Integer Variables Research Articles

Active Model Discrimination for Piecewise Affine Inclusion Systems

This paper proposes a novel set-membership active model discrimination (AMD) algorithm for actively separating/discriminating among a set of piecewise Affine inclusion systems with bounded noise. Specifically, to overcome the difficulties of dealing the integer variables in the lower/inner level of the associated bilevel optimization problem that stem from the mapping of the piecewise inclusions and subregions, we propose an alternative reformulation that moves the integer variables into the higher/outer level. This reformulation allows us to leverage Karush-Kuhn-Tucker (KKT) conditions to obtain an equivalent single level mixed-integer linear programming (MILP) problem. Moreover, in contrast to standard AMD algorithms that strictly enforces model separation, we propose a slight modification/extension that separates as many models as possible when a strict separation of all models is not possible.

A unit commitment based-co-optimization of generation and transmission expansion planning to mitigate market power

• A unit-commitment-based generation and transmission expansion planning model is proposed. • The planning problem is subject to the market power's constraint. • The scenario-based model is structured as a mixed-integer bi-level programming (MIBP). • The lower-level problem computes the must-run generation (MRG) as a market index. • An exact algorithm using the reformulation-and-decomposition technique is utilized to attain the optimal solution. This paper aims to construct a novel strategy for coordinated generation and transmission expansion planning (CGTEP) considering market power. The integrated model constitutes bi-level programming from a centralized planning point of view. The upper level seeks to minimize the investment and operation cost subject to technical constraints, while the lower level's objective is to mitigate the market power. A stochastic unit commitment-based approach is employed at the upper level to find the least-cost solution and at the lower level to minimize the transmission-constrained market power index. Since the lower level contains integer variables, it is impossible to utilize the Karush-Kuhn-Tucker (KKT) conditions or duality theory (DT) to convert the bi-level problem into a single level. Hence, an exact algorithm using the reformulation-and-decomposition technique (RDT) is utilized to attain the optimal solution to this complex mixed-integer bi-level programming (MIBP) problem. The IEEE 118-bus electric power network is used for numerical studies. Results from the numerical studies signify the effectiveness of the presented model showing that a well-designated power system can significantly mitigate market power.

Otimização multiobjetivo de outriggers em edifícios altos submetidos a cargas de vento

abstract: This paper aims to investigate a methodology for determining the optimum floor positioning of outriggers (ORs) and belt-trusses (BTs) over tall buildings height. The primary goal is to reduce the maximum lateral drift (MLD) and the core base moment (CBM), individually and concurrently. Furthermore, the influence of these elements on other criteria such as maximum acceleration and natural frequencies are analyzed. Throughout the work, the behavior of the structure is verified when the stiffness ratio of the main elements used in the bracing system (core, perimeter columns, OR, and BT) are varied. Therefore, a three-dimensional model of a tall building under lateral wind load is analyzed, using the finite element method with ANSYS software. The mono and multi-objective optimizations were solved, respectively, by the Nelder-Mead method with the author’s modifications to deal with integer variables and by a utility function. Based on the results, it is concluded that by specifically adding ORs/ORs-BTs in tall buildings the influence on the reduction of the mentioned objectives is extremely relevant, reaching up to 68% for the CBM and 71% for the MLD, depending on the amounts employed.

Modified differential evolution method for parametric synthesis of fuzzy control system

A modification for differential evolution method is developed to solve the problem of synthesizing a fuzzy system with optimal parameters. This modification allows you to handle both integer and continuous variables, making it possible to solve any mixed integer-continuous problems, including parametric synthesis of fuzzy control system, as it contains both types of parameters. The main idea of the modification is to change the procedure for generating the initial population, as well as the introduction of additional restrictions that ensure the correct operation of the fuzzy system. The key idea of the modification is to change the procedure for the formation of the initial population, as well as the introduction of additional restrictions that ensure the correct operation of the fuzzy system. The problem of optimizing the parameters of a fuzzy system was formalized: a fuzzy system is represented by a vector of parameters characterizing it, and a control quality criterion is considered as an object function. To illustrate the operation of the algorithm, a fuzzy system was compiled that allows solving the problem of optimal speed performance.

