Using GPU Computing for Solving the Two-Dimensional Guillotine Cutting Problem

This research is about the development of a dynamic programming model for solving fuzzy linear programming problems. Initially, fuzzy dynamic linear programming model FDLP is developed. This research revises the established dynamic programming model for solving linear programming problems in a crisp environment. The mentioned approach is upgraded to address the problem in an uncertain environment. Dynamic programming model can either be passing forward or backward. In the proposed approach backward dynamic programming approach is adopted to address the problem. It is then followed by implementing the proposed method on the education system of Pakistan. The education system of Pakistan comprises of the Primary, Middle, Secondary, and Tertiary education stages. The problem is to maximize the efficiency of the education system while achieving the targets with minimum usage of the constrained resources. Likewise the model tries to maximize the enrollment in the Primary, Middle, Secondary and Tertiary educational categories, subject to the total available resources in a fuzzy uncertain environment. The solution proposes that the enrollment can be increased by an amount 9997130, by increasing the enrollment in the Middle and Tertiary educational categories. Thus the proposed method contributes to increase the objective function value by 30%. Moreover, the proposed solutions violate none of the constraints. In other words, the problem of resources allocation in education system is efficiently managed to increase efficiency while remaining in the available constrained resources. The motivation behind using the dynamic programming methodology is that it always possesses a numerical solution, unlike the other approaches having no solution at certain times. The proposed fuzzy model takes into account uncertainty in the linear programming modeling process and is more robust, flexible and practicable.

In the next decades, many public infrastructure assets will reach the end of their life that they were originally designed for. Replacement costs are high, and therefore increasing effort is put into lifetime-extending maintenance, including major overhauls and renovations. A key question is whether the investments in lifetime-extending maintenance justify the postponement of a full replacement. This question becomes more complicated when future life cycle cash flows are non-repeatable. Differential inflation and technological change, including multiple intervention strategies to maintain a desired functionality, cause such non-repeatability. In this case, classic replacement analysis techniques will not suffice in answering this question. Literature demonstrates that case-specific modelling with dynamic or linear programming techniques is required to find economic optimisation. However, such literature primarily addresses replacement interval optimisation of new investments within relative short time horizons, whereas the current research develops a nested dynamic programming (DP) approach for typical ageing infrastructure assets over long service life periods. The model can deal with multiple and various successive intervention strategies and addresses differential inflation and age-related cost increases. Finally, it is shown in an infrastructure case study that this DP approach leads to a better decision in comparison to the application of classical replacement techniques.

In this paper, the application of the dynamic programming approach to constrained stochastic control problems with expected value constraints is demonstrated. Specifically, two such problems are analyzed using this approach. The problems analyzed are the problem of minimizing a discounted cost infinite horizon expectation objective subject to an identically structured constraint, and the problem of minimizing a discounted cost infinite horizon minimax objective subject to a discounted expectation constraint. Using the dynamic programming approach, optimality equations, which are the chief contribution of this paper, are obtained for these problems. In particular, the dynamic programming operators for problems with expectation constraints differ significantly from those of standard dynamic programming and problems with worst-case constraints. For the discounted cost infinite horizon cases, existence and uniqueness of solutions to the dynamic programming equations are explicitly shown by using the Banach fixed point theorem to show that the corresponding dynamic programming operators are contractions. The theory developed is illustrated by numerically solving the constrained stochastic control dynamic programming equations derived for simple example problems. The example problems are based on a two-state Markov model that represents an error prone system that is to be maintained.

Sequence alignment has been widely utilized in biological computing science. To obtain the optimal alignment results many algorithms adopts dynamic programming method to achieve this goal. Smith-Waterman algorithm is the famous in the sequence alignment approach. However, such dynamic programming algorithms are computation-consuming. It is impossible to use these algorithms to compare query sequence with a sequence database such as GenBank and PDB. Recently, GPU computing has been applied in many sequence alignment algorithms to enhance the performance. In this paper, we proposed a GPU-based Smith-Waterman algorithm by combining the CPU and GPU computing capabilities to accelerate alignments on a sequence database. In the proposed algorithm, a filtration mechanism using frequency distance is used to decrease the number of compared sequences. We implemented the Smith-Waterman alignments by CUDA on the NVIDIA Tesla C2050. The experimental results show that the highest speedup ratio is about 80 to 90 times over CPU-based Smith-Waterman algorithm.

A technique called dynamic programming can be used to identify an optimal rebalancing schedule, which significantly reduces rebalancing and sub-optimality costs. Dynamic programming provides solutions to multi-stage decision processes in which the decisions made in prior periods affect the choices available in later periods. Dynamic programming provides the optimal year-by-year decision policy by working backwards from year 10. The results of the test of the relative efficacy of dynamic programming and the MvD heuristic with data on domestic equities, domestic fixed income, non-US equities, non-US fixed income, and emerging market equities, show that the MvD heuristic performs quite well compared to the dynamic programming solution for the two-asset case and substantially better than other heuristics. The increase in the number of assets reduces the advantage of dynamic programming over the MvD heuristic and is reversed at the level of five assets. Dynamic programming cannot be applied beyond five assets, but the MvD heuristic can be extended up to 100 assets. The MvD heuristic reduces total costs relative to all of the other heuristics by substantial amounts. The performance of the MvD heuristic improves relative to the dynamic programming solution as more assets are added but this improvement reflects a growing reliance on an approximation for the dynamic programming approach.

