Binary Programming Problem Research Articles

Optimizing Combined Emission Economic Dispatch for Solar Integrated Power Systems

The dispatch of power at minimum operational cost of thermal energy sources has been a significant part of research since decades. Recently, with increasing interests in renewable energy resources, the optimal economic dispatch has become a challenging issue. This paper presents combined emission economic dispatch model for a solar photo voltaic integrated power system with multiple solar and thermal generating plants. We formulate mixed integer binary programming problem subject to various practical constraints. A decomposition framework is proposed where the original problem is split into two sub-problems. Particle swarm optimization, Newton–Raphson method, and binary integer programming techniques are exploited to find the joint optimization solution. The proposed model is tested on the IEEE 30 bus system. The simulation results demonstrate the effectiveness of the proposed model.

Joint Optimization of Resource Allocation and Relay Selection for Network Coding Aided Device-to-Device Communications

Device-to-device (D2D) communication underlaying cellular networks enhances system capacity through using spectrum resources of idle cellular users, which at the same time can act as relays to form cooperative D2D transmissions. On the other hand, network coding increases the efficiency of relay cooperation. In this letter, we investigate the random linear network coding aided D2D communications by addressing the problem of joint resource allocation and relay selection among multiple idle cellular users and D2D pairs. By formulating it as a binary integer non-linear programming problem, we obtain the optimal solution by introducing the concept of D2D cluster. Extensive simulations demonstrate that our proposed scheme increases the system sum rate by about 50% on average, while guaranteeing the minimum required rate of D2D pair.

Global blending optimization of laminated composites with discrete material candidate selection and thickness variation

A method capable of simultaneous topology and thickness optimization of laminated composites has previously been published by one of the authors. Mass constrained compliance minimization subject to certain manufacturing constraints was solved on basis of interpolation schemes with penalization. In order to obtain large patchwise material candidate continuity while also accommodating variable laminate thickness, a bi-linear stiffness parameterization was introduced, causing a non-convex problem. In this present work, we introduce an alternative problem formulation that holds identical capabilities but is, however, convex in the original mixed binary nested form. Convexity is the foremost important property of optimization problems, and the proposed method can guarantee the global or near-global optimal solution; unlike most topology optimization methods. The material selection is limited to a distinct choice among predefined numbers of candidates. The laminate thickness is variable but the number of plies must be integer. We solve the convex mixed binary non-linear programming problem by an outer approximation cutting-plane method augmented with a few heuristics to accelerate the convergence rate. The capabilities of the method and the effect of active versus inactive manufacturing constraints are demonstrated on several numerical examples of limited size, involving at most 320 binary variables. Most examples are solved to guaranteed global optimality and may constitute benchmark examples for popular topology optimization methods and heuristics based on solving sequences of non-convex problems. The results will among others demonstrate that the difficulty of the posed problem is highly dependent upon the composition of the constitutive properties of the material candidates.

Optimal Charging Strategy for Plug-In Electric Taxi With Time-Varying Profits

This paper studies the optimal charging problem for future plug-in electric taxi (PET) with time-varying profits, i.e., time-varying service incomes and charging costs. Aiming at maximizing the average profit of a PET in long term under the constraint of state of charge (SoC) dynamics of PET battery, this problem is formulated as a constrained binary programming problem in infinite time horizon. The main contribution of this paper consists of three parts. First, because the original infinite binary programming problem cannot be directly solved, it is divided into a series of periodic subproblems. Each of the subproblems is in finite time horizon and much easier to solve, which is also proven rigorously to be equivalent to the original one. Second, an efficient and optimal algorithm is proposed to solve the finite time constrained binary programming subproblem, which also yields the optimal initial SoC of PET. Third, a transient control strategy is proposed to transfer the any initial SoC to the optimal one, if they are not identical. The performance of the proposed method is verified by numerical results.

Multistage Transmission Expansion Planning Considering Fixed Series Compensation Allocation

This paper proposes a mathematical model for multistage transmission expansion planning (TEP) considering fixed series compensation (FSC) allocation and N-1 security constraints for both transmission lines and FSCs. FSCs can increase the transmission lines transfer capacity, but the importance of using them in TEP is to dispatch the power more efficiently, resulting in a different topology with less investment cost compared with planning without FSCs. This problem is modeled as a linear mixed binary programming problem and is solved by a commercial branch-and-cut solver to obtain the optimum solution. FSC is modeled as a fixed impedance located in the transmission lines in discrete steps and with an investment cost based on the prices of reinforcement lines. The results obtained using two known test systems show the economic benefits of using FSC in multistage TEP problems.

