Multi-pass Dynamic Programming Research Articles

DynASP2.5: Dynamic Programming on Tree Decompositions in Action

Efficient exact parameterized algorithms are an active research area. Such algorithms exhibit a broad interest in the theoretical community. In the last few years, implementations for computing various parameters (parameter detection) have been established in parameterized challenges, such as treewidth, treedepth, hypertree width, feedback vertex set, or vertex cover. In theory, instances, for which the considered parameter is small, can be solved fast (problem evaluation), i.e., the runtime is bounded exponential in the parameter. While such favorable theoretical guarantees exists, it is often unclear whether one can successfully implement these algorithms under practical considerations. In other words, can we design and construct implementations of parameterized algorithms such that they perform similar or even better than well-established problem solvers on instances where the parameter is small. Indeed, we can build an implementation that performs well under the theoretical assumptions. However, it could also well be that an existing solver implicitly takes advantage of a structure, which is often claimed for solvers that build on Sat-solving. In this paper, we consider finding one solution to instances of answer set programming (ASP), which is a logic-based declarative modeling and solving framework. Solutions for ASP instances are so-called answer sets. Interestingly, the problem of deciding whether an instance has an answer set is already located on the second level of the polynomial hierarchy. An ASP solver that employs treewidth as parameter and runs dynamic programming on tree decompositions is DynASP2. Empirical experiments show that this solver is fast on instances of small treewidth and can outperform modern ASP when one counts answer sets. It remains open, whether one can improve the solver such that it also finds one answer set fast and shows competitive behavior to modern ASP solvers on instances of low treewidth. Unfortunately, theoretical models of modern ASP solvers already indicate that these solvers can solve instances of low treewidth fast, since they are based on Sat-solving algorithms. In this paper, we improve DynASP2 and construct the solver DynASP2.5, which uses a different approach. The new solver shows competitive behavior to state-of-the-art ASP solvers even for finding just one solution. We present empirical experiments where one can see that our new implementation solves ASP instances, which encode the Steiner tree problem on graphs with low treewidth, fast. Our implementation is based on a novel approach that we call multi-pass dynamic programming (M-DPSINC). In the paper, we describe the underlying concepts of our implementation (DynASP2.5) and we argue why the techniques still yield correct algorithms.

Fast Volume Seam Carving With Multipass Dynamic Programming

In volume seam carving, i.e., seam carving for 3D cost volume, an optimal seam surface can be derived by graph cuts, resulting from sophisticated graph construction. To date, the graph-cut algorithm is the only solution for volume seam carving. However, it is not suitable for practical use because it incurs a heavy computational load. We propose a multipass dynamic programming (DP)-based approach for volume seam carving, which reduces computation time and memory consumption while maintaining a similar image quality as that of graph cuts. Our multipass DP scheme is achieved by conducting DP in two directions to accumulate the cost in a 3D volume and then tracing back to find the best seam. In our multipass DP, a suboptimal seam surface is created instead of a global optimal one, and it has been experimentally confirmed by more than 198 crowdsourced workers that such suboptimal seams are good enough for image processing. The proposed scheme offers two options: a continuous method that ensures the connectivity of seam surfaces and a discontinuous method that ensures the connectivity in only one direction. We applied the proposed volume seam carving method based on multipass DP to conventional video retargeting and tone mapping. These two applications are completely different; however, the volume seam carving method can be applied similarly by changing the axes of the cost volume. Even though the results obtained using our methods were similar to those obtained by graph cuts, our computation time was approximately 90 times faster that of graph cuts and the memory usage was eight times smaller than that of graph cuts. We also extend the idea of tone mapping to the contrast enhancement method based on volume seam carving.

Determination of edge correspondence using color codes for one-shot shape acquisition

A robust method for measuring 3D shapes is proposed, in which only one stripe pattern image is required. To determine edge correspondence, we match color codes instead of edge codes because the former are more stable and immune to the standard deviation of the Gaussian filter in edge detection and width of the color band. The color code is identified by K-means. This method exhibits huge advantages in adaptability and automation over thresholding techniques. The proposed decoding method is compared with two well-known algorithms, dynamic programming and multi-pass dynamic programming. Using ground truth, we evaluate the performance of the methods in measuring three different objects. Quantitative and qualitative comparisons are shown in the experiments, and results affirm that our method is effective and robust.

