Linear Programming Algorithm Research Articles

Revised simplex algorithm for linear programming on GPUs with CUDA

The revised simplex algorithm (RSA) is a typical algorithm for solving linear programming problems. Many theoretical modifications have been done to make the algorithm more efficient, but almost all of them were based on single-instruction single-data architecture processors (CPUs), which could not make full use of the inherent parallel characteristics of RSAs. We propose a novel single-instruction multiple-data architecture processor (GPU) based on the RSA in this paper. The intensive matrix manipulations of a traditional RSA are offloaded to the GPU, which helps to make full use of its powerful parallel processing ability. We implemented the GPU-based RSA on compute unified device architecture (CUDA). Numerical experiments on randomly generated linear programs show that the GPU-based RSA can not only find the correct optimal solutions, but can also reach a speed of up to 100 times as fast as that of a CPU-based RSA: it also runs 3 to 11 times as fast as MATLAB.

Markov velocity predictor and radial basis function neural network-based real-time energy management strategy for plug-in hybrid electric vehicles

Power management strategy of plug-in hybrid electric vehicle for real-time application is a major challenge as the driving pattern is unknown beforehand. In this work, an innovative real-time power management strategy framework is proposed, including short horizon driving pattern prediction, driving pattern recognition, parameter off-line optimisation, parameter on-line prediction modelling, and power management strategy real-time application. A group of characteristic parameters is used to recognise driving patterns and the engine and motor working points are optimised globally by distributed genetic algorithm off-line. The optimised results approximation model is built on the basis of a radial basis function-neural network. Based on a linear programming algorithm, the higher order Markov velocity predictor is designed to obtain the short-horizon driving conditions. Combining the optimisation results approximation model, the real-time power management strategy is proposed. The on-line optimisation power management strategy comparing to the rule-based is analysed and the MATLAB/Simulink/AVL Cruise co-simulation results demonstrate that the fuel economy of real-time power management strategy improved by 16.3%, 12.7%, and 9.1% in HWFET, LA92, and Japanese urban driving patterns, respectively, which is largely higher than with a traditional rule-based strategy and slightly lower than, or approximately equal to, the global optimisation strategy.

Solving a selective dial-a-ride problem with logic-based Benders decomposition

Today’s society is facing an ever-growing demand for mobility. To a high degree these needs can be fulfilled by individual and public transport. People that do not have access to the former and cannot use the latter require additional means of transportation. This is where dial-a-ride services come into play. The dial-a-ride problem considers transportation requests of people from pick-up to drop-off locations. Users specify time windows with respect to these points. Requests are served by a given vehicle fleet with limited capacity and tour duration per vehicle. Moreover, user inconvenience considerations are taken into account by limiting the travel time between origin and destination for each request.Previous research on the dial-a-ride problem primarily focused on serving a given set of requests with a fixed-size vehicle fleet at minimal traveling costs. It is assumed that the request set is sufficiently small to be served by the available vehicles. We consider a different scenario in which a maximal number of requests shall be served under the given constraints, i.e., it is no longer guaranteed that all requests can be accepted. For this new problem variant we propose a compact mixed integer linear programming model as well as algorithms based on Benders decomposition. In particular, we employ logic-based Benders decomposition and branch-and-check using mixed integer linear programming and constraint programming algorithms. We consider different variants on how to generate Benders cuts as well as heuristic boosting techniques and different types of valid inequalities. Computational experiments illustrate the effectiveness of the suggested algorithms.