Joint Empirical Mode Decomposition and Sparse Binary Programming for Underlying Trend Extraction

This paper presents a novel methodology for extracting the underlying trends of signals via a joint empirical mode decomposition (EMD) and sparse binary programming approach. The EMD is applied to the signals and the corresponding intrinsic mode functions (IMFs) are obtained. The underlying trends of the signals are obtained by the sums of the IMFs where these IMFs are either selected or discarded. The total number of the selected IMFs is minimized subject to a specification on the maximum absolute differences between the denoised signals (signals obtained by discarding the first IMFs) and the underlying trends. Since the total number of the selected IMFs is minimized, the obtained solutions are sparse and only few IMFs are selected. The selected IMFs correspond to the components of the underlying trend of the signals. On the other hand, the L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> norm specification guarantees that the maximum absolute differences between the underlying trends and the denoised signals are bounded by an acceptable level. This forces the underlying trends to follow the global changes of the signals. As the IMFs are either selected or discarded, the coefficients are either zero or one. This problem is actually a sparse binary programming problem with an L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> norm objective function subject to an L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> norm constraint. Nevertheless, the problem is nonconvex, nonsmooth, and NP hard. It requires an exhaustive search for solving the problem. However, the required computational effort is too heavy to be implemented practically. To address these difficulties, we approximate the L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> norm objective function by the L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> norm objective function, and the solution of the sparse binary programming problem is obtained by applying the zero and one quantization to the solution of the corresponding continuous-valued L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> norm optimization problem. Since the isometry condition is satisfied and the number of the IMFs is small for most of practical signals, this approximation is valid and verified via our experiments conducted on practical data. As the L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> norm optimization problem can be reformulated as a linear programming problem and many efficient algorithms such as simplex or interior point methods can be applied for solving the linear programming problem, our proposed method can be implemented in real time. Also, unlike previously reported techniques that require precursor models or parameter specifications, our proposed adaptive method does not make any assumption on the characteristics of the original signals. Hence, it can be applied to extract the underlying trends of more general signals. The results show that our proposed method outperforms existing EMD, classical lowpass filtering and the wavelet methods in terms of the efficacy.

Energy-Efficient Cooperative Sensing Scheduling for Multi-Band Cognitive Radio Networks

In this paper, by taking both sensing performance and energy efficiency into consideration, the Cooperative Sensing Scheduling (CSS) problem for multi-band Cognitive Radio Networks (CRNs) is investigated under a practical scenario where both Primary User (PU) channels and Secondary Users (SUs) have heterogeneous characteristics. Unlike many existing works that merely claim that the CSS problem is NP-hard and then turn to heuristic methods, we analyze this problem under a solid discrete-convex framework. After formulating the CSS problem as a nonlinear binary programming problem, we adopt a three-step approach to solve it. In the first step, the number of SUs assigned to sense each PU channel is determined with the M/M^natural-convex theory. Based on the results obtained in the first step, we then find the SU assignment using the L/L^natural-convex theory in the second step. In the last step, the optimal number of SUs participating in sensing is obtained based on the SU assignment obtained in step two. By combining these three steps, a complete and efficient SU assignment scheme is obtained. Numerical results are provided to evaluate the performance of our proposed SU assignment scheme and validate the theoretical analysis.

Decomposition algorithms for data placement problem based on Lagrangian relaxation and randomized rounding

The data placement problem arises in the design and operation of Content Delivery Networks—computer systems used to efficiently distribute Internet traffic to the users by replicating data objects (media files, applications, database queries, etc.) and caching them at multiple locations in the network. This allows not only to reduce the processing load on the server hardware, but also helps eliminating transmission network congestion. Currently all major Internet content providers entrust their offered services to such systems. In this paper we formulate the data placement problem as quadratic binary programming problem, taking into account server processing time, storage capacity and communication bandwidth. Two decomposition-based solution approaches are proposed: the Lagrangian relaxation and randomized rounding. Computational experiments are conducted in order to evaluate and compare the performance of presented algorithms.

A Joint Resource Allocation Scheme for Relay Enhanced Multi-cell Orthogonal Frequency Division Multiple Networks

This paper formulates resource allocation for decode-and-forward (DF) relay assisted multi-cell orthogonal frequency division multiple (OFDM) networks as an optimization problem taking into account of inter-cell interference and users fairness. To maximize the transmit rate of system we propose a joint interference coordination, subcarrier and power allocation algorithm. To reduce the complexity, this semi-distributed algorithm divides the primal optimization into three sub-optimization problems, which transforms the mixed binary nonlinear programming problem (BNLP) into standard convex optimization problems. The first layer optimization problem is used to get the optimal subcarrier distribution index. The second is to solve the problem that how to allocate power optimally in a certain subcarrier distribution order. Based on the concept of equivalent channel gain (ECG) we transform the max-min function into standard closed expression. Subsequently, with the aid of dual decomposition, water-filling theorem and iterative power allocation algorithm the optimal solution of the original problem can be got with acceptable complexity. The third sub-problem considers dynamic co-channel interference caused by adjacent cells and redistributes resources to achieve the goal of maximizing system throughput. Finally, simulation results are provided to corroborate the proposed algorithm.