Operating Schedule of Battery Energy Storage System in a Time-of-Use Rate Industrial User With Wind Turbine Generators: A Multipass Iteration Particle Swarm Optimization Approach

This paper presents a new algorithm for the solution of nonlinear optimal scheduling problems. This algorithm is called ldquomultipass iteration particle swarm optimizationrdquo (MIPSO). A new index called ldquoiteration bestrdquo is incorporated into ldquoparticle swarm optimizationrdquo (PSO) to improve solution quality. The concept of multipass dynamic programming is applied to further modify the PSO to improve computation efficiency. The MIPSO algorithm is used to solve the optimal operating schedule of a battery energy storage system (BESS) for an industrial time-of-use (TOU) rate user with wind turbine generators (WTGs). The effects of wind speed uncertainty and load are considered in this paper, and the resulting optimal operating schedule of the BESS reaches the minimum electricity charge of TOU rates users with WTGs. The feasibility of the new algorithm is demonstrated by a numerical example, and MIPSO solution quality and computation efficiency are compared to those of other algorithms.

Short term hydroelectric power system scheduling with wind turbine generators using the multi-pass iteration particle swarm optimization approach

This paper uses multi-pass iteration particle swarm optimization (MIPSO) to solve short term hydroelectric generation scheduling of a power system with wind turbine generators. MIPSO is a new algorithm for solving nonlinear optimal scheduling problems. A new index called iteration best (IB) is incorporated into particle swarm optimization (PSO) to improve solution quality. The concept of multi-pass dynamic programming is applied to modify PSO further and improve computation efficiency. The feasible operational regions of the hydro units and pumped storage plants over the whole scheduling time range must be determined before applying MIPSO to the problem. Wind turbine power generation then shaves the power system load curves. Next, MIPSO calculates hydroelectric generation scheduling. It begins with a coarse time stage and searching space and refines the time interval between two time stages and the search spacing pass by pass (iteration). With the cooperation of agents called particles, the near optimal solution of the scheduling problem can be effectively reached. The effects of wind speed uncertainty were also considered in this paper. The feasibility of the new algorithm is demonstrated by a numerical example, and MIPSO solution quality and computation efficiency are compared to those of other algorithms.

Economic dispatch and optimal sizing of battery energy storage systems in utility load-leveling operations

Battery energy storage (BES) systems show promise of savings for both the utility and the customer. An algorithm combining multi-pass dynamic programming (MPDP) with a time-shift technique has been developed for two purposes: economic dispatch of BES; and finding optimal BES power and energy capacities in a power system. Due to the daily cyclic nature of the load curve, a 168-hour load curve is decomposed into seven 24-hour subsections for easy management. Each subsection is treated independently. Decomposition can save computation time and computer memory. A time-shift technique provides better starting state values and improves the finding process of the MPDP approach. The Kansas City Power and Light system is used as an example to test this algorithm. The results obtained in this research have been compared with those from EPRI's DYNASTORE with reasonable discrepancy.

A flexible approach to short-term hydro-thermal coordination. II. Dual problem solution procedure

The dual problem formulation is the crucial point in all Lagrangian relaxation based hydro-thermal generation coordination approaches. Such an approach is presented in Part I of this work. In this paper, an original dual problem solution procedure is presented. The dual is divided into independent thermal and hydro subproblems. Thermal subproblems are solved using the dynamic programming method. Hydro subproblems are treated by employing the special approximation in the state-space within the multi-pass dynamic programming method. Particular attention is paid to hydraulically coupled reservoirs. The special structure of these hydro subproblems is used and the successive approximation is applied to make the dynamic programming method more effective. Simulations performed on a realistic power system are presented to illustrate the efficiency of the proposed approach and the sensitivity of the dual problem solution regarding values of Lagrangian multipliers.

Optimal battery energy storage system (BESS) charge scheduling with dynamic programming

A dynamic programming algorithm for the optimal charge/discharge scheduling of BESS energy storage is presented. It ensures the minimisation of the electricity bill for a given battery capacity, while reducing stress on the battery and prolonging battery life. Optimal scheduling of the battery charge state is in itself unique; the methods of multipass dynamic programming are used to accomplish this. Maximum payoff for load redistribution and peak load shaving is determined while accounting for charging rate, battery voltage fluctuation and internal losses as a function of charge state. The optimal charging curve is significantly different from the curve conventionally published for BESS.

