Dynamic Programming Procedure Research Articles

ABOUT OPTIMIZING OF INVESTMENT VOLUMES TO IMPROVE THE BASIC INDICATORS OF THE ENTERPRISE EFFECTIVENESS

Purpose. Profit and profitability of any, including transport enterprises are the main economic indicators of the enterprise effectiveness. These indicators reflect the results and successful performance of the enterprise. On the other hand the enterprise effectiveness in the long term, assurance of rapid development and competitiveness is largely determined by the level of investment activity and the range of investment activity. The purpose of this study is the feasibility of the method to determine optimal investments volume for improving these or others (selectable by the management) principal economic indicators of the enterprise effectiveness. Methodology. The basis of the proposed methodology for determining the optimal investments volume is the theory of optimal control, in particular, the procedure of dynamic programming since a managed development process of the enterprise is a multiple stage. This procedure, using a phased plan, allows not only simplifying the solution of optimization problems, but also solving those, which are impossible to apply the methods of mathematical analysis. Findings. The expediency of performing the calculations to determine the optimal investments volume to ensure high rates of enterprise development was proved, it is a key to the effectiveness of the enterprise in the long term and it improves its competitiveness. Originality. It is shown that using methods of the optimum control theory one can calculate the minimum volume of capital investments for the improvement of economic indicators, which determine the enterprise effectiveness. The proposed method of calculation does not depend on the specific content of economic indicators. The effectiveness of this calculation method is demonstrated on a model example. Practical value. The proposed method of calculating the minimum volume of capital investments to improve the economic effectiveness of enterprises is quite simple, but at the same time enables, on the one hand, to determine priority directions of investment activity of the enterprise. On the other hand it improves the manageability and transparency of business enterprises, increases the head's confidence in the correctness of decisions.

Variable Neighborhood Search for Integrated Timetable Based Design of Railway Infrastructure

In this paper we deal with the problem of building new or extending an existing railway infrastructure. The goal is to determine a minimum cost infrastructure fulfilling the requirements defined by an integrated timetable and the operation of the railway system. We first model this planning task as a combinatorial network optimization problem, capturing the essential aspects. We then present a metaheuristic solution method based on general variable neighborhood search that makes use of a dynamic programming procedure for realizing individual connections. Computational experiments indicate that the suggested approach is promising and the analysis of obtained results gives useful hints for future work in this area.

Ordering of Elements for the Volume & Neighbors Algorithm Constructing Elimination Trees for 2D and 3D h- adaptive FEM

In this paper we analyze the optimality of the volume and neighbors algorithm constructing elimination trees for three dimensional h-adaptive finite element method codes. The algorithm is a greedy algorithm that constructs the elimination trees based on the bottom up analysis of the computational mesh. We compare the results of the volume and neighbors greedy algorithm with the global dynamic programming optimization performed on a class of elimination trees. The comparison is based on the Directed Acyclic Graph (DAG) constructed for model grids. We construct DAGs for two model grids: a two dimensional grid refined towards point singularitiy and a two dimensional grid refined towards edge singularity. We show that the quasi-optimal trees created by the volume and neighbors algorithm for the model grids are also captured by the dynamic programming procedure. It means that created elimination trees are optimal in the considered class of elimination trees. We show that different element orderings at the input of the volume and neighbors algorithm result in different computational costs of the multi-frontal solver algorithm executed over the resulting elimination trees. Finally we present the ordering of elements that results in optimal (in the considered class) elimination trees. The theoretical results are verified with numerical experiments performed on a three dimensional grids with point, edge and face singularities.

Automatic Classification and Quantification of Cell Adhesion Locations on the Endothelium.

