced production. Whereas the model aims to achieve multiple objectives through nonlinear integer programming, a genetic algorithm based on automatic transformation (AT-GA) was designed to solve the model. Specifically, the chromosomes were encoded as integers to satisfy the model constraints; the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) was adopted to handle the four nonlinear objectives of the model, thereby obtaining the fitness function; the fuzzy logic control (FLC) was introduced to automatically adjust the crossover and mutation parameters, and balance the global and local search abilities of the GA, enhancing the computing power of the algorithm. The experimental results show that the AT-GA can effectively solve the multi-objective MPS optimization problem under balanced production. [ABSTRACT FROM AUTHOR]

In signal optimization problems, incompatible movements are usually in either of two states: predecessor or successor. However, if the exit lane is well allocated, the incompatible movements merging at the same destination arm can exist in parallel. The corresponding longer green duration is expected to increase the capacity of intersections. This paper aims to solve the exit lane allocation problem with the lane-based method by applying the three states among incompatible movements at conventional signalized intersections. After introducing auxiliary variables, the problem is formulated as a mixed integer programming and can be solved using a standard branch-and-cut algorithm. In addition to the exit lane allocation results, this proposed method can also determine the cycle length, green duration, start of green, and signal sequence. The results show that the proposed method can obtain a higher capacity than that without the exit lane allocation. The pavement markings are further suggested for safety. [ABSTRACT FROM AUTHOR]

The discrete variable topology optimization method based on Sequential Approximate Integer Programming (SAIP) and Canonical relaxation algorithm demonstrates its potential to solve large-scale topology optimization problem with 0–1 optimum designs. However, currently, this discrete variable method mainly applies to the minimum compliance problem. The compliant mechanism design is another widely studied topic with distinguishing features. First, the objective function for the compliant mechanism design is non-monotonic with the material usage. Second, since de facto hinges always occur, the minimum length scale control is indispensable for manufacturability. These two issues are well studied in the SIMP approach but bring great challenges when topology optimization problems are formulated in the frame of discrete variables. The present paper generalizes this discrete variable method for the compliant mechanism design problems with minimum length scale control. Firstly, the sequential approximate integer programming with trust region (SAIP-TR) framework is proposed to directly restrict the variation of discrete design variables. Different from the continuous variable optimization, the non-linear trust region constraint can be formulated as a linear constraint under the SAIP framework. By using a merit function, two different trust region adjustment strategies that can self-adaptively adjust the precision of the sub-problems from SAIP-TR are explored. Secondly, a geometric constraint to control the minimum length scale for the material phase and void phase in the framework of discrete design variables is proposed, which suppresses de facto hinges and reduces stress concentration in optimum design. The related issue of feasibility of sub-problem is discussed. By combining the SAIP-TR framework with the geometric constraint, some different hinge-free compliant mechanism designs are successfully obtained. [ABSTRACT FROM AUTHOR]

An airport gate is the core resource of an airport operation, which is an important place for passengers to get on and off the aircraft and for maintaining aircraft. It is the prerequisite for other related dispatch. Effective and reasonable allocation of gates can reduce airport operating costs and increase passenger satisfaction. Therefore, an airport gate assignment problem (AGAP) needs to be urgently solved in the actual operation of the airport. In this paper, considering the actual operation of the airport, we formulate an integer programming model for AGAP by considering multiple constraints. The model aims to maximize the number of passengers on flights parked at the gate. A tabu search-based algorithm is designed to solve the problem. In the process of algorithm design, an effective initial solution is obtained. A unique neighborhood structure and search strategy for tabu search are designed. The algorithm can adapt to the dynamic scheduling of airports. Finally, tests are performed using actual airport data selected from Kunming Changshui International Airport in China. The experimental results indicate that the proposed method can enhance the local search ability and global search ability and get satisfactory results in a limited time. These results provide an effective support for the actual gate assignment in airport operations. [ABSTRACT FROM AUTHOR]

