Integer Optimization Problem Research Articles

Optimal power quality monitor placement to ensure reliable monitoring of sensitive loads in the presence of voltage sags and harmonic resonances conditions

Nowadays, sensitive nonlinear loads such as load commutated inverter drives are increasingly being used by industrial consumers. In one hand, sensitive nonlinear loads can induce parallel resonance condition to the network and in the other hand their continuous operation may be interrupted due to voltage sags. Therefore, power quality parameters associated with the secure performance of sensitive nonlinear loads must be monitored to avoid the adverse effects of parallel resonances and financial losses due to voltage sags. In this paper, a new approach based on the area of vulnerability to voltage sags and harmonic resonance mode analysis is proposed to determine the optimal number and the best location of power quality monitors (PQMs). The proposed method is formulated as a linear integer optimization problem which is simply solved. In addition, in case where a budget limitation does not allow to purchase the required number of monitors and the optimization problem does not converge an alternative approach is proposed for allocating very limited number of monitors in a hierarchical manner to ensure monitoring of the most severe conditions. The proposed approach is applied on the IEEE 30-bus system and an Iranian real industrial network. © 2017 Elsevier Inc. All rights reserved.

Simultaneous layout and size optimization of nonlinear viscous dampers for frame buildings under stochastic seismic excitation

Viscous dampers, as effective energy-dissipation devices, have been widely used for seismic mitigation of building structures. Due to the intrinsic uncertainties of structural parameters and earthquake ground motions, to obtain an optimal performance of structural control, the stochastic design optimization of viscous dampers for buildings is essential. This paper establishes a new dynamic reliability-based optimization framework to address the simultaneous layout and size design of nonlinear viscous dampers in frame buildings, considering the dual randomness of both nonstationary seismic excitations and uncertain structural model parameters. Firstly, a mixed integer optimization problem for nonlinear viscous dampers, including discrete and continuous design variables, is formulated, and the design target is to minimize the cost of the dampers subjected to performance constraints on dynamic reliability of building structures. Then, sequential approximate mixed integer programming with trust region is proposed to solve the optimization problem. Moreover, direct probability integral method is suggested to assess the dynamic reliability and its sensitivity with respect to design variables. Finally, accounting for both stochastic nonstationary seismic excitations and random structural parameters, the optimized results of two numerical examples indicate that the proposed method is a competitive choice for realizing the layout and size optimization of limiting types of nonlinear viscous dampers in frame buildings. To ensure the same target performance of buildings in terms of the probability of exceeding the target value of inter-story drift, the larger peak ground acceleration of stochastic ground motions is, the more cost of dampers is required for seismic protection of buildings.

A combinatorial flow-based formulation for temporal bin packing problems

We consider two neighboring generalizations of the classical bin packing problem: the temporal bin packing problem (TBPP) and the temporal bin packing problem with fire-ups (TBPP-FU). In both cases, the task is to arrange a set of given jobs, characterized by a resource consumption and an activity window, on homogeneous servers of limited capacity. To keep operational costs but also energy consumption low, TBPP is concerned with minimizing the number of servers in use, whereas TBPP-FU additionally takes into account the switch-on processes required for their operation. Either way, challenging integer optimization problems are obtained, which can differ significantly from each other despite the seemingly only marginal variation of the problems. In the literature, a branch-and-price method enriched with many preprocessing steps (for TBPP) and compact formulations (for TBPP-FU), benefiting from numerous reduction methods, have emerged as, currently, the most promising solution methods. In this paper, we introduce, in a sense, a unified solution framework for both problems (and, in fact, a wide variety of further interval scheduling applications) based on graph theory. Any scientific contributions in this direction failed so far because of the exponential size of the associated networks. The approach we present in this article does not change the theoretical exponentiality itself, but it can make it controllable by clever construction of the resulting graphs. In particular, for the first time all classical benchmark instances (and even larger ones) for the two problems can be solved – in times that significantly improve those of the previous approaches.