To target tumor hematogenous metastasis and to understand how leukocytes cross the microvessel wall to perform immune functions, it is necessary to elucidate the adhesion location and transmigration pathway of tumor cells and leukocytes on/across the endothelial cells forming the microvessel wall. We developed an algorithm to classify and quantify cell adhesion locations from photomicrographs taken from the experiments of tumor cell/leukocyte adhesion in individual microvessels. The first step is to identify the microvessel by a novel gravity-field dynamic programming (DP) procedure. Next, an anisotropic image smoothing suppresses noises without unduly mitigating crucial visual features. After an adaptive thresholding process further tackles uneven lighting conditions during the imaging process, a series of local mathematical morphological operators and eigenanalysis identify tumor cells or leukocytes. Finally, a novel double component labeling procedure categorizes the cell adhesion locations. This algorithm has generated consistently encouraging performances on photomicrographs obtained from in vivo experiments for tumor cell and leukocyte adhesion locations on the endothelium forming the microvessel wall. Compared with human experts, this algorithm used 1/500-1/200 of the time without having the errors due to human subjectivity. Our automatic classification and quantification method provides a reliable and cost effective approach for biomedical image processing.

A dynamic programming based heuristic for locating stops in public transportation networks

This paper investigates the maximum covering location problem in networks.We introduce a heuristic nested dynamic programming procedure, which:Is fast, i.e., instances with up to 5000 customers are...

Low Carbon Iron-making Supply Chain Planning in Steel Industry

This paper investigates a new low carbon iron-making supply chain planning problem in the steel industry under the carbon cap and trade mechanism, in which a steel company uses carbon emission quota to produce iron to meet determined demands over the planning horizon, and buys or sells the rights to emit carbon in the carbon trading market. The problem decides optimal carbon trade, raw material purchasing, raw materials and sinters inventory levels, as well as sintering and iron making production schemes, so as to minimize the total cost. A novel mixed integer programming model incorporating carbon emission reduction into operational decision making is developed and we propose a branch and price algorithm to solve it. The model is decomposed equally into a master problem and two subproblems. The branch and price algorithm is enhanced by two tailored techniques. First, the relaxation of the master problem is strengthened by introducing two families of valid inequalities. Second, we use a dynamic programming procedure to eliminate variables by path reduced cost. We test our algorithm on randomly generated data that simulate the practical production, and the computational results over the instances illustrate the effectiveness of the proposed algorithm. In addition, we derive the optimal operational decisions, and examine the impacts of carbon cap and carbon price analytically and numerically on total cost and carbon emissions. We make interesting observations based on numerical results and provide managerial insight to highlight the opportunity to reduce carbon emissions.

An approximation scheme for stochastic controls in continuous time

We propose a simple time-discretization scheme for multi-dimensional stochastic optimal control problems in continuous time. It is based on a probabilistic representation for the convolution of the value function by a probability density function. We show the convergence results under mild conditions on coefficients of the problems by Barles–Souganidis viscosity solution method. Resulting numerical methods allow us to use uncontrolled Markov processes to estimate the conditional expectations in the dynamic programming procedure. Moreover, it can be implemented without the interpolation of the value function or the adjustment of the diffusion matrix.

Symmetry properties of resolving sets and metric bases in hypercubes

In this paper we consider some special characteristics of distances between vertices in the \(n\)-dimensional hypercube graph \(Q_n\) and, as a consequence, the corresponding symmetry properties of its resolving sets. It is illustrated how these properties can be implemented within a simple greedy heuristic in order to find efficiently an upper bound of the so called metric dimension \(\beta (Q_n)\) of \(Q_n\), i.e. the minimal cardinality of a resolving set in \(Q_n\). This heuristic was applied to generate upper bounds of \(\beta (Q_n)\) for \(n\) up to \(22\), which are for \(n\ge 19\) better than the existing ones. Starting from these new bounds, some existing upper bounds for \(23\le n\le 90\) are improved by a dynamic programming procedure.

Optimization of generic progressive queries based on dependency analysis and materialized views

Progressive queries (PQ) are a new type of queries emerging from numerous contemporary database applications such as e-commerce, social network, business intelligence, and decision support. Such a PQ is formulated on the fly in several steps via a set of inter-related step-queries (SQ). In our previous work, we presented a framework to process a restricted type of PQs. However, how to process generic PQs remains an open problem. In this paper, we develop a novel technique to efficiently process generic PQs based on materialized views. The SQs of an in-process PQ can utilize the results of previous SQs not only from the same PQ but also from other in-process and completed PQs. The key idea is to create a multiple query dependency graph (MQDG), which captures the data source dependency relationships among SQs from multiple PQs. A mathematic model is developed to estimate the benefit of keeping the result of an SQ as a materialized view (critical SQ/node) based on the MQDG. The kept materialized views are used to improve the performance of the future SQs. Strategies for constructing the MQDG and identifying the critical SQs for materialization by using the MQDG are presented. To manage the storage of the materialized views, we introduce two approaches --- one employs a greedy method and the other adopts a dynamic programming (DP) based method. Strategies are also suggested to reduce the input problem size for the DP procedure. Experimental results demonstrate that our technique is quite promising in efficiently processing PQs.

