Linear Programming Algorithm Research Articles

Transiently stable intentional controlled islanding considering post-islanding voltage and frequency stability constraints

Intentional controlled islanding (ICI) is proposed to split the power system into a certain number of self-healing islands as the ultimate protective solution to avoid blackout after a large disturbance. Finding the separation boundaries and stabilising the created islands are two aspects of the ICI problem investigated in this paper. Most studies do not address the transient stability along with stability constraints in one framework. These studies ignore the impact of power flow disruption (PFD) on the stability of ICI. This study proposes a framework to solve the ICI problem in a timely manner by combining transient stability constraints with both frequency and voltage stability constraints. Transient stability is addressed in the first stage. A Mixed Integer Linear Programming (MILP) model of islanding is formulated to minimise the PFD caused by network splitting. In the second stage, which deals with the frequency and voltage stability of islands, a multi-stage Linear Programming (LP) algorithm determines the final generation-load adjustments necessary to be undertaken in each island after splitting to achieve acceptable voltage and frequency levels. The proposed multi-stage algorithm employs a frequency stability constraint as well as an indicator of risk of voltage instability to improve both voltage and frequency stabilities, while they meet power balance and operational limit constraints. The efficiency of the proposed algorithm is verified by using the New England 39-bus, and IEEE 118-bus systems. It is illustrated that the proposed method can create more stable islands with short computation times compared to other ICI methods with power imbalance as the primary objective.

A Joint Comparative Analysis of Routing Heuristics and Paperless Picking Technologies Using Simulation and Data Envelopment Analysis

Recent literature demonstrates that warehouse order picking performance is reflected in the logistics performance of downstream retailers. Warehouse solutions and policies significantly contribute to the improvement of distribution and delivery to retailers. This paper therefore reports an analysis of the joint performance of routing policies and picking technologies, and provides insights into the best ways to combine routing strategies and paperless solutions in order to optimize cost efficiency. We follow a multistage approach that combines mixed integer linear programming algorithms, data envelopment analysis (DEA), and ranking and selection. The results show that traversal-voice picking and midpoint-voice picking combinations are equally distributed over the most efficient subsets and that superior technology can enhance picking efficiency only to a certain level. The study provides guidelines for logistics managers on ways to combine warehouse solutions and policies in order to better streamline the operations. It offers an original framework to analyze the joint performance of picking routing and picking solutions by considering the effect of picking errors.

Stochastic Unit Commitment Problem, Incorporating Wind Power and an Energy Storage System

This paper presents a modified formulation for the wind-battery-thermal unit commitment problem that combines battery energy storage systems with thermal units to compensate for the power dispatch gap caused by the intermittency of wind power generation. The uncertainty of wind power is described by a chance constraint to escape the probabilistic infeasibility generated by classical approximations of wind power. Furthermore, a mixed-integer linear programming algorithm was applied to solve the unit commitment problem. The uncertainty of wind power was classified as a sub-problem and separately computed from the master problem of the mixed-integer linear programming. The master problem tracked and minimized the overall operation cost of the entire model. To ensure a feasible and efficient solution, the formulation of the wind-battery-thermal unit commitment problem was designed to gather all system operating constraints. The solution to the optimization problem was procured on a personal computer using a general algebraic modeling system. To assess the performance of the proposed model, a simulation study based on the ten-unit power system test was applied. The effects of battery energy storage and wind power were deeply explored and investigated throughout various case studies.