Multi-Domain Resource Scheduling for Simultaneous Wireless Computing and Power Transfer in Fog Radio Access Network

Future 6G is deemed to provide Simultaneous Wireless cOmputing and Power Transfer (SWOPT) services for addressing the shortage of local computation and that of energy at terminal devices in the era of the Internet of Everything (IoE). In this paper, we study a fog radio access network (F-RAN) consisting of enhanced remote radio heads (eRRHs) with multiple antennas and edge computing capabilities. The F-RAN simultaneously supports task offloading of computing users (CUs) and energy harvesting of energy users (EUs). Thanks to the global coordination of a central server, full cooperation among eRRHs in both computing and communication domains can substantially improve the SWOPT performance. Specifically, the energy harvesting performance of EUs is maximised by jointly optimising the bandwidth and the beam resources in the communication domain as well as the computing frequency and the offloading strategy in the computing domain. The original non-convex problem with mixed integer and continuous variables is then solved by sequential convex optimisations in the framework of a greedy algorithm with low complexity. Thorough simulation results demonstrate the advantage of our proposed resource scheduling scheme over the existing state-of-the-art counterparts.

An exact algorithm for linear integer programming problems with distributionally robust chance constraints

The distributionally robust chance constrained integer programming problems are notoriously hard to solve due to the stochastic feature and the discrete nature of integer variables. In this paper, an exact solution method is developed for linear integer programming problems with the distributionally robust chance constraint. By exploring the geometric properties, some domain cut techniques based on feasible points and infeasible points are derived. Thus cut off some sub-boxes which do not contain any optimal solution and the optimality gap is reduced successively in the solution iterations. Then the optimal solution will be found in a finite number of iterations. Encouraging computational results are also reported in the paper.

Throughput Maximization for UAV-Enabled Integrated Periodic Sensing and Communication

Driven by unmanned aerial vehicle (UAV)’s advantages of flexible observation and enhanced communication capability, it is expected to revolutionize the existing integrated sensing and communication (ISAC) system and promise a more flexible joint design. Nevertheless, the existing works on ISAC mainly focus on exploring the performance of both functionalities simultaneously during the entire considered period, which may ignore the practical asymmetric sensing and communication requirements. In particular, always forcing sensing along with communication may make it is harder to balance between these two functionalities due to shared spectrum resources and limited transmit power. To address this issue, we propose a new integrated periodic sensing and communication (IPSAC) mechanism for the UAV-enabled ISAC system to provide a more flexible trade-off between two integrated functionalities. Specifically, the system achievable rate is maximized via jointly optimizing UAV trajectory, user association, target sensing selection, and transmit beamforming, while meeting the sensing frequency and beam pattern gain requirement for the given targets. Despite that this problem is highly non-convex and involves closely coupled integer variables, we derive the closed-form optimal beamforming vector to dramatically reduce the complexity of beamforming design, and present a tight lower bound of the achievable rate to facilitate UAV trajectory design. Based on the above results, we propose a two-layer penalty-based algorithm to efficiently solve the considered problem. To draw more important insights, the optimal achievable rate and the optimal UAV location are analyzed under a special case of infinity number of antennas. Furthermore, we prove the structural symmetry between the optimal solutions in different ISAC frames without location constraints in our considered UAV-enabled ISAC system. Based on this, we propose an efficient algorithm for solving the problem with location constraints. Numerical results validate the effectiveness of our proposed designs and also unveil a more flexible trade-off in ISAC systems over benchmark schemes.

Model Predictive Control for Neuromimetic Quantized Systems

Based on our recent research on neural heuristic quantized systems, we propose an emulation problem consistent with our recently introduced neuromimetic paradigm. This optimal quantization problem can be solved with model predictive control (MPC) by deriving the conditions under which the quantized system can simultaneously guarantee (asymptotic) stability and emulation given dynamical system by optimizing a Lyapunov-like objective function. Taking inspiration from neurobiology, the neuromimetic model features large numbers of discrete inputs that collectively produce stable motions that emulate the behavior of a continuous system. The emulation is produced by solving an optimization problem involving integer variables. The approach in the paper begins by performing the optimization using model predictive control (MPC) and then using a neural network to train a model using the data generated in this process. Complexity is reduced by applying Fincke and Pohst's sphere decoding algorithm to narrow down the search for the optimal solution.