MULTI-OBJECTIVE SYNTHESIS OF CONFLICT-FREE AIRCRAFT TRAJECTORIES

The problem of multi-objective synthesis of trajectories for aircraft conflict resolution is considered. The optimality criteria that characterize the efficiency of conflict resolution are regularity of flights, economy of flights and maneuvers complexity. Resolution of the potential conflict considered as the sequential multistage decision-making process in discrete time and the maneuvering aircraft considered as the discrete dynamic system. The method of sequential conflict-free space-time trajectories synthesis using multi-objective dynamic programming was developed. The functional equations of bottom-up and top-down multi-objective dynamic programming procedures for determining the set of Pareto-efficient estimations of conflict-flight trajectories are shown. The procedure for selection of the optimal trajectory from the set of Pareto-efficient based on method of criteria convolution is defined.

Heuristic Method for Identifying Concave Pareto Frontiers in Multi-Objective Dynamic Programming Problems

Aerospace engineers and analysts tasked with informing system-level decisions commonly seek to identify the frontier of Pareto-optimal solutions with respect to objectives of interest. For problems in which decisions are made over multiple stages or periods, dynamic programming can be an efficient and effective method for identifying such a Pareto frontier. To employ traditional dynamic programming, however, a single objective function must be defined. Aggregation of multiple objectives into a single objective using traditional simple additive weighting has the limitation of permitting identification of only points on convex portions of the Pareto frontier. This can translate into detection of a frontier with significant and misleading gaps. This paper proposes a theory-motivated aggregation function modification and method to improve the ability of dynamic programming procedures to detect concave portions of Pareto frontiers in multi-objective, multistage problems. Following a theoretical motivation and method definition, a military aircraft route planning example is provided to illustrate the method’s accuracy and efficiency.

Reservoir Operation to Minimize Sedimentation

The Wonogiri Reservoir capacity decreases rapidly, caused by serious sedimentation problems. In 2007, JICA was proposed a sediment storage reservoir with a new spillway for the purpose of sediment flushing / sluicing from The Keduang River. Due to the change of reservoir storage and change of reservoir system, it requires a sustainable reservoir operation technique. This technique is aimed to minimize the deviation between the input and output of sediments. The main objective of this study is to explore the optimal Wonogiri reservoir operation by minimizing the sediment trap. The CSUDP incremental dynamic programming procedure is used for the model optimization. This new operating rules will also simulate a five years operation period, to show the effect of the implemented techniques. The result of the study are the newly developed reservoir operation system has many advantages when compared to the actual operation system and the disadvantage of this developed system is that the use is mainly designed for a wet hydrologic year, since its performance for the water supply is lower than the actual reservoir operations. Doi : 10.12777/ijse.6.1.16-23 [How to cite this article: Wulandari, D.A., Legono, D., and Darsono, S., 2014. Reservoir Operation to Minimize Sedimentation. International Journal of Science and Engineering , 5(2),61-65. Doi: 10.12777/ijse.6.1.16-23 ] Normal 0 false false false EN-US X-NONE X-NONE

The influence of global constraints on similarity measures for time-series databases