Minimization of transport costs in an industrial company through linear programming

Businesses and industries are very interested in optimizing processes and minimizing costs. One of the transportation models or problems to optimize relates to the case where the product output can be transported from the manufacturing plant to some warehouses or customers. The transport problem is a case of the linear programming problem. Linear programming algorithms have been used to solve the most difficult optimization problems. Linear programming has been used to manage the problems related to personnel assignment, engineering, distribution, banking, education, oil, transportation, etc. It has been widely used in various fields, like transport, telecommunications, health services, construction, public services, industry, etc.The main purpose of the paper is to look at the problem of linear programming in detail by considering an example and try to solve the problem. The purpose of the transport problem in our case is to minimize the overall cost of transport from origin to destination by meeting supply and demand limits, in order to increase sales profit. This paper aims to determine the problem of minimizing the total cost of transport by determining the optimal distribution of the product, from the 2 sites of production to the 9 major distributors that are geographically dispersed. Management Science and Operational Research will be used to find the best solution for the transportation problem.

Integer linear programming and genetic algorithm (GA)for the optimum placement of phasor measuring units for smart grid

For the optimal replacement of phasor measuring units (PMUs) in the presence of conventional measurements, the integrated linear programming (ILP) and genetic algorithms are proposed. In fact, the power system remains fully measurable for the lines and measuring instruments during all conceivable single contingencies. In doing so, a process of equations entirely utilizes the capability of circuit equations related to standard measurements and PMUs, and the system topology, to attain the minimum possible amount of required PMUs.

Compact MR Magnet Design Methodology for Superconducting Animal MRI Scanner

A 4.7 T compact superconducting magnet system for active shielding animal magnetic resonance imaging scanner was designed in this work. The resulting magnet consists of nine coaxial coils symmetrical about the z -axis. The innermost main coils and outermost shielding coils were made up of six inner coils with the positive current direction and three outer coils with the negative current direction, respectively. These nine superconducting coils contribute their efforts together to produce a 4.7 T main background magnetic field, and the peak-to-peak field homogeneity was 2 ppm over a 20 cm region of interest (ROI). The diameter of room temperature bore was 400 mm, which is large enough for most animals imaging, and five Gauss fringe field is restricted within an elliptical region with the size of 1.5 m in radial and 2.2 m in axial direction, much smaller than the regular requirement 2.5 m and 4.0 m, respectively. A hybrid numerical methodology that combined linear programming and nonlinear optimization algorithm for actively shielding homogeneous superconducting magnet was proposed here. From the simulation results, we can see that the homogeneity over ROI and limitation to the five Gauss fringe field can be well controlled, and so does the maximum electromagnetic stress.

Induced-Equations-Based Stability Analysis and Stabilization of Markovian Jump Boolean Networks

This article considers asymptotic stability and stabilization of Markovian jump Boolean networks (MJBNs) with stochastic state-dependent perturbation. By defining an augmented random variable as the product of the canonical form of switching signal and state variable, asymptotic stability of an MJBN with perturbation is converted into the set stability of a Markov chain (MC). Then, the concept of induced equations is proposed for an MC, and the corresponding criterion is subsequently derived for asymptotic set stability of an MC by utilizing the solutions of induced equations. This criterion can be, respectively, examined by either a linear programming algorithm or a graphical algorithm. With regards to the stabilization of MJBNs, the time complexity is reduced to a certain extent. Furthermore, all time-optimal signal-based state feedback controllers are designed to stabilize an MJBN towards a given target state. Finally, the feasibility of the obtained results is demonstrated by two illustrative biological examples.

A Combinatorial Algorithm for Fuzzy Parameter Estimation with Application to Uncertain Measurements

This paper presents a new method for regression model prediction in an uncertain environment. In practical engineering problems, in order to develop regression or ANN model for making predictions, the average of set of repeated observed values are introduced to the model as an input variable. Therefore, the estimated response of the process is also the average of a set of output values where the variation around the mean is not determinate. However, to provide unbiased and precise estimations, the predictions are required to be correct on average and the spread of date be specified. To address this issue, we proposed a method based on the fuzzy inference system, and genetic and linear programming algorithms. We consider the crisp inputs and the symmetrical triangular fuzzy output. The proposed algorithm is applied to fit the fuzzy regression model. In addition, we apply a simulation example and a practical example in the field of machining process to assess the performance of the proposed method in dealing with practical problems in which the output variables have the nature of uncertainty and impression. Finally, we compare the performance of the suggested method with other methods. Based on the examples, the proposed method is verified for prediction. The results show that the proposed method reduces the error values to a minimum level and is more accurate than the Linear Programming (LP) and fuzzy weights with linear programming (FWLP) methods.

