Linear Programming Algorithm Research Articles

Comparing demand response and battery storage to optimize self-consumption in PV systems

The paper examines and compares the potential of storage in batteries versus demand response strategies for electricity bill reduction in the residential sector, in the context of the new trend of installing PV systems for self-consumption. The performances of the two methodologies are investigated by applying them to the data of a real household which owns a small solar photovoltaic installation. The benefits of storage and demand response are evaluated through an optimization analysis with a linear programming algorithm. The simulations are carried out both for real market prices of the equipment and for reduced ones, to simulate the case of strong technological development and the corresponding price decrease in the coming years. The electricity pricing scheme is a dual tariff regime modeled according to the Portuguese current rules. The results suggest that at the moment, demand response should be preferred with the current market prices of the hardware. However, a significant decrease in the batteries price can make storage an interesting alternative, especially for the cases in which demand response is not easily applicable.

A Homogeneous and Self-Dual Interior-Point Linear Programming Algorithm for Economic Model Predictive Control

We develop an efficient homogeneous and self-dual interior-point method (IPM) for the linear programs arising in economic model predictive control of constrained linear systems with linear objective functions. The algorithm is based on a Riccati iteration procedure, which is adapted to the linear system of equations solved in homogeneous and self-dual IPMs. Fast convergence is further achieved using a warm-start strategy. We implement the algorithm in MATLAB and C. Its performance is tested using a conceptual power management case study. Closed loop simulations show that: 1) the proposed algorithm is significantly faster than several state-of-the-art IPMs based on sparse linear algebra and 2) warm-start reduces the average number of iterations by 35%–40%.

CurveLP-A MATLAB implementation of an infeasible interior-point algorithm for linear programming

Mehrotra's algorithm has been the most successful infeasible interior-point algorithm for linear programming since 1990. Most popular interior-point software packages for linear programming are based on Mehrotra's algorithm. This paper proposes an alternative algorithm, arc-search infeasible interior-point algorithm. We will demonstrate, by testing Netlib problems and comparing the test results obtained by arc-search infeasible interior-point algorithm and Mehrotra's algorithm, that the proposed arc-search infeasible interior-point algorithm is a more efficient algorithm than Mehrotra's algorithm.

Maintenance optimisation of a parallel-series system with stochastic and economic dependence under limited maintenance capacity

Maintenance optimisation of a parallel-series system considering both stochastic and economic dependence among components as well as limited maintenance capacity is studied in this paper. The maintenance strategies of the components are jointly optimised, and the degradation process of the system is modelled to address the stochastic dependence and limited maintenance capacity issues. To overcome the “curse of dimensionality” problem where the state space of a parallel-series system increases rapidly with the increased number of components in the system, the factored Markov decision process (FMDP) is employed for maintenance optimisation in this work. An improved approximate linear programming (ALP) algorithm is then developed. The selection of the basis functions and the state relevance weights for ALP is also investigated to enhance the performance of the ALP algorithm. Results from the numerical study show that the current approach can handle the decision optimisation problem for multi-component systems of moderate size, and the error of maintenance decision-making induced by the improved ALP is negligible. The outcome from this research provides a useful reference to overcome the “curse of dimensionality” problem during the maintenance optimisation of multi-component systems.

A hybrid of max–min ant system and linear programming for the k-covering problem

This paper presents a hybrid algorithm of linear programming (LP), max–min ant system, and local search for solving large instances of the k-covering problem (SCkP). This algorithm exploits the LP-relaxation solution by classifying the columns, based on their reduced costs, into three sets, such that two of these sets have the columns that need to be included or excluded from any solution while ants search the third set, the selection set, to construct their feasible solutions. Moreover, to choose high-quality columns from the selection set, ants rely on heuristic information derived from the rows’ dual costs, which we obtain from the LP-relaxation solution as well. To benchmark our algorithm, we solve a set of 135 instances and compare the results with those of the state-of-the-art algorithm, in addition to the best-known solutions obtained using a branch and bound algorithm. Our algorithm shows superior results in terms of solution quality and computation time. Moreover, it can identify two new best-known solutions.