A time series consists of a series of values or events obtained over repeated measurements in time. Analysis of time series represents an important tool in many application areas, such as stock-market analysis, process and quality control, observation of natural phenomena, and medical diagnosis. A vital component in many types of time-series analyses is the choice of an appropriate distance/similarity measure. Numerous measures have been proposed to date, with the most successful ones based on dynamic programming. Being of quadratic time complexity, however, global constraints are often employed to limit the search space in the matrix during the dynamic programming procedure, in order to speed up computation. Furthermore, it has been reported that such constrained measures can also achieve better accuracy. In this paper, we investigate four representative time-series distance/similarity measures based on dynamic programming, namely Dynamic Time Warping (DTW), Longest Common Subsequence (LCS), Edit distance with Real Penalty (ERP) and Edit Distance on Real sequence (EDR), and the effects of global constraints on them when applied via the Sakoe–Chiba band. To better understand the influence of global constraints and provide deeper insight into their advantages and limitations we explore the change of the 1-nearest neighbor graph with respect to the change of the constraint size. Also, we examine how these changes reflect on the classes of the nearest neighbors of time series, and evaluate the performance of the 1-nearest neighbor classifier with respect to different distance measures and constraints. Since we determine that constraints introduce qualitative differences in all considered measures, and that different measures are affected by constraints in various ways, we expect our results to aid researchers and practitioners in selecting and tuning appropriate time-series similarity measures for their respective tasks.

An improvement of the knapsack function based algorithm of Gilmore and Gomory for the unconstrained two-dimensional guillotine cutting problem

In this paper we tackle the unconstrained non-staged guillotine two-dimensional cutting problem (U2DCP) with rectangular pieces and one rectangular stock sheet. This problem has been widely treated in literature by exact and heuristic solution methods which use the knapsack function introduced by Gilmore and Gomory (1966) and implement more effective variants of their dynamic programming procedure to compute the related recursive expression. We highlight three errors present in the original procedure by Gilmore and Gomory (1966). The first error was noted by Herz (1972) but no correction was provided. The other two errors have never been noted before. These errors affect the accuracy of the solution and cause the increase of the computational requirements. Corrections for these errors are presented and an improved computational procedure is proposed. The new procedure has been tested on a wide set of instances (PackLib2) and compared with the best exact and heuristic methods present in literature. The experimentation shows that the procedure significantly outperforms the best dynamic programming algorithm proposed for the U2DCP and it compares well with the best heuristic and the best exact algorithm for the problem.

A hybrid dynamic programming approach to the biobjective binary knapsack problem

This article is devoted to a study of the impact of using bound sets in biobjective dynamic programming. This notion, introduced by Villareal and Karwan [1981], has been independently revisited by Ehrgott and Gandibleux [2007], as well as by Sourd and Spanjaard [2008]. The idea behind it is very general and can, therefore, be adapted to a wide range of biobjective combinatorial problems. We focus here on the biobjective binary knapsack problem. We show that using bound sets to perform a hybrid dynamic programming procedure embedded in a two-phase method [Ulungu and Teghem 1995] yields numerical results that outperform previous dynamic programming approaches to the problem, both in execution times and memory requirements.

Maximizing the weighted number of just-in-time jobs on a single machine with position-dependent processing times

We study the problem of maximizing the weighted number of just-in-time jobs on a single machine with position-dependent processing times. Unlike the vast majority of the literature, we do not restrict ourselves to a specific model of processing time function. Rather, we assume that the processing time function can be of any functional structure that is according to one of the following two cases. The first is the case where the job processing times are under a learning effect, i.e., each job processing time is a non-increasing function of its position in the sequence. In the second case, an aging effect is assumed, i.e., each job processing time is a non-decreasing function of its position in the sequence. We prove that the problem is strongly $$\mathcal{N }\mathcal{P }$$ N P -hard under a learning effect, even if all the weights are identical. When there is an aging effect, we introduce a dynamic programming (DP) procedure that solves the problem with arbitrary weights in $$O(n^{3})$$ O ( n 3 ) time (where $$n$$ n is the number of jobs). For identical weights, a faster optimization algorithm that runs in $$O(n\log n)$$ O ( n log n ) time is presented. We also extend the analysis to the case of scheduling on a set of $$m$$ m parallel unrelated machines and provide a DP procedure that solves the problem in polynomial time, given that $$m$$ m is fixed and that the jobs are under an aging effect.

