Large-scale Mixed-integer Programming Problem Research Articles

A Nested Cross Decomposition Algorithm for Power System Capacity Expansion with Multiscale Uncertainties

Modern electric power systems have witnessed rapidly increasing penetration of renewable energy, storage, electrical vehicles, and various demand response resources. The electric infrastructure planning is thus facing more challenges as a result of the variability and uncertainties arising from the diverse new resources. This study aims to develop a multistage and multiscale stochastic mixed integer programming (MM-SMIP) model to capture both the coarse-temporal-scale uncertainties, such as investment cost and long-run demand stochasticity, and fine-temporal-scale uncertainties, such as hourly renewable energy output and electricity demand uncertainties, for the power system capacity expansion problem. To be applied to a real power system, the resulting model will lead to extremely large-scale mixed integer programming problems, which suffer not only the well-known curse of dimensionality but also computational difficulties with a vast number of integer variables at each stage. In addressing such challenges associated with the MM-SMIP model, we propose a nested cross decomposition algorithm that consists of two layers of decomposition—that is, the Dantzig–Wolfe decomposition and L-shaped decomposition. The algorithm exhibits promising computational performance under our numerical study and is especially amenable to parallel computing, which will also be demonstrated through the computational results.

A Consortium Blockchain-Enabled Secure and Privacy-Preserving Optimized Charging and Discharging Trading Scheme for Electric Vehicles

This article utilizes consortium blockchain to design a decentralized, secure, and privacy-preserving scheme for bidirectional power trading between electric vehicles (EVs) and the power grid. To reduce adverse effects induced by disordered charging of massive EVs to the power grid, we minimize the total load deviation through optimizing the charging and discharging time period of EVs. Our optimization scheduling is a large-scale mixed-integer programming problem of which the number of variables and constraints are enormous. Hence, we propose to adopt the heuristic algorithm, an improved krill herd (KH) algorithm to solve it. Simulation results indicate that our model can effectively smooth the load fluctuations, and improved KH can improve the rate and accuracy of solving this model effectively. Implementation of Hyperledger Fabric evaluates the performance and scalability of our scheme. Qualitative security and privacy analysis demonstrate that our scheme helps to improve the security and privacy of power trading.

Quantum computing based hybrid solution strategies for large-scale discrete-continuous optimization problems

Quantum computing (QC) has gained popularity due to its unique capabilities that are quite different from that of classical computers in terms of speed and methods of operations. This paper proposes hybrid models and methods that effectively leverage the complementary strengths of deterministic algorithms and QC techniques to overcome combinatorial complexity for solving large-scale mixed-integer programming problems. Four applications, namely the molecular conformation problem, job-shop scheduling problem, manufacturing cell formation problem, and the vehicle routing problem, are specifically addressed. Large-scale instances of these application problems across multiple scales ranging from molecular design to logistics optimization are computationally challenging for deterministic optimization algorithms on classical computers. To address the computational challenges, hybrid QC-based algorithms are proposed and extensive computational experimental results are presented to demonstrate their applicability and efficiency. The proposed QC-based solution strategies enjoy high computational efficiency in terms of solution quality and computation time, by utilizing the unique features of both classical and quantum computers.

A Fast Solution Method for Stochastic Transmission Expansion Planning

Stochastic programming is a cost-effective approach to model the transmission expansion planning (TEP) considering the uncertainties of wind and load, which is known as stochastic TEP (STEP). The uncertainty can be accurately represented by a large number of scenarios, which need to be reduced to a relatively small number in order to shorten the computational time required by the STEP. The forward selection algorithm (FSA) is an accurate scenario reduction method which, however, is quite time consuming. An improved FSA (IFSA) is proposed in order to shorten the computational time. The STEP is a large-scale mixed-integer programming problem, and, therefore, is difficult to be solved directly. Benders decomposition algorithm is suitable to solve the STEP by decomposing it into master and multiple slave problems. The slave problems are nonlinear and thereby are difficult and time consuming to be solved. In this regard, a linearization method is proposed to solve the slave problems faster and to calculate the Lagrangian multipliers needed by the master problem. Two medium and a large datasets are used to demonstrate the efficiency of the IFSA and a 24-, a 300-, and a 2383-bus test systems are used to verify the efficiency of the linearization method.

A Decomposition Approach for Solving Seasonal Transmission Switching

Economic transmission switching has been proposed as a new control paradigm to improve the economics of electric power systems. In practice, the transmission switching operation itself is a disruptive action to the system. Frequently switching lines into or out of service can create undesirable effects on the security and reliability of power systems and may require new investments in the automation and control systems. In this paper, we formulate an economic seasonal transmission switching model where transmission switching occurs once at the beginning of a time period (season) and then the transmission topology remains unchanged during that period. The proposed seasonal transmission switching model is a large-scale mixed integer programming problem. The objective of the optimization model is to minimize the total energy generation cost over the season subject to loads and N-1 reliability requirements. We develop a novel decomposition method that decomposes the seasonal problem into one-hour problems which are then solved efficiently. We demonstrate our model and the decomposition approach on the 14-bus, 39-bus, and 118-bus power systems and show potential cost savings in each case.