Hybrid VNS–LP algorithm for online optimal coordination of directional overcurrent relays

Optimal coordination of directional overcurrent relays (DOCRs) in interconnected power systems is a highly constrained, non-convex and non-linear optimisation problem. In this study, use of a series of linear programming (LP) problems in a variable neighbourhood search (VNS) framework is proposed, in which pickup current settings can be considered either as continuous or discrete variables. Therefore, the proposed hybrid algorithm (VNS–LP) is suitable for coordination problem-solving in a network with different types of DOCRs. Furthermore, two versions of the VNS algorithm are proposed, the first of which is very easy to implement, while, the other is somewhat more sophisticated, and at the same time much faster and possibly suitable for online coordination in smart grids applications. One advantage of the second algorithm is that it relies only on elementary arithmetic and requires low RAM, which makes it implementable in any low-level programming environment. This, in turn, can increase the interoperability, which is of crucial importance when automating tasks. The efficiency of the proposed algorithm was investigated in several test systems. Numerical results indicate that the two proposed approaches outperform the previous methods. Moreover, the coordination problem is solved in a reasonably short time using a faster approach.

A quantum interior-point predictor–corrector algorithm for linear programming

We introduce a new quantum optimization algorithm for dense linear programming problems, which can be seen as the quantization of the interior point predictor–corrector algorithm [] using a quantum linear system algorithm []. The (worst case) work complexity of our method is, up to polylogarithmic factors, for n the number of variables in the cost function, m the number of constraints, ϵ −1 the target precision, L the bit length of the input data, an upper bound to the Frobenius norm of the linear systems of equations that appear, ‖M‖F, and an upper bound to the condition number κ of those systems of equations. This represents a quantum speed-up in the number n of variables in the cost function with respect to the comparable classical interior point algorithms when the initial matrix of the problem A is dense: if we substitute the quantum part of the algorithm by classical algorithms such as conjugate gradient descent, that would mean the whole algorithm has complexity , or with exact methods, at least . Also, in contrast with any quantum linear system algorithm, the algorithm described in this article outputs a classical description of the solution vector, and the value of the optimal solution.

An enhanced branch-and-bound algorithm for bilevel integer linear programming

Bilevel integer linear programming (BILP) problems have been studied for decades. Many exact algorithms have been proposed in recent years for small- or medium-sized instances. However, few of these algorithms were shown to be efficient on large-sized instances. In this paper, we present an enhanced branch-and-bound algorithm for a class of BILP problems, which can discard a subspace from the search space in each iteration larger than that in a benchmark branch-and-bound algorithm. The corresponding enhanced branching rule can efficiently slow down the creation of new node problems so as to significantly reduce the computation time. Our scheme may be suboptimal if the lower-level problem is not unique optimal as the enhanced branching rule may discard bilevel feasible solutions that may turn out to be optimal to the bilevel programming. We present computational studies to evaluate the algorithm speedup and solution quality of our algorithm, compared with state-of-the-art algorithms from the literature on a large testbed of general BILP instances, some of which are still unsolved. The computational results show that our enhanced branching rule can achieve significant speedup on the benchmark branching rule with satisfying solution quality. In particular, our algorithm shows superior performance on large-sized BILP instances with a relatively complex lower-level problem.