The smoothed number of Pareto-optimal solutions in bicriteria integer optimization

A well-established heuristic approach for solving bicriteria optimization problems is to enumerate the set of Pareto-optimal solutions. The heuristics following this principle are often successful in practice. Their running time, however, depends on the number of enumerated solutions, which is exponential in the worst case. We study bicriteria integer optimization problems in the model of smoothed analysis, in which inputs are subject to a small amount of random noise, and we prove an almost tight polynomial bound on the expected number of Pareto-optimal solutions. Our results give rise to tight polynomial bounds for the expected running time of the Nemhauser-Ullmann algorithm for the knapsack problem and they improve known results on the running times of heuristics for the bounded knapsack problem and the bicriteria shortest path problem.

A review on the studies employing artificial bee colony algorithm to solve combinatorial optimization problems

The ABC algorithm is one of the popular optimization algorithms and has been used successfully in solving many real-world problems. Numeric, binary, integer, mixed integer and combinatorial optimization problems are among the areas where ABC algorithm is used. Combinatorial optimization problems appear in many problem groups in real life. Due to the nature of these problems, they are classified as difficult problems. It is seen in the literature that hundreds of studies have been conducted using the ABC algorithm in solving combinatorial optimization problems. In this study, combinatorial optimization approaches based on ABC algorithm are examined in detail, in order to shed light on new studies. Combinatorial optimization problems are analyzed under 12 groups. These are assembly/disassembly, bioinformatic, graph coloring, routing, rule mining, aware web service composition, socially network analysis, team orienteering, timetabling, traveling salesman, vehicle routing and other problems. 251 studies of related problems are examined. Brief summaries of the studies on combinatorial optimization problems are presented and the ABC algorithm-based approaches used are introduced. Tables, images and equations are included for better understanding of the subject. The added mechanisms to improve the local search capability of the ABC algorithm are evaluated. Neighborhood operators used in ABC algorithms are examined. The used selection schemes and initial populations determination approaches are given. It is stated which mechanisms are included in hybrid approaches based on ABC algorithm. The test instances used to evaluate the performances of the ABC algorithms are mentioned.

Branch-and-bound and objective branching with three or more objectives

The recent success of bi-objective Branch-and-Bound (B&B) algorithms heavily relies on the efficient computation of upper and lower bound sets. These bound sets are used as a supplement to the classical dominance test to improve the computational time by imposing inequalities derived from (partial) dominance in the objective space. This process is called objective branching since it is mostly applied when generating child nodes. In this paper, we extend the concept of objective branching to multi-objective integer optimization problems with three or more objective functions. Several difficulties arise in this case, as there is no longer a lexicographic order among non-dominated outcome vectors when there are three or more objectives. We discuss the general concept of objective branching in any number of dimensions and suggest a merging operation of local upper bounds to avoid the generation of redundant sub-problems. Finally, results from extensive experimental studies on several classes of multi-objective optimization problems is reported.

Special Issue: Global Solution of Integer, Stochastic and Nonconvex Optimization Problems

Special Issue: Global Solution of Integer, Stochastic and Nonconvex Optimization Problems

Age-Driven Spatially Temporally Correlative Updating in the Satellite-Integrated Internet of Things via Markov Decision Process

In this article, we consider the data updating problem in the Satellite-integrated Internet of Things network for the time-critical scenarios, i.e., animal tracking and environmental monitoring. Due to the limited channel rate during contact of transmission, however, constantly updating data with huge volume over the uplink will incur obvious waiting and transmission delay bringing stale information to the satellite node. To address this issue, we propose a novel metric, spatially temporally correlative mutual information (STI), to characterize the information timeliness from perspective of information entropy by considering the correlations between the last update message and the status of the information source. By maximizing the averaged STI, we find the optimal allocation policy of channel slots with a fixed updating period by formulating the problem as a Markov decision process (MDP) with possibly infinite state space. Furthermore, we derive the optimal amounts of allocated time slots in a unit frame by solving a constrained range integer optimization problem with respect to the average STI. The simulation results show that the proposed periodically updating policy can significantly improve the information freshness compared with the original slot allocation strategy and current commonly used scheduled access strategies, i.e., slotted ALOHA and Threshold-ALOHA.