Optimal sizing of distributed generation in gas/electricity/heat supply networks

Multi-energy supply systems are expected to play an important role in smart grids. Today's energy supply systems are large nodes networks, and different types of energy are needed at each node to satisfy the different energy demands. These different types of energy can then be converted to each other through specific devices. How to decide the ratings of these devices at each node to make the system cost-effective is addressed in this paper. The focus is set on a gas/electricity/heat hybrid network. A hydrogen storage system (fuel cell, electrolyzer, and tanks) is used as electricity storage system, a combined heat and power device is used to produce heat and electric power, etc. A mixed integer linear programming algorithm is used to determine the optimal operation schedule of the system, where the goal is to minimize shed load. A genetic algorithm is also used to search for the best size of each component, where the goal is to minimize the total investment costs. In order to resist to contingency events, betweenness centrality (describing the relative importance of each node) is then used to find the worst case under contingency events. This worst case scenario is used to research about the influence of contingencies on the sizing results. At last, two cases (modified 13-node network and IEEE 30 + Gas 20 + Heat 14 nodes system) are tested using the proposed sizing method. The results show that the renewable energy location, investment cost of components, and the structure of the whole system influence the sizing results. When the installed capacity of photovoltaic panels is reduced by 50%, the capacity of the electrolyzer decreases by 3%, the capacity for the hydrogen tanks increases by 2%; when the investment cost of the fuel cell and electrolyzer decreases by 50%, the capacity of photovoltaic increases by 14%, the electrolyzer increases by 13%, and hydrogen tanks increase by 2%. After considering the worst case contingency event, for case I, the capacity of photovoltaic and fuel cell increase by 12% and 11%, and the electrolyzer increases by 34%; for case II, the capacity of photovoltaic and fuel cell increase by 8% and 11%, and the electrolyzer increases by 57%.

A vector linear programming approach for certain global optimization problems

Global optimization problems with a quasi-concave objective function and linear constraints are studied. We point out that various other classes of global optimization problems can be expressed in this way. We present two algorithms, which can be seen as slight modifications of Benson-type algorithms for multiple objective linear programs (MOLP). The modification of the MOLP algorithms results in a more efficient treatment of the studied optimization problems. This paper generalizes results of Schulz and Mittal on quasi-concave problems and Shao and Ehrgott on multiplicative linear programs. Furthermore, it improves results of L\"ohne and Wagner on minimizing the difference $f=g-h$ of two convex functions $g$, $h$ where either $g$ or $h$ is polyhedral. Numerical examples are given and the results are compared with the global optimization software BARON.

Simultaneous optimization of piezoelectric actuator topology and polarization

This article addresses the problem of piezoelectric actuator design for active structural vibration control. The topology optimization method using the Piezoelectric Material with Penalization and Polarization (PEMAP-P) model is employed in this work to find the optimum actuator layout and polarization profile simultaneously. A coupled finite element model of the structure is derived assuming a two-phase material, and this structural model is written into the state-space representation. The proposed optimization formulation aims to determine the distribution of piezoelectric material which maximizes the controllability for a given vibration mode. The optimization of the layout and poling direction of embedded in-plane piezoelectric actuators are carried out using a Sequential Linear Programming (SLP) algorithm. Numerical examples are presented considering the control of the bending vibration modes for a cantilever and a fixed beam. A Linear-Quadratic Regulator (LQR) is synthesized for each case of controlled structure in order to compare the influence of the polarization profile.

Trade-off preservation in inverse multi-objective convex optimization

Given an input solution that may not be Pareto optimal, we present a new inverse optimization methodology for multi-objective convex optimization that determines a weight vector producing a weakly Pareto optimal solution that preserves the decision maker’s trade-off intention encoded in the input solution. We introduce a notion of trade-off preservation, which we use as a measure of similarity for approximating the input solution, and show its connection with minimizing an optimality gap. We propose a linear approximation to the inverse model and a successive linear programming algorithm that balance between trade-off preservation and computational efficiency, and show that our model encompasses many of the existing inverse optimization models from the literature. We demonstrate the proposed method using clinical data from prostate cancer radiation therapy.

A new efficient short-step projective interior point method for linear programming

In this paper, we are interested in the performance of Karmarkar’s projective algorithm for linear programming. We propose a new displacement step to accelerate and improve the convergence of this algorithm. This purpose is confirmed by numerical experimentations showing the efficiency and the robustness of the obtained algorithm over Schrijver’s one for small problem dimensions.