In this paper, a resource allocation problem is formulated to maximize the throughput of vehicular user equipments (VUEs) in both licensed, and unlicensed frequency bands under constraints of reliability, and latency for vehicular communications as well as the Quality of Service (QoS) for WiFi network based on a network system with coexisting VUEs, and WiFi user equipments (WUEs). In the system, the VUEs are able to access to the unlicensed frequency bands, and the interference among the VUEs, and WUEs are mitigated by the listen-before-talk (LBT) scheme or the duty cycle scheme. Due to the mixed integer nonlinear programming (MINLP) objective in the optimization problem, the problem is hard to be solved directly. Instead, we solve the problem by two steps. The number of VUEs offloaded to unlicensed frequency bands as well as the time factor for duty cycle scheme is firstly determined, and then, the optimization problem is converted into a convex optimization problem, which is solved by the proposed Lagrange Duality Method (LDM). Numerical results show the efficiency of our proposed application scenario compared to case with only LTE system or only WiFi system. Moreover, compared to traditional Greedy algorithm, the proposed algorithm performs better in terms of throughput with a guaranteed QoS of WUEs. [ABSTRACT FROM AUTHOR]

In this paper, we present recent developments in the global optimization software BARON to address problems with integer variables. A primary development was the addition of mixed-integer linear programming relaxations to BARON's portfolio of linear and nonlinear programming relaxations, aiming to improve dual bounds and offer good starting points for primal heuristics. Since such relaxations necessitate the solution of NP-hard problems, their introduction to a branch-and-bound algorithm raises many practical issues regarding their effective implementation. In addition to describing BARON's dynamic strategy for deciding under what conditions to activate integer programming relaxations in the course of branch-and-bound, the paper also describes cutting plane and probing techniques that originate from the literature of integer linear programming and have been adapted in BARON to solve nonlinear problems. Finally, we describe BARON's primal heuristics for finding good solutions of mixed-integer nonlinear programmes. For all these techniques, we report extensive computational results on a public data set, aiming to analyse the impact of each technique in the solution process and identify techniques that expedite solution the most. [ABSTRACT FROM AUTHOR]

For a positive integer k, a radio k-coloring of a simple connected graph G = (V(G), E(G)) is a mapping f : V (G) → { 0 , 1 , 2 , ... } such that | f (u) - f (v) | ≥ k + 1 - d (u , v) for each pair of distinct vertices u and v of G, where d(u, v) is the distance between u and v in G. The span of a radio k-coloring f, rck(f), is the maximum integer assigned by it to some vertex of G. The radio k-chromatic number, rck(G) of G is min{rck(f)}, where the minimum is taken over all radio k-colorings f of G. If k is the diameter of G, then rck(G) is known as the radio number of G. In this paper, we propose an improved upper bound of radio k-chromatic number for a given graph against the other which is due to Saha and Panigrahi (in: Arumugan, Smyth (eds) Combinatorial algorithms (IWOCA 2012). Lecure notes in computer science, vol 7643, Springer, Berlin, 2012). The computational study shows that the proposed algorithm overcomes the previous algorithm. We introduce a polynomial algorithm [differs from the other that is due to Liu and Zhu (SIAM J Discrete Math 19(3):610–621, 2005)] which determines the radio number of the path graph Pn. Finally, we propose a new integer linear programming model for the radio k-coloring problem. The computational study between the proposed algorithm and LINGO solver shows that the proposed algorithm overcomes LINGO solver. [ABSTRACT FROM AUTHOR]

In this paper, we propose a two-stage robust optimization framework to evaluate widely controllable commuter flow strategies that can help mitigate uncertain disruption impacts on rail transit commuter flows. In the operation-as-usual stage, preemptive control strategies including timetable adjustment, commuter path choice diversion, and commuter trip starting time diversion are planned within budget and other requirement constraints. In the disruption stage, optimal contingency routing is derived to minimize disruption impacts. To this end, a linear programming model that simulates the commuter movement logic under train service and platform disruption events is developed, which is then integrated in a mixed-integer max-min optimization model to evaluate the worst-case impacts on commuter flows arising from a set of uncertain disruption scenarios. We show that the two-stage robust optimization framework can be solved by a cutting plane algorithm efficiently using high performance and parallel computing platforms. Finally, we demonstrate the application of the model in mitigating disruption impacts through computational studies based on an actual rail transit network. [ABSTRACT FROM AUTHOR]