Power Yield and Power Consumption in Thermo-Electro-Chemical Systems – A Synthesizing Approach

In this synthesizing research methods of mathematical programming and dynamic optimization are applied to determine limits on power yield or power consumption in various energy systems, such as thermal engines, heat pumps, solar dryers, electrolysers, and fuel cells. Methodological similarities are enunciated when treating power limits in engines, separators, and heat pumps. Numerical approaches to multistage systems are based on the methods of dynamic programming (DP) or Pontryagin’s maximum principle. The first method searches for properties of optimal work and is limited to systems with low dimensionality of state vector, whereas the second investigates properties of differential (canonical) equations derived from the process Hamiltonian. In this paper a relatively unknown symmetry in behaviour of power producers (engines) and power consumers is shown. An approximate evaluation shows that, at least 1/4 of power dissipated in the natural transfer process must be added to a separator or heat pump in order to assure a required process rate.Applications include drying systems which, by nature, require a large amount of thermal or solar energy. We search for minimum power consumed in one-stage and multistage operation of fluidized drying. This multistage system is supported by heat pumps. We outline the related dynamic programming procedure, and also point out a link between the present irreversible approach and the classical problem of minimum reversible work driving the system.

Mobile Sensor Motion Planning for Identification of a Contamination Source Using Iterative Dynamic Programming

A systematic iterative dynamic programming procedure is proposed for on-line motion planning of mobile sensor network nodes in a specified spatial domain in such a way as to maximize the identification accuracy of an unknown contamination source. The design criterion is a general scalar measure defined on the Fisher information matrix associated with the estimated coordinates of the contamination source. The approach converts the problem to an optimal control one in which the control forces of the sensors are optimized using iterative dynamic programming.

An Unified Approach to Limits on Power Generation and Power Consumption in Thermo-Electro-Chemical Systems

This research presents a unified approach to power limits in power producing and power consuming systems, in particular those using renewable resources. As a benchmark system which generates or consumes power, a well-known standardized arrangement is considered, in which two different reservoirs are separated by an engine or a heat pump. Either of these units is located between a resource fluid (‘upper’ fluid 1) and the environmental fluid (‘lower’ fluid, 2). Power yield or power consumption is determined in terms of conductivities, reservoir temperatures and internal irreversibility coefficient, F. While bulk temperatures Ti of reservoirs’ are the only necessary state coordinates describing purely thermal units, in chemical (electrochemical) engines, heat pumps or separators it is necessary to use both temperatures and chemical potentials mk. Methods of mathematical programming and dynamic optimization are applied to determine limits on power yield or power consumption in various energy systems, such as thermal engines, heat pumps, solar dryers, electrolysers, fuel cells, etc. Methodological similarities when treating power limits in engines, separators, and heat pumps are shown. Numerical approaches to multistage systems are based on methods of dynamic programming (DP) or on Pontryagin’s maximum principle. The first method searches for properties of optimal work and is limited to systems with low dimensionality of state vector, whereas the second investigates properties of differential (canonical) equations derived from the process Hamiltonian. A relatively unknown symmetry in behaviour of power producers (engines) and power consumers is enunciated in this paper. An approximate evaluation shows that, at least ¼ of power dissipated in the natural transfer process must be added to a separator or a heat pump in order to assure a required process rate. Applications focus on drying systems which, by nature, require a large amount of thermal or solar energy. We search for minimum power consumed in one-stage and multi-stage operation of fluidized drying. This multi-stage system is supported by heat pumps. We outline the related dynamic programming procedure, and also point out a link between the present irreversible approach and the classical problem of minimum reversible work driving the system.

Dynamic Programming Approach for Arterial Signal Optimization

Link performance functions (LPFs) are essential components of macroscopic models for signal optimization, traffic assignment, or combined control-assignment models. Numerous studies have developed a variety of performance functions for signal optimization. Most of these studies attempted to use simplified LPFs that did not capture the important relationships and dependencies among the variables. Dependent LPFs are introduced; in these LPFs the performance on any link depends on the flow pattern not only on that link alone but also on the feeder links. Such functions represent with greater fidelity the performance characteristics of the link and can lead to better control and assignment. An optimization model explicitly considers flow interactions among successive links and applies it in a dynamic programming procedure to determine optimal signal settings. The procedure, which is an offshoot of the combination method for offset optimization, is illustrated for an arterial street and demonstrates its efficacy in comparison with existing optimization models.