Optimization Techniques for Incremental Planning of Multilayer Elastic Optical Networks

As optical networks become increasingly flexible and software driven, network operators need to reconsider their present mode of network planning and operation, which traditionally relies on long planning periods, performed independently for the IP edges (logical topology) and the optical transport layer (physical topology). Network planning assuming fully loaded end-of-life conditions fails to follow traffic evolution and results in capacity overprovisioning, underutilized equipment, and stranded investments. We argue that it would be beneficial to have shorter upgrade cycles and a multiperiod network planning approach that accounts jointly for the upgrade of the optical but also the IP edges of the network. We formulate the incremental multilayer planning problem of an IP over elastic optical network and propose an integer linear programming (ILP) algorithm to solve it. The ILP model leverages the reconfigurability of both network layers to delay equipment deployment and benefit from cost erosion. Our objective is, through repurposing of existing network resources, to deploy in a period the minimum additional network equipment (capital expenditures) to cope with traffic changes from the previous period but also to minimize changes in transitioning between the two periods (operational expenditures). The proposed planning approaches are validated through simulations based on realistic network scenarios, where we also study the effect of the upgrade period duration.

Single/Cross-Camera Multiple-Person Traffic Tracking by Graph Matching

Multiple person tracking is a very useful task in intelligent video surveillance, which is hindered by many challenges such as the variations of illumination, the irregular changes of human shapes and the particle occlusions. To tackle these challenges, in this paper, we propose a new online learning tracking system to generate the complete trajectory for each tracking object. In detection stage, we build a classifier for each tracking object by online learning in order to provide more accurate detection results. Online learning could real-time update the classifier for an accurately tracking results in the future. In the tracklet generation stage, we apply the spatiotemporal constrain to generate a set of reliable tracklets. Finally, we propose a new Part-based matching method to get the correlation between different tracklets and apply linear programming and greedy algorithm to handle the data association problem to generate the complete trajectory for each tracking object. In particular, our approach is able to cast the multiple cameras tracking problem as a data association problem. The experiments on our proposed method demonstrate state-of-the-art performance in multiple person tracking.

Examining military medical evacuation dispatching policies utilizing a Markov decision process model of a controlled queueing system

Military medical planners must develop dispatching policies that dictate how aerial medical evacuation (MEDEVAC) units are utilized during major combat operations. The objective of this research is to determine how to optimally dispatch MEDEVAC units in response to 9-line MEDEVAC requests to maximize MEDEVAC system performance. A discounted, infinite horizon Markov decision process (MDP) model is developed to examine the MEDEVAC dispatching problem. The MDP model allows the dispatching authority to accept, reject, or queue incoming requests based on a request’s classification (i.e., zone and precedence level) and the state of the MEDEVAC system. A representative planning scenario based on contingency operations in southern Afghanistan is utilized to investigate the differences between the optimal dispatching policy and three practitioner-friendly myopic policies. Two computational experiments are conducted to examine the impact of selected MEDEVAC problem features on the optimal policy and the system performance measure. Several excursions are examined to identify how the 9-line MEDEVAC request arrival rate and the MEDEVAC flight speeds impact the optimal dispatching policy. Results indicate that dispatching MEDEVAC units considering the precedence level of requests and the locations of busy MEDEVAC units increases the performance of the MEDEVAC system. These results inform the development and implementation of MEDEVAC tactics, techniques, and procedures by military medical planners. Moreover, an analysis of solution approaches for the MEDEVAC dispatching problem reveals that the policy iteration algorithm substantially outperforms the linear programming algorithms executed by CPLEX 12.6 with regard to computational effort. This result supports the claim that policy iteration remains the superlative solution algorithm for exactly solving computationally tractable Markov decision problems.

MinGenome: An In Silico Top-Down Approach for the Synthesis of Minimized Genomes.

Genome minimized strains offer advantages as production chassis by reducing transcriptional cost, eliminating competing functions and limiting unwanted regulatory interactions. Existing approaches for identifying stretches of DNA to remove are largely ad hoc based on information on presumably dispensable regions through experimentally determined nonessential genes and comparative genomics. Here we introduce a versatile genome reduction algorithm MinGenome that implements a mixed-integer linear programming (MILP) algorithm to identify in size descending order all dispensable contiguous sequences without affecting the organism's growth or other desirable traits. Known essential genes or genes that cause significant fitness or performance loss can be flagged and their deletion can be prohibited. MinGenome also preserves needed transcription factors and promoter regions ensuring that retained genes will be properly transcribed while also avoiding the simultaneous deletion of synthetic lethal pairs. The potential benefit of removing even larger contiguous stretches of DNA if only one or two essential genes (to be reinserted elsewhere) are within the deleted sequence is explored. We applied the algorithm to design a minimized E.coli strain and found that we were able to recapitulate the long deletions identified in previous experimental studies and discover alternative combinations of deletions that have not yet been explored in vivo.