Potts model solver based on hybrid physical and digital architecture

The Potts model describes Ising-model-like interacting spin systems with multivalued spin components, and ground-state search problems of the Potts model can be efficiently mapped onto various integer optimization problems thanks to the rich expression of the multivalued spins. Here, we demonstrate a solver of this model based on hybrid computation using physical and digital architectures, wherein a digital computer updates the interaction matrices in the iterative calculations of the physical Ising-model solvers. This update of interactions corresponds to learning from the Ising solutions, which allows us to save resources when embedding a problem in a physical system. We experimentally solved integer optimization problems (graph coloring and graph clustering) with this hybrid architecture in which the physical solver consisted of coupled degenerate optical parametric oscillators.

Clustering Based on Continuous Hopfield Network

Clustering aims to group n data samples into k clusters. In this paper, we reformulate the clustering problem into an integer optimization problem and propose a recurrent neural network with n×k neurons to solve it. We prove the stability and convergence of the proposed recurrent neural network theoretically. Moreover, clustering experiments demonstrate that the proposed clustering algorithm based on the recurrent neural network can achieve the better clustering performance than existing clustering algorithms.

Intrinsic mixed-integer polycubes for hexahedral meshing

Polycube mapping is an attractive approach for the generation of all-hexahedral meshes with a fully regular interior, i.e. free of internal singular edges or vertices. It is based on determining a low distortion map between the input model and a polycube domain, which then pulls back the regular voxel grid to form a hexahedral mesh for the model. Automatically finding an appropriate polycube domain for a given model, however, is a challenging problem. Existing algorithms are either very sensitive to the embedding and orientation of the input model, restricted to only subclasses of possible domains, or depend crucially on some initialization because they rely on a non-convex optimization formulation. This can easily lead to unsatisfactory and unnecessary corners and edges in the polycube structure. We present a novel approach to the problem of finding high-quality polycube domains. It is based on an entirely intrinsic formulation as a mixed integer optimization problem, which can be tackled by solving a series of simple convex problems, each of which can be solved to the global optimum. Experiments demonstrate that our method avoids many of the undesired corners and surface irregularities common to many previous methods.

Satisficing Models Under Uncertainty

Satisficing, as an approach to decision making under uncertainty, aims at achieving solutions that satisfy the problem’s constraints as well as possible. Mathematical optimization problems that are related to this form of decision making include the P-model. In this paper, we propose a general framework of satisficing decision criteria and show a representation termed the S-model, of which the P-model and robust optimization models are special cases. We then focus on the linear optimization case and obtain a tractable probabilistic S-model, termed the T-model, whose objective is a lower bound of the P-model. We show that when probability densities of the uncertainties are log-concave, the T-model can admit a tractable concave objective function. In the case of discrete probability distributions, the T-model is a linear mixed integer optimization problem of moderate dimensions. Our computational experiments on a stochastic maximum coverage problem suggest that the T-model solutions can be highly competitive compared with standard sample average approximation models.

Optimal ship lifetime fuel and power system selection

Alternative fuels and fuel-flexible ships are often seen as promising solutions for achieving significant greenhouse gas reductions in shipping. We formulate the selection of alternative fuels and corresponding ship power systems as a bi-objective integer optimization problem. We apply our model to a Supramax Dry-bulker and solve it for a lower bound price scenario including a carbon tax. Within this setting, the question whether bio-fuels will be available to shipping has significant effect on the lifetime costs. For the given scenario and case study ship, our model identifies LNG as a robust power system choice today for a broad range of GHG reduction ambitions. For high GHG reduction ambitions, a retrofit to ammonia, produced from renewable electricity, appears to be the most cost-effective option. While these findings are case-specific, the model may be applied to a broad range of cargo ships.