Air conditioner direct load control by multi-pass dynamic programming

The dispatch of air conditioner direct load control (DLC) using multi-pass dynamic programming (MPDP) methods is presented. The objective of this work is to schedule the control of air conditioner load by MPDP methods such that the peak load reduction and production cost saving have optimum results for the whole study period. The algorithm can quickly converge to an optimal schedule. To demonstrate the effectiveness of this approach, results of a sample study on the Taiwan Power Company power system are described in this paper.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Determination of optimal contract capacities and optimal sizes of battery energy storage systems for time-of-use rates industrial customers

This paper sets up a formulation to determine the optimal contract capacities and optimal sizes of battery energy storage systems for time-of-use rate customers. The advanced multi-pass dynamic programming and expert knowledge base rules are then applied to solve this problem. Two industrial customers of the Taiwan Power Company System are used as examples to test this algorithm. Results show that the optimal sizes of battery energy storage systems and the optimal contract capacities of customers during the life cycle of battery energy storage systems can be achieved by this algorithm; therefore the maximum economic benefits of battery energy storage systems for time-of-use rate customers can be estimated. >

Effect of the battery energy storage system on the time-of-use rates industrial customers

The paper develops a new algorithm known as advanced multi-pass dynamic programming (AMPDP), and it applies this algorithm to the solution of the optimal operation schedule of the battery energy storage (BES) system of time-of-use rates industrial customers. A suitable BES model is also presented. Two industrial customers with one year of recorded load curves are used as examples to test this algorithm. The results show that this algorithm can quickly converge to the optimal operation schedule while meeting all constraints. Therefore, the effect of BES on the time-of-use rates industrial customers can be studied.

Unit commitment and hydrothermal generation scheduling by multi‐pass dynamic programming

Abstract This paper applies a very efficient new technique, multi‐pass dynamic programming (MPDP) combined with successive approximations, to solve the weekly thermal unit commitment and hydrothermal generation scheduling problem. Conceptually, dynamic programming is suited for solving this problem, but the long computing time and the large storage memory required become unacceptable for large power systems and long scheduling periods. The MPDP technique can overcome these difficulties. Furthermore, the unit start‐up cost and pumped storage plants are considered in the hydrothermal coordination instead of only the production cost as in the previous application. The algorithm is tested on Taipower system with forty thermal units, seven conventional hydro units and one pumped storage plant. The results show that this method is suitable for practical systems.

The effect of pumped storage and battery energy storage systems on hydrothermal generation coordination

A simulated battery energy storage (BES) system is considered for integration into Taiwan Power Company System to study the economic benefits of the BES. The system had a pumped storage power plant with four units. The authors applied multipass dynamic programming to the solution of the short term hydrothermal coordination problem considering pumped storage and battery energy storage systems. The algorithm can quickly converge to an optimal generation schedule while achieving the minimum production cost of power systems. Substantial savings of memory and CPU time were realized by using this efficient algorithm. The load, committed units, and available water usage data from 9:00 PM June 17, 1988 to 9:00 PM June 24 were used to test this algorithm. Results showed that within 20 minutes on a PC/386 this algorithm could find the optimal generation schedule of all the units and the switching time of the BES while satisfying all the constraints.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Short term hydrothermal coordination using multi-pass dynamic programming

A technique that combines multipass dynamic programming (MPDP) technique with successive approximations to solve the daily hydrothermal coordination problem is presented. The long computation time and the large storage memory requirement are reduced. Due to the characteristics of hydrothermal coordination, the resulting load-following capability is much better than that achieved by applying MPDP to area automatic generation control. The generation can follow any shape load curve instead of only constant loads and ramps as in previous applications. >

Area automatic generation control by multi-pass dynamic programming

Current research in Automatic Generation Control emphasizes coordination of the regulation and the economic dispatch functions into a single systems problem. A dynamic optimal control problem formulation has previously been suggested. In this paper optimal trajectories are found for up to five maneuverable generators, using a new multi-pass dynamic programming method to make such solutions feasible. Dynamic valve point loading and singular solutions are considered. Computer studies have applied the method to several examples, including sudden changes in area load, and supplying the morning rise in area load.