Modeling and control of automated vehicle access on dedicated bus rapid transit lanes

The establishment of dedicated automated vehicle (AV) lanes has been regarded as an effective approach for addressing heterogeneous traffic with both AVs and regular vehicles (RVs), promoting both traffic efficiency and safety. However, building new dedicated AV lanes in urban areas is not cost effective in the early stage of AV adoption. Fortunately, dedicated bus rapid transit (BRT) lanes can provide a separate right-of-way (ROW) for AVs, which is a practical and economical alternative for promoting AV development. In this paper, we propose an innovative idea of allowing AVs to use dedicated BRT lanes, and quantitatively analyze the stationary performance of mixed-use lanes. Specifically, the analysis is conducted through a cyclic space–time model for AVs on the mixed-use lane, and a sequential optimization method (SOM) is proposed to approximately solve the model. With the SOM providing a valid tool for performance evaluation, we then develop an assignment model for the routing of AVs on a traffic corridor with both mixed-use lane and general-purpose lanes to minimize the total travel time of both AVs and RVs. The model is formulated as a black-box nonlinear program without an explicit analytical form; a successive linear programming (SLP) algorithm with finite difference for gradient approximation is then utilized to solve the nonlinear program. Numerical experiments are conducted in different scenarios, which reveal that the establishment of the mixed-use lane can not only improve the efficiency of AVs but also alleviate the congestion on general-purpose lanes.

A Techno-Economic Framework for Replacing Aged XLPE Cables in the Distribution Network

In this paper, a stochastic framework is proposed for optimizing replacement strategies of aged XLPE cables in the electric power distribution network. The proposed framework facilitates realizing an economic value for the risk of unplanned outages, thereby shifting the paradigm of replacing aged XLPE cable from a technical decision that is solely based on diagnostic measurements to a techno-economic strategy. The proposed framework constitutes of three main phases: (1) obtaining a distribution for the aging process of XLPE cable due to water-trees, (2) modeling the replacement of the aged XLPE cable as a Markov decision process, and (3) applying a linear programming algorithm in order to solve for the optimal replacement policy. Based on the proposed framework, a critical health index is defined for optimum replacement, depending on the installation costs of a new cable and the unplanned outage cost.

Integrated Energy System Planning Based on Equipment Performance

The Integrated Energy System (IES) has the advantage of improving energy utilization and promoting energy flexibility. Its equipment configuration is one of the keys to Integrated Energy System planning. This paper takes equipment selection and capacity planning as the goal establishes the IES equipment selection and capacity planning model makes the minimum annual inclusive cost as the optimization goal and uses the mixed-integer linear programming algorithm to solve the practical problem. Finally, a typical southern park is taken as an example to analyze and verify the feasibility of the model and algorithm.

Integrated energy system planning method considering electric-heat-gas coupling

In order to determine the optimal configuration of energy equipment types and capacities in an integrated energy system, this paper proposes a method of equipment selection and capacity planning for an integrated energy system (IES) that considers the coupling of electricity, heat, and gas. Starting from the type of optional equipment and the form of input energy, the basic structure of IES is established. On this basis, for the equipment selection and capacity planning, an optimization model with the minimum annual comprehensive cost as the objective function is established, and the mixed integer linear programming algorithm is used to optimize the equipment type and capacity at the same time. Finally, taking an IES park as an example, the planning schemes in different scenarios are given, and the effectiveness of the proposed method is verified.

Fail‐safe optimization of viscous dampers for seismic retrofitting

SummaryThis paper presents a new optimization approach for designing minimum‐cost fail‐safe distributions of fluid viscous dampers for seismic retrofitting. Failure is modeled as either complete damage of the dampers or partial degradation of the dampers' properties. In general, this leads to optimization problems with large number of constraints. This may result in high computational costs if all the constraints are simultaneously considered during the optimization analysis. Thus, to reduce the computational effort, the use of a working‐set optimization algorithm is proposed in this paper. The main idea is to solve a sequence of relaxed optimization subproblems with a small subset of all constraints. The algorithm terminates once a solution of a subproblem is found that satisfies all the constraints of the problem. The retrofitting cost is minimized with constraints on the interstory drifts at the peripheries of frame structures. The structures considered are subjected to a realistic ensemble of ground motions, and their response is evaluated with time‐history analyses. The transient optimization problem is efficiently solved with a gradient‐based sequential linear programming algorithm. The gradients of the response functions are calculated with a consistent adjoint sensitivity analysis procedure. Promising results attained for 3‐D irregular frames are presented and discussed. The numerical results highlight the fact that the optimized layout and size of the dampers can change significantly even for moderate levels of damage.