Accelerated and Adaptive Power Scheduling for More Electric Aircraft Via Hybrid Learning

In recent studies, the power scheduling in more electric aircraft (MEA) has been formulated as a mixed-integer quadratic programming problem. Many model-driven methods, such as branch-and-bound algorithms, are advocated to solve it. However, these methods are often prone to considerably high complexities, which makes real-time processing a problem. In this article, a two-stage hybrid learning-based optimization approach is proposed to address this challenging issue. In the first stage, the task of optimizing integer variables is considered as a multilabel classification problem, which is solved by a data-driven method, i.e., ensemble deep neural networks (EDNNs). In the second stage, with the obtained integer solutions, the problem is transformed into a quadratic programming problem that can be quickly solved by <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">model-driven</i> numerical optimization methods. Compared to the state-of-the-art power scheduling algorithms, the model-driven and data-driven methods can compensate each other so that this two-stage hybrid learning-based approach can achieve orders of magnitude speedup in computational time, while guaranteeing the optimal scheduling performance. The structures of EDNNs are well designed so that the proposed approach can adapt to varying operating conditions in MEA. An offline simulation test and an online hardware-in-the-loop test validate the above advantages of the proposed approach.

Bivariate Variations of Fibonacci and Narayana Sequences and Universal Codes

In this study, we worked on the third-order bivariate variant of the Fibonacci universal code and the second-order bivariate variant of the Narayana universal code, depending on two negative integer variables u and v. We then showed in tables these codes for 1≤k≤100, u=-1,-2,…,-20, and v=-2,-3,…,-21 (u and v are consecutive, v$

An efficient and reliable scheduling algorithm for unit commitment scheme in microgrid systems using enhanced mixed integer particle swarm optimizer considering uncertainties

The use of an electrical energy storage system (EESS) in a microgrid (MG) is widely recognized as a feasible method for mitigating the unpredictability and stochastic nature of sustainable distributed generators and other intermittent energy sources. The battery energy storage (BES) system is the most effective of the several power storage methods available today. The unit commitment (UC) determines the number of dedicated dispatchable distributed generators, respective power, the amount of energy transferred to and absorbed from the microgrid, as well as the power and influence of EESSs, among other factors. The BES deterioration is considered in the UC conceptualization, and an enhanced mixed particle swarm optimizer (EMPSO) is suggested to solve UC in MGs with EESS. Compared to the traditional PSO, the acceleration constants in EMPSO are exponentially adapted, and the inertial weight in EMPSO decreases linearly during each iteration. The proposed EMPSO is a mixed integer optimization algorithm that can handle continuous, binary, and integer variables. A part of the decision variables in EMPSO is transformed into a binary variable by introducing the quadratic transfer function (TF). This paper also considers the uncertainties in renewable power generation, load demand, and electricity market prices. In addition, a case study with a multiobjective optimization function with MG operating cost and BES deterioration defines the additional UC problem discussed in this paper. The transformation of a single-objective model into a multiobjective optimization model is carried out using the weighted sum approach, and the impacts of different weights on the operating cost and lifespan of the BES are also analyzed. The performance of the EMPSO with quadratic TF (EMPSO-Q) is compared with EMPSO with V-shaped TF (EMPSO-V), EMPSO with S-shaped TF (EMPSO-S), and PSO with S-shaped TF (PSO-S). The performance of EMPSO-Q is 15%, 35%, and 45% better than EMPSO-V, EMPSO-S, and PSO-S, respectively. In addition, when uncertainties are considered, the operating cost falls from $8729.87 to $8986.98. Considering BES deterioration, the BES lifespan improves from 350 to 590, and the operating cost increases from $8729.87 to $8917.7. Therefore, the obtained results prove that the EMPSO-Q algorithm could effectively and efficiently handle the UC problem.

Coordinated scheduling of production and logistics for large-scale closed-loop manufacturing using Benders decomposition optimization

This paper studies coordinated scheduling of production and logistics for a large-scale closed-loop manufacturing system by integrating its manufacturing and recycling process. In addition to the forward manufacturing process, different recycling units in reverse recycling process are also studied. A decentralized network is designed to formulate the coordinated scheduling problem as a mixed integer programming model with both binary and integer variables. As the problem for closed-loop manufacturing is large-scale and computational-consuming in nature, the model is divided into integer variable sub-models and complex binary variable sub-models for preprocessing and reprocessing respectively. An iterative solution approach by Benders decomposition is developed to accelerate the solving efficiency in large-scale case by updating custom constraints. A case study is conducted to investigate the managerial implications of the decentralized network for the closed-loop manufacturing system. Computational experiments demonstrate the validity and efficiency of the proposed iterative solution approach for the large-scale scenarios.