P-Hub approach for the optimal park-and-ride facility location problem

Park and Ride facilities (P&R) are car parks at which users can transfer to public transportation to reach their final destination. We propose a mixed linear programming formulation to determine the location of a fixed number of P&R facilities so that their usage is maximized. The facilities are modeled as hubs. Commuters can use one of the P&R facilities or choose to travel by car to their destinations, and their behavior follows a logit model. We apply a p-hub approach considering that users incur in a known generalized cost of using each P&R facility as input for the logit model. For small instances of the problem, we propose a novel linearization of the logit model, which allows transforming the binary nonlinear programming problem into a mixed linear programming formulation. A modification of the Heuristic Concentration Integer (HCI) procedure is applied to solve larger instances of the problem. Numerical experiments are performed, including a case in Queens, NY. Further research is proposed.

A fast method for binary programming using first‐order derivatives, with application to topology optimization with buckling constraints

SUMMARYWe present a method for finding solutions of large‐scale binary programming problems where the calculation of derivatives is very expensive. We then apply this method to a topology optimization problem of weight minimization subject to compliance and buckling constraints. We derive an analytic expression for the derivative of the stress stiffness matrix with respect to the density of an element in the finite‐element setting. Results are presented for a number of two‐dimensional test problems.Copyright © 2012 John Wiley &amp; Sons, Ltd.

Applying Minimum-Risk Criterion to Stochastic Hub Location Problems

This paper presents a new class of two-stage stochastic hub location (HL) programming problems with minimum-risk criterion, in which uncertain demands are characterized by random vector. Meanwhile we demonstrate that the twostage programming problem is equivalent to a single-stage stochastic P-model. Under mild assumptions, we develop a deterministic binary programming problem by using standardization, which is equivalent to a binary fractional programming problem. Moreover, we show that the relaxation problem of the binary fractional programming problem is a convex programming problem. Taking advantage of branch-and-bound method, we provide a number of experiments to illustrate the efficiency of the proposed modeling idea.

Proactive load balancing with admission control for heterogeneous overlay networks

ABSTRACTThe next generation wireless networks will be the coexistence of heterogeneous wireless technologies. Balancing the traffic load among different networks can effectively utilize the overall radio resources in the system. In this paper, we propose an efficient load balancing scheme for the heterogeneous overlay systems, which is applied in the call admission control process. If the available network(s) cannot provide enough resource for the request call without degrading the quality‐of‐service (QoS) obtained by the ongoing calls, the system will perform load balancing operations first by initiating vertical handoffs among networks in order to create more rooms for the request call. The load balancing algorithm is to minimize the variance between the network utilizations of the entire system, which can be formulated as a quadratic binary programming problem. Simulation results show that the proposed scheme can admit more calls into the system compared with the other three reference schemes and then improve the overall throughput. Meanwhile, the scheme can keep the networks working in effective states and provide a better QoS support for users. Copyright © 2011 John Wiley &amp; Sons, Ltd.

A primal-dual backtracking optimization method for blended composite structures

A combinatorial optimization method is proposed for finding the optimal stacking sequence and the ply drop-offs of a blended composite structure. This method assumes that the thicknesses of the regions of the structure are fixed in advance. It is able to handle efficiently design and manufacturing rules which are of combinatorial type. The optimization problem is formulated as a constrained binary programming problem and it is solved by applying both a primal and a dual backtracking procedures with a local search method. Some numerical experiments are carried out to show the efficiency of the optimization method with respect to both computational time and quality criteria.

Congestion management considering hydro–thermal combined operation in a pool based electricity market

This paper proposes a novel congestion management strategy for a pool based electricity market considering combined operation of hydro and thermal generator companies. The proposed congestion management problem is formulated as mixed binary nonlinear programming problem to minimize the cost of re-dispatching the hydro and thermal generator companies to alleviate congestion subject to operational, line overloading and water availability constraints. A piecewise-linearized unit performance curve is used in this formulation, which takes into account its non-concave nature. The effectiveness of the proposed technique is demonstrated by solving the modified IEEE 57-bus and IEEE 118-bus systems for congestion management under line outages.