Who should get vaccinated? Individualized allocation of vaccines over SIR network

How to allocate vaccines over heterogeneous individuals is one of the important policy decisions in pandemic times. This paper develops a procedure to estimate an individualized vaccine allocation policy under limited supply, exploiting social network data containing individual demographic characteristics and health status. We model the spillover effects of vaccination based on a Heterogeneous-Interacted-SIR network model and estimate an individualized vaccine allocation policy by maximizing an estimated social welfare (public health) criterion incorporating these spillovers. While this optimization problem is generally an NP-hard integer optimization problem, we show that the SIR structure leads to a submodular objective function, and provide a computationally attractive greedy algorithm for approximating a solution that has a theoretical performance guarantee. Moreover, we characterize a finite sample welfare regret bound and examine how its uniform convergence rate depends on the complexity and riskiness of the social network. In the simulation, we illustrate the importance of considering spillovers by comparing our method with targeting without network information.

Auto-Tuning for Cellular Scheduling Through Bandit-Learning and Low-Dimensional Clustering

We propose an online algorithm for clustering channel-states and learning the associated achievable multiuser rates. Our motivation stems from the complexity of multiuser scheduling. For instance, MU-MIMO scheduling involves the selection of a user subset and associated rate selection each time-slot for varying channel states (the vector of quantized channels matrices for each of the users) — a complex integer optimization problem that is different for each channel state. Instead, our algorithm clusters the collection of channel states to a much lower dimension, and for each cluster provides achievable multiuser capacity trade-offs, which can be used for user and rate selection. Our algorithm uses a bandit approach, where it learns both the unknown partitions of the channel-state space (channel-state clustering) as well as the rate region for each cluster along a pre-specified set of directions, by observing the success/failure of the scheduling decisions (e.g. through packet loss). We propose an epoch-greedy learning algorithm that achieves a sub-linear regret, given access to a class of classifying functions over the channel-state space. We empirically validate our approach on a high-fidelity 5G New Radio (NR) wireless simulator developed within AT&T Labs. We show that our epoch-greedy bandit algorithm learns the channel-state clusters and the associated rate regions. Further, adaptive scheduling using this learned rate-region model (map from channel-state to the set of feasible rates) outperforms the corresponding hand-tuned static maps in multiple settings. Thus, we believe that auto-tuning cellular systems through learning-assisted scheduling algorithms can significantly improve performance in real deployments.

Indirect Multi-Mapping for Burstiness Management in Software Defined Networks

Large software defined networks use a cluster of distributed controllers to process flow requests from a massive number of switches. To cope with traffic dynamics, this paper studies a new problem of how to improve the residual capacity available at the controllers to handle request bursts experienced at the switches. While the total residual capacity is a constant under a given total capacity of all controllers and a given total workload from all switches, this paper considers the residual capacity available to each individual switch, which depends on how the switches are mapped to the controllers for management. We focus on how to maximize the minimum residual capacity available to any switch . The prior work either provides poor residual capacity or incurs heavy synchronization overhead by simulation results. This paper proposes a new method called indirect multi-mapping that achieves both high residual capacity and low synchronization cost. We formally define a non-linear integer optimization problem for max-min residual capacity under indirect multi-mapping. We then approximate the problem as two sub-problems: switch-controller mapping selection and weight assignment for each switch-controller mapping. We solve these sub-problems and formally analyze their approximate factor. We implement the proposed solution on an SDN testbed for experimental studies and use simulations for large-scale investigation. Our evaluation shows that indirect multi-mapping improves the minimum residual capacity by 49.8% on average and reduces the synchronization cost by 41.9-60.3% on average when compared with the alternatives.