Stochastic optimization models for the airport gate assignment problem

Uncertainties inherent in the airport traffic may lead to the unavailability of gates for accommodating scheduled flights. Incorporating random disruptions is crucial in constructing effective flight-gate assignments. We consider the gate assignment problem under uncertainty in flight arrival and departure times and develop stochastic programming models incorporating robustness measures based on the number of conflicting flights, idle and buffer times. The proposed models are formulated as large-scale mixed-integer programming problems and tabu search algorithms are implemented to obtain assignments of reasonable quality. We conduct a computational study to analyze the proposed alternate models and show the effectiveness of the solution methods.

CONGESTION MANAGEMENT AND LOOP FLOW CONTROL BY TRANSMISSION NETWORK RECONFIGURATION

In this paper the problem of finding the optimal topological reconfiguration of a power transmission system is considered with the aim of providing a tool suited for congestion management. Network reconfiguration looks particularly appealing since it allows the relief of overloads by means of switching operations that may avoid generation or load curtailments. The techniques of corrective switching are profitably employed to formulate the problem of network reconfiguration for the purpose of congestion management. It is shown in the paper that the same optimization model employed in corrective switching can be used to solve the loop (or parallel) flow problem which occurs in today large interconnected systems. The solution of the resulting large-scale mixed-integer programming problem is carried out by a deterministic branch-and-bound algorithm included in the CPLEX optimization package. Tests were performed on the Italian network and on the European (UCTE) system.

Optimal network reconfiguration for congestion management by deterministic and genetic algorithms

In this paper, the problem of finding the optimal topological configuration of a power transmission system is considered with the aim of providing system operators with a tool suited for congestion management. Network reconfiguration looks particularly appealing since it allows transmission system operators to alleviate overloads by means of switching operations that may avoid costly generation or load curtailments. The techniques of corrective switching proposed in the 1980s are profitably employed to formulate the problem of network reconfiguration for the purpose of congestion management. The solution of the resulting large-scale mixed-integer programming problem is carried out both by a deterministic branch-and-bound algorithm included in the CPLEX optimization package and by a genetic algorithm. Tests were performed on a 33-bus CIGRE test system and on an actual 432-bus network of Italian origin.

A nested partitions framework for solving large-scale multicommodity facility location problems

Large-scale multicommodity facility location problems are generally intractable with respect to standard mixed-integer programming (MIP) tools such as the direct application of general-purpose Branch & Cut (BC) commercial solvers i.e. CPLEX. In this paper, the authors investigate a nested partitions (NP) framework that combines meta-heuristics with MIP tools (including branch-and-cut). We also consider a variety of alternative formulations and decomposition methods for this problem class. Our results show that our NP framework is capable of efficiently producing very high quality solutions to multicommodity facility location problems. For large-scale problems in this class, this approach is significantly faster and generates better feasible solutions than either CPLEX (applied directly to the given MIP) or the iterative Lagrangian-based methods that have generally been regarded as the most effective structure-based techniques for optimization of these problems. We also briefly discuss some other large-scale MIP problem classes for which this approach is expected to be very effective.

Optimization of the assignment of circuit cards to assembly lines in electronics assembly

Process planning is an important and integral function for ensuring efficient operations in printed circuit card assembly systems. This paper presents a new approach for solving the circuit card to assembly line assignment problem to minimize assembly time. This problem occurs frequently in process planning for electronic assembly systems and involves considering other interelated process planning problems. The line assignment problem is formulated as a large-scale mixed-integer programming problem and then solved using problem decomposition along with the branch-and-bound algorithm. Techniques for improving the solution time are discussed, and the solution approach is demonstrated using industry representative data sets from Lucent Technologies. For the data sets considered, the solution approach provides solutions within 3% of optimal in approximately 6 min of computation time on a Sun UltraSparc 2 Workstation. The solution approach developed for addressing the line assignment problem can serve as a useful decision-support tool by offering significant opportunities to improve the productivity and throughput of the assembly lines with improved process plans. The approach also allows planning engineers to respond faster to changes in production requirements. This research will be of interest to researchers in printed circuit card assembly systems and to practitioners in both original equipment manufacturing and contract assembly firms.

An application of Lagrangian relaxation to a capacity planning problem under uncertainty

A supply chain network-planning problem is presented as a two-stage resource allocation model with 0-1 discrete variables. In contrast to the deterministic mathematical programming approach, we use scenarios, to represent the uncertainties in demand. This formulation leads to a very large scale mixed integer-programming problem which is intractable. We apply Lagrangian relaxation and its corresponding decomposition of the initial problem in a novel way, whereby the Lagrangian relaxation is reinterpreted as a column generator and the integer feasible solutions are used to approximate the given problem. This approach addresses two closely related problems of scenario analysis and two-stage stochastic programs. Computational solutions for large data instances of these problems are carried out successfully and their solutions analysed and reported. The model and the solution system have been applied to study supply chain capacity investment and planning.