An Interior-Point Algorithm for Linear Programming with Optimal Selection of Centering Parameter and Step Size

For interior-point algorithms in linear programming, it is well-known that the selection of the centering parameter is crucial for proving polynomility in theory and for efficiency in practice. However, the selection of the centering parameter is usually by heuristics and separate from the selection of the line-search step size. The heuristics are quite different while developing practically efficient algorithms, such as MPC, and theoretically efficient algorithms, such as short-step path-following algorithm. This introduces a dilemma that some algorithms with the best-known polynomial bound are least efficient in practice, and some most efficient algorithms may not be polynomial. In this paper, we propose a systematic way to optimally select the centering parameter and line-search step size at the same time, and we show that the algorithm based on this strategy has the best-known polynomial bound and may be very efficient in computation for real problems.

Lifting the knapsack cover inequalities for the knapsack polytope

Valid inequalities for the knapsack polytope have proven to be very useful in exact algorithms for mixed-integer linear programming. In this paper, we focus on the knapsack cover inequalities, introduced in 2000 by Carr and co-authors. In general, these inequalities can be rather weak. To strengthen them, we use lifting. Since exact lifting can be time-consuming, we present two fast approximate lifting procedures. The first procedure is based on mixed-integer rounding, whereas the second uses superadditivity.

Resilient distribution network planning under the severe windstorms using a risk-based approach

This paper proposes a risk-based approach for planning resilient radial distribution networks to severe windstorms. The proposed approach is based on the concept of interval analysis, Relative Distance Measure (RDM) interval arithmetic, mixed integer linear programming, and risk analysis. It enables obtaining a number of different resilient network plans taking into account dependence among the following uncertain inputs: maximum wind speed, storm duration and its annual frequency of occurrence, fragility of network components, repair duration, forecasted load and generation from renewable generators. In order to improve the computational efficiency of the proposed approach a hybrid simulated annealing and mixed integer linear programming algorithm is introduced. The best resilient plan is selected by employing the Minimal risk (Minimax) criterion for measuring and managing risk. In this way, the proposed approach provides a decision-maker with a means of determining the resilient network plan that minimizes the risk of significant costs due to severe windstorms.

A reinforcement learning approach for optimizing multiple traveling salesman problems over graphs

This paper proposes a learning-based approach to optimize the multiple traveling salesman problem (MTSP), which is one classic representative of cooperative combinatorial optimization problems. The MTSP is interesting to study, because the problem arises from numerous practical applications and efficient approaches to optimize the MTSP can potentially be adapted for other cooperative optimization problems. However, the MTSP is rarely researched in the deep learning domain because of certain difficulties, including the huge search space, the lack of training data that is labeled with optimal solutions and the lack of architectures that extract interactive behaviors among agents. This paper constructs an architecture consisting of a shared graph neural network and distributed policy networks to learn a common policy representation to produce near-optimal solutions for the MTSP. We use a reinforcement learning approach to train the model, overcoming the requirement data labeled with ground truth. We use a two-stage approach, where reinforcement learning is used to learn an allocation of agents to vertices, and a regular optimization method is used to solve the single-agent traveling salesman problems associated with each agent. We introduce a S-samples batch training method to reduce the variance of the gradient, improving the performance significantly. Experiments demonstrate our approach successfully learns a strong policy representation that outperforms integer linear programming and heuristic algorithms, especially on large scale problems.