Semi-Supervised Kernel Matching for Domain Adaptation

In this paper, we propose a semi-supervised kernel matching method to address domain adaptation problems where the source distribution substantially differs from the target distribution. Specifically, we learn a prediction function on the labeled source data while mapping the target data points to similar source data points by matching the target kernel matrix to a submatrix of the source kernel matrix based on a Hilbert Schmidt Independence Criterion. We formulate this simultaneous learning and mapping process as a non-convex integer optimization problem and present a local minimization procedure for its relaxed continuous form. Our empirical results show the proposed kernel matching method significantly outperforms alternative methods on the task of across domain sentiment classification.

Sparse Network Optimization for Synchronization

We propose new mathematical optimization models for generating sparse dynamical graphs, or networks, that can achieve synchronization. The synchronization phenomenon is studied using the Kuramoto model, defined in terms of the adjacency matrix of the graph and the coupling strength of the network, modelling the so-called coupled oscillators. Besides sparsity, we aim to obtain graphs which have good connectivity properties, resulting in small coupling strength for synchronization. We formulate three mathematical optimization models for this purpose. Our first model is a mixed integer optimization problem, subject to ODE constraints, reminiscent of an optimal control problem. As expected, this problem is computationally very challenging, if not impossible, to solve, not only because it involves binary variables but also some of its variables are functions. The second model is a continuous relaxation of the first one, and the third is a discretization of the second, which is computationally tractable by employing standard optimization software. We design dynamical graphs that synchronize, by solving the relaxed problem and applying a practical algorithm for various graph sizes, with randomly generated intrinsic natural frequencies and initial phase variables. We test robustness of these graphs by carrying out numerical simulations with random data and constructing the expected value of the network’s order parameter and its variance under this random data, as a guide for assessment.

About stability of mixed integer optimization problems under perturbations of input data of vector criterion

The article is devoted to the study of the influence of uncertainty in initial data on the solutions of mixed integer optimization vector problems. In the optimization problems, including problems with vector criterion, small perturbations in initial data can result in solutions strongly different from the true ones. The problem of stability of the indicated tasks is studied from the point of view of direct coupled with her question in relation to stability of solutions belonging to some subsets of feasible set.

Resilience improvement of multi-microgrid distribution networks using distributed generation

Natural disasters such as earthquakes, hurricanes, and other extreme weather events along with human sabotage attacks pose serious risks to critical infrastructures especially electrical energy systems. Hardening and operational actions are the measures to improve the resiliency of the power systems against extreme events. The long-term hardening actions strive to organize the reinforcement of power system infrastructures which accomplished at the pre-events stage. Besides, the short-term operational measures such as network reconfiguration and generation scheduling are applied to form the multiple microgrids aimed at increasing the flexibility of the power system to cope with the severe events. These measures are taken during and after the occurrence of the disasters. In this paper, an integrated framework has been proposed to increase the resiliency of distribution system. In the proposed framework, there are two models so called defender–attacker–defender which are made to find the best possible solution in order to reduce the load-shedding of the system during extreme events. In the first model, the hardening measures are examined at the first level to increase the robustness of the system. The worst scenarios with the highest load-shedding are calculated in the second level and subsequently reconfiguration is performed in the third level to decrease the load-shedding. In the second model, the first and second levels specify the best reinforcement plan and the worst attack scenario respectively, and in the third level, optimal distributed generation placement is accomplished to supply the demand during islanding mode of microgrids. The proposed models are organized as tri-level mixed integer optimization problem and column constraint generation algorithm is utilized to make them computationally obedient. At the end, we have implemented the suggested models on the well-known IEEE 33-bus and 69-bus systems to prove their effectiveness and applicability at improving the resiliency of the distribution systems. • Two models are considered to increase the resilience of the distribution network against extreme events. • In the first model, a three-level framework is performed by considering reinforcement and reconfiguration programs. • In the second model, a three-level model with reinforcement programs and optimal DG placement is examined. • The proposed models find the worst possible attack scenario.