Alternating direction augmented Lagrangian methods for semidefinite programming

We present an alternating direction dual augmented Lagrangian method for solving semidefinite programming (SDP) problems in standard form. At each iteration, our basic algorithm minimizes the augmented Lagrangian function for the dual SDP problem sequentially, first with respect to the dual variables corresponding to the linear constraints, and then with respect to the dual slack variables, while in each minimization keeping the other variables fixed, and then finally it updates the Lagrange multipliers (i.e., primal variables). Convergence is proved by using a fixed-point argument. For SDPs with inequality constraints and positivity constraints, our algorithm is extended to separately minimize the dual augmented Lagrangian function over four sets of variables. Numerical results for frequency assignment, maximum stable set and binary integer quadratic programming problems demonstrate that our algorithms are robust and very efficient due to their ability or exploit special structures, such as sparsity and constraint orthogonality in these problems.

A Constructive Heuristic Algorithm for Distribution System Planning

A constructive heuristic algorithm (CHA) to solve distribution system planning (DSP) problem is presented. The DSP is a very complex mixed binary nonlinear programming problem. A CHA is aimed at obtaining an excellent quality solution for the DSP problem. However, a local improvement phase and a branching technique were implemented in the CHA to improve its solution. In each step of the CHA, a sensitivity index is used to add a circuit or a substation to the distribution system. This sensitivity index is obtained by solving the DSP problem considering the numbers of circuits and substations to be added as continuous variables (relaxed problem). The relaxed problem is a large and complex nonlinear programming and was solved through an efficient nonlinear optimization solver. Results of two tests systems and one real distribution system are presented in this paper in order to show the ability of the proposed algorithm.

An integer decomposition algorithm for solving a two‐stage facility location problem with second‐stage activation costs

AbstractWe study a stochastic scenario‐based facility location problem arising in situations when facilities must first be located, then activated in a particular scenario before they can be used to satisfy scenario demands. Unlike typical facility location problems, fixed charges arise in the initial location of the facilities, and then in the activation of located facilities. The first‐stage variables in our problem are the traditional binary facility‐location variables, whereas the second‐stage variables involve a mix of binary facility‐activation variables and continuous flow variables. Benders decomposition is not applicable for these problems due to the presence of the second‐stage integer activation variables. Instead, we derive cutting planes tailored to the problem under investigation from recourse solution data. These cutting planes are derived by solving a series of specialized shortest path problems based on a modified residual graph from the recourse solution, and are tighter than the general cuts established by Laporte and Louveaux for two‐stage binary programming problems. We demonstrate the computational efficacy of our approach on a variety of randomly generated test problems. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010

A goal programming approach for fuzzy multiobjective fractional programming problems

Fuzzy multiple objective fractional programming (FMOFP) is an important technique for solving many real-world problems involving the nature of vagueness, imprecision and/or random. Following the idea of binary behaviour of fuzzy programming (Chang 2007), there may exist a situation where a decision-maker would like to make a decision on FMOFP involving the achievement of fuzzy goals, in which some of them may meet the behaviour of fuzzy programming (i.e. level achieved) or the behaviour of binary programming (i.e. completely not achieved). This is turned into a fuzzy multiple objective mixed binary fractional programming (FMOMBFP) problem. However, to the best of our knowledge, this problem is not well formulated by mathematical programming. Therefore, this article proposes a linearisation strategy to formulate the FMOMBFP problem in which extra binary variable is not required. In addition, achieving the highest membership value of each fuzzy goal defined for the fractional objective function, the proposed method can alleviate the computational difficulties when solving the FMOMBFP problem. To demonstrate the usefulness of the proposed method, a real-world case is also included.

Rostering in a rail passenger carrier

In this paper we present an applied study, commissioned by the regional rail passenger carrier EuskoTren, into how the annual workload of drivers can be allocated in an egalitarian fashion. The allocation must meet the constraints arising from working conditions and the preferences of employees, as reflected in collective bargaining agreements. The workload varies over the five periods, into which the year is divided, and according to the day of the week. Moreover, not all morning, evening and night shifts are of equal duration. Reduced services on public holidays are also considered. The solution to the problem proposed is obtained in four linked steps, at each of which a binary programming problem is solved using commercial software. Step one is to build five lists of weekly multi-shift patterns, two of them rotating, that contain all the shifts in the week. Step two consists of the partially rotating annual assignment of patterns to drivers, step three involves the extraction of shifts by reduction of services on public holidays, and step four incorporates the durations in hours into the shifts already assigned. The final solution obtained is quite satisfactory: all drivers are assigned a similar number of morning, evening and night shifts and Sundays off, and they work practically the same number of days and hours per year. The results obtained, the adaptability of the system to new requirements and the computation time used are fully satisfactory to the firm, which has decided to implement the model.