Solving the assignment of customers to trucks and visiting days in a periodic routing real-world case

Introduction: this work proposes a model, and two heuristic algorithms to assign customers to trucks and visiting days, as a first phase in the solution of a real-world routing problem, which is closely related to the Periodic vehicle routing problem, but a strategic decision of the company imposes the additional constraint that every customer must always be visited by the same truck. Methods: The proposed model aims to group the customers that are visited the same day by the same truck as close as possible. The first proposed heuristic has a constructive stage, and five underlying improvement heuristic, the second one uses an exact linear programming algorithm. Results: The algorithms are evaluated by instances taken from the literature and generated, taking into account the characteristics presented in the real-world case addressed.

Two computationally efficient polynomial-iteration infeasible interior-point algorithms for linear programming

Since the beginning of the development of interior-point methods, there exists a puzzling gap between the results in theory and the observations in numerical experience, i.e., algorithms with good polynomial bounds are not computationally efficient and algorithms demonstrated efficiency in computation do not have a good or any polynomial bound. Todd raised a question in 2002: “Can we find a theoretically and practically efficient way to reoptimize?” This paper is an effort to close the gap. We propose two arc-search infeasible interior-point algorithms with infeasible central path neighborhood wider than all existing infeasible interior-point algorithms that are proved to be convergent. We show that the first algorithm is polynomial and its simplified version has a complexity bound equal to the best known complexity bound for all (feasible or infeasible) interior-point algorithms. We demonstrate the computational efficiency of the proposed algorithms by testing all Netlib linear programming problems in standard form and comparing the numerical results to those obtained by Mehrotra’s predictor-corrector algorithm and a recently developed more efficient arc-search algorithm (the convergence of these two algorithms is unknown). We conclude that the newly proposed algorithms are not only polynomial but also computationally competitive compared to both Mehrotra’s predictor-corrector algorithm and the efficient arc-search algorithm.

Yaw Moment Control Strategy for Four Wheel Side Driven EV

When four wheel side driven EV travals in steering or changes lanes in high speed, the vehicle is easy to side-slip or flick due to the difference of wheel hub motor and a direct effect of vehicle nonlinear factors on vehicle yaw motion, which would affect vehicle handling and stability seriously. To solve this problem, a joint control strategy, combined with the linear programming algorithm and improved sliding mode algorithm, which combines the exponential reaching law and saturation function was proposed. Firstly, the vehicle dynamics model and the reference model according with the structure and driving characteristics of four wheel side driven EV were set up. Then, introduced the basic method of the improved sliding mode variable structure control and complete the sliding mode variable structure controller design basic on vehicle sideslip angle and yaw velocity.The controller accomplish optimal allocation of vehicle braking force through a linear programming algorithm, according to yaw moment produced by the vehicle motion state. Single lane driving simulation results show that the proposed control strategy can not only control vehicle sideslip angle and yaw velocity well, but also accomplish good controlling of the vehicle yaw moment, so as to significantly improve the handling and stability of vehicle.

The Sliding Gradient Algorithm for Linear Programming

The existence of strongly polynomial algorithm for linear programming (LP) has been widely sought after for decades. Recently, a new approach called Gravity Sliding algorithm [1] has emerged. It is a gradient descending method whereby the descending trajectory slides along the inner surfaces of a polyhedron until it reaches the optimal point. In R3, a water droplet pulled by gravitational force traces the shortest path to descend to the lowest point. As the Gravity Sliding algorithm emulates the water droplet trajectory, it exhibits strongly polynomial behavior in R3. We believe that it could be a strongly polynomial algorithm for linear programming in Rn too. In fact, our algorithm can solve the Klee-Minty deformed cube problem in only two iterations, irrespective of the dimension of the cube. The core of gravity sliding algorithm is how to calculate the projection of the gravity vector g onto the intersection of a group of facets, which is disclosed in the same paper [1]. In this paper, we introduce a more efficient method to compute the gradient projections on complementary facets, and rename it the Sliding Gradient algorithm under the new projection calculation.