Crash start of interior point methods

The starting point used by an interior point algorithm for linear and convex quadratic programming may significantly influence the behaviour of the method. A widely used heuristic to construct such a point consists of dropping variable nonnegativity constraints and computing a solution which minimizes the Euclidean norm of the primal (or dual) point while satisfying the appropriate primal (or dual) equality constraints, followed by shifting the variables so that all their components are positive and bounded away from zero. In this Short Communication a new approach for finding a starting point is proposed. It relies on a few inexact Newton steps performed at the start of the solution process. A formal justification of the new heuristic is given and computational results are presented to demonstrate its advantages in practice. Computational experience with a large collection of small- and medium-size test problems reveals that the new starting point is superior to the old one and saves 20–40% of iterations needed by the primal-dual method. For larger and more difficult problems this translates into remarkable savings in the solution time.

Minimizing Stack Memory for Hard Real-Time Applications on Multicore Platforms with Partitioned Fixed-Priority or EDF Scheduling

Multicore processors are increasingly adopted in resource-constrained real-time embedded applications. In the development of such applications, efficient use of RAM memory is as important as the effective scheduling of software tasks. Preemption Threshold Scheduling (PTS) is a well-known technique for controlling the degree of preemption, possibly improving system schedulability, and to reduce system stack usage. In this paper, we consider partitioned multi-processor scheduling on a multicore processor with either Fixed-Priority or Earliest Deadline First scheduling algorithms with PTS and address the design optimization problem of mapping tasks to processor cores and assignment of task priorities and preemption thresholds with the optimization objective of minimizing system stack usage. We present both optimal solution techniques based on Mixed Integer Linear Programming and efficient heuristic algorithms that can achieve high-quality results. We perform extensive performance evaluations using both synthetic tasksets and industrial case studies.

Implementation of P-graph modules in undergraduate chemical engineering degree programs: experiences in Malaysia and the Philippines

The process graph (P-graph) framework was introduced in the early 1990s as a graph theoretic approach to Process Network Synthesis (PNS) problems in chemical engineering. This framework has several advantageous features, such as mathematically rigorous generation of maximal structures (i.e., superstructures), elucidation of combinatorially feasible solution structures, and efficient search of solution space for optimal PNS compared to conventional branch-and-bound algorithms for mixed integer linear programming (MILP) models. In the three decades since its inception, the P-graph framework has proven to be a viable approach to a wide array of PNS and other structurally analogous problems; the methodology has also matured, as evidenced by the development of key software tools (PNS Draw, PNS Studio and P-graph Studio) and its appearance in modern textbooks. Nevertheless, the P-graph framework has yet to achieve broad, mainstream penetration among grassroots chemical engineering users, especially those without a strong mathematical programming background. In this paper, we discuss the implementation of instructional P-graph modules in undergraduate chemical engineering degree programs at the University of Nottingham, Malaysia Campus and De La Salle University, Manila, Philippines. These modules have primarily focused on the design of Green Processes. Results show that the visual nature of the P-graph methodology is an advantage for practical engineering decision-making, and that it complements the learning of mainstream techniques such as mathematical programming.

Heuristic Search in Dual Space for Constrained Stochastic Shortest Path Problems

We consider the problem of generating optimal stochastic policies for Constrained Stochastic Shortest Path problems, which are a natural model for planning under uncertainty for resource-bounded agents with multiple competing objectives. While unconstrained SSPs enjoy a multitude of efficient heuristic search solution methods with the ability to focus on promising areas reachable from the initial state, the state of the art for constrained SSPs revolves around linear and dynamic programming algorithms which explore the entire state space. In this paper, we present i-dual, which, to the best of our knowledge, is the first heuristic search algorithm for constrained SSPs. To concisely represent constraints and efficiently decide their violation, i-dual operates in the space of dual variables describing the policy occupation measures. It does so while retaining the ability to use standard value function heuristics computed by well-known methods. Our experiments on a suite of PPDDL problems augmented with constraints show that these features enable i-dual to achieve up to two orders of magnitude improvement in run-time and memory over linear programming algorithms.