Large-scale var optimization and planning by tabu search

A generalization on the tabu search method, recently developed for combinatorial optimization problems, is described in this paper. The novel version of the tabu search method can be used to solve a larger class of combinatorial optimization problems. Application of this method to var optimization and planning, which is formulated as a nonlinear large-scale mixed integer programming problem with non-differentiable objective function, is demonstrated. Judicious engineering judgment which is essential for a successful application of the proposed tabu search is developed. Simulation results of a real-world power system are included. A simulation comparison is done between the proposed method and the simulated annealing method, which is currently one of the most popular method for combinatorial optimization problem.

Experiments in Solving Mixed Integer Programming Problems on a Small Array of Transputers

The time-consuming process of solving large-scale Mixed Integer Programming problems using the branch-and-bound technique can be speeded up by introducing a degree of parallelism into the basic algorithm. This paper describes the development and implementation of a parallel branch-and-bound algorithm created by adapting a commercial MIP solver. Inherent in the design of this software are certain ad hoc methods, the use of which are necessary in the effective solution of real problems. The extent to which these ad hoc methods can successfully be transferred to a parallel environment, in this case an array of at most nine transputers, is discussed. Computational results on a variety of real integer programming problems are reported.

Experiments in Solving Mixed Integer Programming Problems on a Small Array of Transputers

The time-consuming process of solving large-scale Mixed Integer Programming problems using the branch-and-bound technique can be speeded up by introducing a degree of parallelism into the basic algorithm. This paper describes the development and implementation of a parallel branch-and-bound algorithm created by adapting a commercial MIP solver. Inherent in the design of this software are certain ad hoc methods, the use of which are necessary in the effective solution of real problems. The extent to which these ad hoc methods can successfully be transferred to a parallel environment, in this case an array of at most nine transputers, is discussed. Computational results on a variety of real integer programming problems are reported.

Formulation and solution of a combined train routing and makeup, and empty car distribution model

This paper presents the formulation and solution of a combined train routing and makeup, and empty car distribution model. This formulation results in a large scale mixed-integer programming problem with nonlinear objective function and linear constraints. A heuristic decomposition technique is developed to solve the model. This solution procedure exploits the special structure of the problem and decomposes it into smaller subproblems based on the type of decision variables. Model testing results are also presented.

Lagrangian Relaxation Method for Long-term Unit Commitment

This paper presents a new method for large-scale long-term unit commitment problem composed of three types of generating units. In the proposed unit commitment algorithm, the transmission loss is expressed as a quadratic function of generator outputs. In the demand increasing period in the morning, the planning period (one hour) should be divided into shorter periods such as half an hour or fifteen minutes, and the ramping rate constraints should be imposed on generator outputs. Since the unit commitment problem (primal problem) is formulated as a large-scale mixed-integer programming problem, the Lagrangian relaxation method is employed to solve the problem efficiently. In the Lagrangian relaxation method, the metric matrix (an approximate Hessian inverse) may become too large. So the metric matrix is approximated by a block diagonal matrix. Since the primal problem is not a convex programming problem, the solution to the dual problem is not always a feasible one to the primal problem. Therefore, after solving the dual problem, a new device for finding a feasible solution must be developed. Moreover, a heuristic commitment modification procedure is proposed and it is combined with the commitment modification using the least square problem.

Solving large-scale mixed-integer programs with fixed charge variables

We consider large-scale mixed-integer programming problems containing fixed charge variables. In practice such problems are frequently approached by using commercial mathematical programming systems. Depending on the formulation, size and structure of the problem this approach may or may not be successful. We describe algorithms for preprocessing and optimization of such problems and discuss the design of an experimental software system based on MPSX/370. Numerical results for solving some large real life problems are also presented.

The Bangladesh grain model

Determining the “optimal” number, size, location and design of grain storage facilities in a developing country is a complex problem with significant health, social, political, demographic and financial implications. Formulating and “solving” such a problem requires the consideration not only of average measures of demand (e.g. minimum per capita requirements), supply and costs, but of population movements, rationing systems, developments in domestic production due to new methods and fertilizers, severe limitations in foreign currency, the infra-structure of the transportation system, improvements in vermin control and many other factors which are most often of but minor importance in corresponding logistic studies in more developed countries. Furthermore, in comparison to more developed countries, there is a dearth of reasonably detailed and accurate historical data to say nothing of relevant prognoses. The following case study describes how such a nationwide logistics problem was tackled in Bangladesh. Although it leads up to a discussion of a solution procedure based upon the solution of rather large-scale mixed integer programming problems, the article is primarily intended for a target audience of OR practioners, economic planners and decision makers involved in operational planning for developing countries.