Infrastructure planning for ride-hailing services using shared autonomous electric vehicles

Ride-hailing services using shared autonomous electric vehicles (SAEVs) are soon expected to serve a significant portion of the public transportation demands, especially in metropolitan cities. The transportation demands will arise randomly across all transportation nodes and during all hours of operation. This spatio-temporal nature of the transportation demand together with the constraints of trip length, battery size and consumption rate, and power network will guide the actions of the SAEVs. These actions are pair-with-demand, park, charge, and relocate, which in turn will determine the necessary infrastructure plan for ride-hailing services. The plan will comprise SAEV fleet size, charging hub locations across the nodes of the transportation network, and the number of charging stations in each hub. We formulate a profit-maximizing mixed integer linear model comprising a space-time-battery representation of the transportation network and a DC power flow representation of the power network. The model, intended for developing infrastructure plans for ride-hailing services, is robustified to accommodate randomness in travel and electric power demand. The model solution is demonstrated via an illustrative numerical case study representing the Tampa Bay region of Florida, USA. The results show how the infrastructure plans and their profitability depend on the demand fulfillment goal, battery size, battery consumption rate, and power network configurations. A linear relaxation of some of the integer variables of the model to reduce computational time is discussed.

Computation bits maximization in backscatter-aided wireless powered MEC using binary offloading

This article considers a backscatter-aided wireless powered mobile edge computing (BC-aided WPMEC) network, in which the tasks data of each Internet of Things (IoT) device can be computed locally or offloaded to the MEC server via backscatter communications, and design a resource allocation scheme regarding the weighted sum computation bits (WSCB) maximization of all the IoT devices. Towards this end, by optimizing the mobile edge computing (MEC) server’s transmit power, IoT devices’ power reflection coefficients, local computing frequencies and time, the time allocation between the energy harvesting and task offloading, as well as the binary offloading decision at each IoT device, we built a WSCB maximization problem, which belongs to a non-convex mixed integer programming problem. For solving this, the proof by contradiction and the objective function’s monotonicity are considered to determine the optimal local computing time of each IoT device and the optimal transmit power of the MEC server, and the time-sharing relaxation (TSR) is adopted to tackle the integer variables, which are used to simplify the original problem. Then, we decouple the simplified problem into two sub-problems by means of the block coordinate decent (BCD) technology, and each of the sub-problems is transformed to a convex one by introducing auxiliary variables. Based on this, we design a two-stage alternative (TSA) optimization algorithm to solve the formulated WSCB problem. Computer simulations validate that the TSA algorithm has a fast convergent rate and also demonstrate that the proposed scheme achieves a higher WSCB than the existing schemes.

A surrogate-assisted differential evolution for expensive constrained optimization problems involving mixed-integer variables

Many Surrogate-Assisted Evolutionary Algorithms (SAEAs) have been developed for expensive constrained optimization problems (ECOPs) with continuous variables. However, there exist some ECOPs that contain mixed-integer variables in real world engineering applications. The mixed-integer variables make the feasible regions of ECOPs exhibit complex disjoint characteristics, which brings two challenges for the existing methods, i.e., the classical surrogate-assisted pre-screening may easily fall into a local optimum and the population diversity tends to reduce with the influence of integer variables. For tackling these problems, a surrogate-assisted differential evolution for solving ECOPs involving mixed-integer variables (SADE-MI) is proposed. Firstly, the mutation strategy DE/best/2 is used to balance the local and global characteristics of the candidate solutions. Secondly, an adaptive pre-screening operation where the information of the population is effectively employed to construct the distance constraints is designed to avoid excessive exploitation in local regions. Finally, by selecting diversely-located individuals and limiting the number of individuals with the same integer variables, a population diversity maintenance operation is introduced to strengthen global exploration. Experimental studies on some benchmark problems and engineering optimization cases demonstrate that SADE-MI outperforms other classical algorithms for solving ECOPs with mixed-integer variables.

An approximation algorithm for indefinite mixed integer quadratic programming

In this paper, we give an algorithm that finds an \(\epsilon \)-approximate solution to a mixed integer quadratic programming (MIQP) problem. The algorithm runs in polynomial time if the rank of the quadratic function and the number of integer variables are fixed. The running time of the algorithm is expected unless P = NP. In order to design this algorithm we introduce the novel concepts of spherical form MIQP and of aligned vectors, and we provide a number of results of independent interest. In particular, we give a strongly polynomial algorithm to find a symmetric decomposition of a matrix, and show a related result on simultaneous diagonalization of matrices.