A New Primal–Dual Predictor–Corrector Interior-Point Method for Linear Programming Based on a Wide Neighbourhood

In this paper, we propose a new predictor---corrector interior-point algorithm for linear programming based on a wide neighbourhood. In each iteration, the algorithm computes the Ai-Zhang's predictor direction (SIAM J. Optim. 16(2):400---417, 2005) and a new corrector direction, in an attempt to improve its performance. We drive that the duality gap reduces in both predictor and corrector steps. Moreover, we also prove that the complexity of the algorithm coincides with the best iteration bound for small neighbourhood algorithms. Finally, some numerical experiments are provided which reveal capability and effectiveness of the proposed method.

Cogeneration systems optimization: Comparison of multi-step and mixed integer linear programming approaches

ABSTRACTThe presented work compares two optimization models for combined heat and power (CHP) energy systems scheduling. Both models are focused on the evaluation of the best operating strategy to run a defined cogeneration system that is dealing with time-variable loads and tariffs. The simultaneous usage of different prime movers operating in parallel is taken into consideration as well as their part load performance, the influence of ambient temperature, and the usage of a heat storage system. One of the models is heuristic and adopts an optimization strategy based on a multi-step approach: it simulates several cases according to a pre-defined path exploring the most reasonable operational modes and comparing them systematically. The other one relies on a mathematical approach. A Mixed Integer Linear Programming (MILP) algorithm has been developed in order to deal with more complex systems without the need of predefining a too large variety of optimization paths according to the case. Results of the two models are compared against a test case based on real plant specifications, discussing their performance, by the point of view of simulation capabilities, quality of the optimization results, and calculation time.

Tactical Assets Allocation: Evidence from the Nigerian Banking Industry

The core of portfolio selection theory centers on striking a balance between risk-return trade-off of a given investment layout so as to maximize benefits. Literature reveals that portfolio selection or asset allocation problems often involve the use of mathematical programming in propounding solution. This paper uses a blend of simultaneous equation and graphical approach to linear programming algorithm to help solve investors’ problem in allocating assets among various alternatives when faced with problems associated with risk-return trade-off. We strongly suggest that practitioners as well as policy makers use this approach to obtain optimal solution when faced with decision making given various investment alternatives.

Fast power flow scheduling and sensitivity analysis for sizing a microgrid with storage

This article proposes a fast strategy for optimal dispatching of power flows in a microgrid with storage. The investigated approach is based on the use of standard mixed integer linear programming (MILP) algorithm in association with a coarse linear model of the microgrid. The resulting computational time is compatible with simulations over long periods of time allowing the integration of seasonal and stochastic features related to renewable energies. By using this fast scheduling strategy over a complete year of simulation, the microgrid cost effectiveness is considered. Finally, a sensitivity analysis is carried out in order to identify the most influent parameters that should be considered in a sizing loop. Different microgrid configurations are also investigated and compared in terms of cost-effectiveness.

Integrated production and delivery withmultiple factories and multiple customers

ABSTRACTThis paper considers coordinated scheduling of production and delivery with multiple factories and multiple customers. Due to the variation of cost, the production and delivery costs of a job are dependent on the factory to which it is assigned. Our problem is to find a schedule that minimises the makespan or the total completion time, subject to the constraint that the total cost does not exceed a given threshold. We first describe a linear programming algorithm to solve the preemptive case. The result of the linear program serves as a lower bound of the nonpreemptive case and suggests heuristics to solve the nonpreemptive case. We also show that minimising the total completion time subject to a given threshold of the cost is NP-complete. Computational experiments are conducted and the results show that the heuristics perform very well in practice.

Distributed Renewable Generation and Storage System Sizing Based on Smart Dispatch of Microgrids

This paper considers the contribution of independent owners (IOs) operating within microgrids (MGs) toward green power generation in deregulated energy markets. An optimization scheme is introduced for sizing distributed renewable generation (DRG) and a distributed energy storage system (DESS) based on a novel energy management system (EMS) that accounts for demand response (DR), DESS dispatch and performance degradation, dynamic pricing environments, power distribution loss and irregular renewable generation. The proposed EMS utilizes an iterative Newton-Raphson linear programming algorithm that schedules resources in order to minimize the objective function, to deal with the complicated nonlinear nature of the problem and to enable efficient long-term assessments. The EMS is used to evaluate candidate solutions that are generated by a genetic algorithm (GA) to determine the optimal combination of DRG and DESS. A case study for IEEE 34-bus distribution MG in Okinawa, Japan, is used for testing the algorithm and analyzing the potential for IO/MG investments and their strategies.