Facial Reduction and Partial Polyhedrality

We present FRA-Poly, a facial reduction algorithm (FRA) for conic linear programs that is sensitive to the presence of polyhedral faces in the cone. The main goals of FRA and FRA-Poly are the same, i.e., finding the minimal face containing the feasible region and detecting infeasibility, but FRA-Poly treats polyhedral constraints separately. This idea enables us to reduce the number of iterations drastically when there are many linear inequality constraints. The worst case number of iterations for FRA-poly is written in the terms of a "distance to polyhedrality" quantity and provides better bounds than FRA under mild conditions. In particular, in the case of the doubly nonnegative cone, FRA-Poly gives a worst case bound of $n$ whereas the classical FRA is $\mathcal{O}(n^2)$. Of possible independent interest, we prove a variant of Gordan-Stiemke's Theorem and a proper separation theorem that takes into account partial polyhedrality. We provide a discussion on the optimal facial reduction strategy and an instance that forces FRAs to perform many steps. We also present a few applications. In particular, we will use FRA-poly to improve the bounds recently obtained by Liu and Pataki on the dimension of certain affine subspaces which appear in weakly infeasible problems.

Cost-Optimal Caching for D2D Networks With User Mobility: Modeling, Analysis, and Computational Approaches

Caching popular files at the user equipments (UEs) provides an effective way to alleviate the burden of the backhaul networks. Generally, popularity-based caching is not a system-wide optimal strategy, especially for user mobility scenarios. Motivated by this observation, we consider optimal caching with the presence of mobility. A cost-optimal caching problem (COCP) for device-to-device (D2D) networks is modeled, in which the impact of user mobility, cache size, and total number of encoded segments are all taken into account. The hardness of the problem is proved via a reduction from the satisfiability problem. Next, a lower-bounding function of the objective function is derived. By the function, an approximation of COCP (ACOCP) achieving linearization is obtained, which features two advantages. First, the ACOCP approach can use an off-the-shelf integer linear programming algorithm to obtain the global optimal solution, and it can effectively deliver solutions for small-scale and medium-scale system scenarios. Second, and more importantly, based on the ACOCP approach, one can derive a lower bound of global optimum of COCP, thus enabling performance benchmarking of any sub-optimal algorithm. To tackle large scenarios with low complexity, we first prove that the optimal caching placement of one user, giving other users’ caching placements, can be derived in polynomial time. Then, based on this proof, a mobility aware multi-user algorithm is developed. Simulation results verify the effectivenesses of the two approaches by comparing them to the lower bound of global optimum and conventional caching algorithms.

Optimal Sizing for Grid-Tied Microgrids With Consideration of Joint Optimization of Planning and Operation

This paper presents a multiobjective optimization method to jointly optimize the planning and operation of a grid-tied microgrid (MG) with various distributed generation sources such as wind turbine and photovoltaic arrays with the assistance of demand side management. In order to explore the economy and demand variety, the problem is formulated as a double-objective optimization to minimize the total annual cost and to maximize the customer satisfaction. To solve the multiobjective optimization problem, a fuzzy satisfaction-maximizing method is adopted to convert the original problem into a single objective optimization problem and a mixed integer linear programming algorithm is then used to solve the problem. To verify the proposed solution, various case studies have been carried out and compared. The results show that the proposed method is effective in minimizing the cost of an MG without sacrificing the satisfaction of customers.

Optimal Operation of Residential Microgrids in the Harbin Area

The popularization of electric vehicles and new forms of power generation has led to a change in the architecture of the residential microgrid. As the mode of power distribution on the user side must be re-planned, the optimization of user costs for a residential building in Harbin was selected as the research focus. From local electricity prices and building characteristics, this paper uses a linear programming algorithm to calculate the optimization of power distributions. The results show that users can save an average of 15.6% on their electric bills annually throughout the life cycle of residential microgrid equipment and save up to 55.3% in the summer. The results of this paper can guide structural designs and modes of power distribution for residents of Harbin.