Joint Task Offloading and Resource Allocation for Cooperative Mobile-Edge Computing Under Sequential Task Dependency

The emergence of mobile-edge computing (MEC) makes it possible to run intelligent applications on Internet of Things (IoT) devices. However, due to blockage or deep fading, one IoT device may not have direct link with the edge server. In this case, many surrounding wireless devices can serve as a cooperative node. In this article, we study a cooperative MEC system running sequential task, which is composed of a series of subtasks and can support many intelligent applications. To minimize the energy consumption of the IoT device and cooperative node, a task offloading policy together with the allocation of communication and computation resources is designed jointly. The cases when the cooperative node has no/has private task to complete are investigated, which are denoted as cases I and II, respectively. Although both cases involve the optimization of integer variables, their optimal solutions are achieved. For the first case, the associated problem is simplified equivalently and then decomposed into two levels, with the upper level dealing with integer variables and the lower level handling continuous variables. Bisection search is employed to reach optimality in the lower level and the searching space is compressed in the upper level. For the second case, the associated problem is subdivided into three subproblems. To solve every subproblem optimally, a similar operation like case I is followed, with a semiclosed form solution derived in the lower level. Numerical results verify the effectiveness of our proposed methods compared with benchmark methods and our effort on reducing computation complexity.

A Hybrid Integer Encoding Method for Obtaining High-Quality Solutions of Quadratic Knapsack Problems on Solid-State Annealers

For formulating Quadratic Knapsack Problems (QKPs) into the form of Quadratic Unconstrained Binary Optimization (QUBO), it is necessary to introduce an integer variable, which converts and incorporates the knapsack capacity constraint into the overall energy function. In QUBO, this integer variable is encoded with auxiliary binary variables, and the encoding method used for it affects the behavior of Simulated Annealing (SA) significantly. For improving the efficiency of SA for QKP instances, this paper first visualized and analyzed their annealing processes encoded by conventional binary and unary encoding methods. Based on this analysis, we proposed a novel hybrid encoding (HE), getting the best of both worlds. The proposed HE obtained feasible solutions in the evaluation, outperforming the others in small- and medium-scale models.

Optimal energy management of nanogrid using battery storage system

This paper presents the optimal energy management approach with optimum sizing of the battery storage system (BSS) for the minimal possible total operating cost of the considered nanogrid. The five various operating modes are tested to achieve the optimal operating mode on an hourly basis. Linear programming (LP) is used to get optimal solutions for objective functions having non-integer variables whereas mixed-integer linear programming (MILP) is used to optimize the objective function having an integer variable. The proposed hourly-based optimal operating mode produces 17.8–94.5 % savings in the day operating cost compared to the best individual operating mode. The optimal capacity of the battery storage system is also derived by using the proposed operating modes. The achieved optimal capacity of BSS based on the day operating cost is further modified with the help of investment cost and its interest paid during the life span which suggests that the optimal capacity range will be 4–19 kWh for this nanogrid.

Improving structure identifiability of hydrological processes by temporal sensitivity with a flexible modeling framework

Structure identifiability of hydrological processes refers to the ability to select appropriate mathematical representation from multiple structural options. Although the influence of hydrological processes on model behavior varies in time, this temporal relative influence has not been used to identify process structures. In this work, a framework is proposed to investigate the impacts of temporal relative influence of hydrological processes on structure identification. The framework consists of four elements: (1) a blended model, where hydrological process options and parameter values are regarded as integer and continuous decision variables, respectively, is built based on the flexible modeling framework Raven; (2) the temporal sensitivities of each process are derived by using Sobol’ sensitivity analysis on a moving window; (3) performance metrics with and without sensitivity-weights, which are derived from the temporal sensitivities, are used to identify process structures, respectively; and (4) models identified by these two methods are compared to evaluate performance. A synthetic experiment is designed to validate the proposed framework. Three case studies are carried out in the Tongtianhe, Xunhe, and Wudinghe basins in China. Results are summarized as follows: (1) sensitivity-weighted performance metrics improve the identifiability of process structures by considering the temporal relative influence of hydrological processes on model behavior; (2) quickflow and soil evaporation processes are the two most identifiable processes, followed by infiltration, baseflow, and snow balance processes; and (3) the model identified by sensitivity-weighted performance metrics is more efficient than that selected by the performance metric without sensitivity-weights. It is recommended that the temporal sensitivity of hydrological processes be used to identify model structures based on flexible modeling frameworks.