다중공항 시스템의 도착-출발 가용량 배정 알고리즘

This paper suggests a heuristic algorithm to obtain optimal solution of minimum number of aircraft delay in multi-airport arrivals/departures problem. This single airport arrivals/departures problem can be solved by mathematical optimization method only. The linear programming or genetic algorithm that is a kind of metaheuristic method is used for a multi-airport arrivals/departures problem. Firstly, the proposed algorithm selects the median minimum delays capacity in various arrivals/departures capacities at an airport for the number of aircraft in time interval (15 minutes) at each airport. Next, we suggest reallocate method for arrival aircraft between airports. This algorithm better result of the number of delayed aircraft then genetic algorithm.

Station Cone Algorithm for Linear Programming

Recently we have proposed anew method combininginterior and exterior approaches to solve linear programming problems. This method uses an interior point, and from there connected to the vertex of the so called station cone which is also a solution of the dual problem. This allows us to determine the entering vector and the new station cone. Here in this paper, we present a new modified algorithm for the case, when at each iteration we determine a new interior point. The new building interior point moves toward the optimal vertex. Thanks to the shortened from both inside and outside, the new version allows to find quicker the optimal solution. The computational experiments show that the number of iterations of the new modified algorithm is significantly smaller than that of the second phase of the dual simplex method.

Optimization of Urban Rail Transportation in Emerging Countries Using Operational Research Techniques

Rail systems are gradually becoming the most desirable form of transit infrastructure around the world, partly because they are becoming more environmentally friendly compared with airplanes and automobiles. This paper examines the place of emerging countries in this move of implementing modern rail system that will eventually enhance the realization of a low-carbon society. Network model, transportation model and linear programming algorithms are used to model the present urban rail transport system in Nigeria, as an emerging country, in order to optimize it. Operational research methods, including simplex method and MODI, with the aids of computer software (excel solver and LIP solver) were adopted to solve the resulting models. The results showed that optimization of rail transport system will not only reduce carbon emission but also bring about economic development which is required for the eradication of prevalent poverty in these emerging countries.

Optimal Control Policy of an Inventory System with Postponed Demand

This paper deals with the problem of controlling the selection rates of the pooled customer of a single commodity inventory system with postponed demands. The demands arrive according to a Poisson process. The maximum inventory level is fixed at S . The ordering policy is (s,S ) policy that is as and when the inventory level drops to s an order for Q ( = S − s ) items is placed. The ordered items are received after a random time, which is distributed as exponential. We assume that the demands that occur during stock out period either enter a pool of finite size or leave the system according to a Bernoulli distribution. Whenever the on-hand inventory level is positive, customers are selected one-by-one and the selection rate can be chosen from a given set. The problem is to determine a decision rule that specifies the rate of these selections as a function of the on-hand inventory level and the number of customers waiting in the pool at each instant of time to minimise the long-run total expected cost rate. The problem is modelled as a semi-Markov decision problem. The optimal policy is computed using Linear Programming algorithm and the results are illustrated numerically.

Shortest path in a polygon using sublinear space

We resolve an open problem due to Tetsuo Asano, showing how to compute the shortest path in a polygon, given in a read only memory, using sublinear space and subquadratic time. Specifically, given a simple polygon $P$ with $n$ vertices in a read only memory, and additional working memory of size $m$, the new algorithm computes the shortest path (in $P$) in $O( n^2 / m )$ expected time, assuming $m = O(n/\log^2 n)$. This requires several new tools, which we believe to be of independent interest. Specifically, we show that violator space problems, an abstraction of low dimensional linear-programming (and LP-type problems), can be solved using constant space and expected linear time, by modifying Seidel's linear programming algorithm and using pseudo-random sequences.