This study formulates and solves an advertising pulsation problem for a monopolistic firm using dynamic programming (DP). The firm aims at maximising profit through an optimal allocation of the advertising budget in terms of rectangular pulses over a finite planning horizon. Aggregate sales response to the advertising effort is assumed to be governed by a modified version of the Vidale–Wolfe model in continuous time proposed by Little. Using a numerical example in which a planning horizon of one year is divided into one, two through ten equal time periods, computing routines are developed to solve 150 DP problems. Computational results show among other findings that the performance yielded by the DP policy dominates the uniform advertising policy (constant spending) for a concave advertising response function and the advertising pulsing policy (turning advertising on and off) for a linear or convex response function.

This study introduces a practical approach to implement real-time signal processing algorithms for general surveillance radar based on NVIDIA graphical processing units (GPUs). The pulse compression algorithms are implemented using compute unified device architecture (CUDA) libraries such as CUDA basic linear algebra subroutines and CUDA fast Fourier transform library, which are adopted from open source libraries and optimized for the NVIDIA GPUs. For more advanced, adaptive processing algorithms such as adaptive pulse compression, customized kernel optimization is needed and investigated. A statistical optimization approach is developed for this purpose without needing much knowledge of the physical configurations of the kernels. It was found that the kernel optimization approach can significantly improve the performance. Benchmark performance is compared with the CPU performance in terms of processing accelerations. The proposed implementation framework can be used in various radar systems including ground-based phased array radar, airborne sense and avoid radar, and aerospace surveillance radar.

We study the approximate dynamic programming approach to revenue management in the context of attended home delivery. We draw on results from dynamic programming theory for Markov decision problems, convex optimisation and discrete convex analysis to show that the underlying dynamic programming operator has a unique fixed point. Moreover, we also show that - under certain assumptions - for all time steps in the dynamic program, the value function admits a continuous extension, which is a finite-valued, concave function of its state variables. This result opens the road for achieving scalable implementations of the proposed formulation, as it allows making informed choices of basis functions in an approximate dynamic programming context. We illustrate our findings using a simple numerical example and conclude with suggestions on how our results can be exploited in future work to obtain closer approximations of the value function.

The basic procedures for solving different types of dynamic programming problem were explained in Part II. This was followed in Parts III and IV by an examination of how some of the problems encountered in agriculture and natural resource industries can be solved by dynamic programming. In this final chapter some reflections are presented on the usefulness of the dynamic programming approach, the extent to which the technique has been applied in agriculture and natural resource industries to date, and the scope for its use in the future.

Ship voyage optimization for safe and energy-efficient navigation: A dynamic programming approach

Dynamic programming is a mathematical technique for optimizing decisions in stages by breaking a problem inton stages mthat solve recursively. It display the quantity and arrangement of invemtory to maintain production and ,businness revenue efficiently when used in inventory control management. This production planning uses a dynamic programming method based on the results of advanced calculations start from stage 1 and move forward to stage 12. the dynamic programming approach in this writing is deterministic because the pattern of the number of requests for bread is known absolutely. Decisions involving a problem are simplified little by little rather than directly. This research uses linear regression with a mathematical formula that is: followed by the defect percetage formula to forecast demand for the next 12 months and apply a dynamic program to achieve the minimum total quantity.

This article presents a novel dynamic programming approach to determine the robust controllability of Boolean control networks (BCNs) subject to stochastic disturbances. By applying Bellman's optimality principle, we derive the recurrence relation for computing the optimal time matrix, a crucial concept characterizing robust reachability between two arbitrary states. We develop a finite-termination dynamic programming algorithm to calculate the optimal time matrix exactly and efficiently, with a rigorously certified iteration count. Sufficient and necessary conditions for robust controllability are then established based on the optimal time matrix. Furthermore, for any pair of reachable states, we construct time-optimal state feedback control laws to steer the system from the initial state to the target state, regardless of disturbances. Finally, extensive numerical experiments with biological networks validate the effectiveness of the proposed approach, showing significant improvements in computational efficiency. Additionally, we introduce a Q-learning-based algorithm and compare its performance, highlighting the advantages of our dynamic programming approach in terms of both efficiency and solution quality.

Many Cyber-Physical Systems (CPSs) demonstrate high-dimensional environmental uncertainties that modulate the physical system dynamics and complicate the computational decision-making tasks. As an example, strategic air traffic flow management (ATFM) aims to resolve air traffic congestion through managing traffic flows at a long look-ahead time. The convective weather, a dominant factor of traffic congestion, is very uncertain and significantly complicates the decision-making process. Other uncertainties such as traffic demands further expand the uncertainty space and complicate the design of optimal control solutions that are robust to uncertainties. In this paper, we formulate the strategic ATFM as a stochastic optimal control problem, and use scalable sampling based dynamic programming and Q-learning approaches to address high-dimensional uncertainties. Simulation studies demonstrate the effectiveness of these approaches. These approaches generally apply to CPSs that operate under high-dimensional environmental uncertainties.

Parallel dynamic programming and automata theory

Optimal Consumption Plans—A Dynamic Programming Approach