Dynamic Programming and Hill-Climbing Techniques for Constrained Two-Dimensional Cutting Stock Problems

An examination is made of the dynamic programming technique implemented on a distributed-memory multiprocessor system. The matrix chain product algorithm is investigated as an example problem. A method for parallelizing the dynamic programming technique for solving the matrix chain product problem is presented and load-balancing considerations are examined. The sequential dynamic programming technique is a fine grain algorithm and considered by many researchers to be too fine grain to execute effectively on a hypercube. The parallel algorithm yielded modest speedups for fixed-size problems. Scaled problems promise even better speedups. Results show that respectable performance for the dynamic programming algorithmic technique can be achieved on a hypercube. >

A hybrid threshold curve model for optimal yield management: neural networks and dynamic programming

The aim of this study is to optimize the decision-making in the production process of a company through Monte Carlo simulation and dynamic programming methods. First, the Sequential Likelihood Ratio Test (SPRT) is designed to improve the efficiency of sampling and inspection of supplied spare parts and the performance of the method is evaluated through Monte Carlo simulation. Second, a profit model is defined and dynamic programming is applied to solve the multi-stage decision-making problem, which specifies whether or not to inspect spare parts and finished products at each decision point and how to deal with non-conforming finished products. Then, the minimum cost of each stage is calculated by exhaustively enumerating different decision combinations to obtain the maximum profit and the optimal decision combination. Finally, the objective function of maximizing profit is constructed for the increased number of spare parts and process complexity, and the dynamic programming technique is applied again to recursively calculate the optimal decision and potential revenue from the first stage, so that the profit model can be updated during the dynamic decision-making process.

Dynamic programming techniques have proven much more flexible than calculus of variations and other techniques in performing redundancy resolution through global optimization of performance indices. When the state and input spaces are discrete, and the time horizon is finite, they can easily accommodate generic constraints and objective functions and find Pareto-optimal sets. Several implementations have been proposed in previous works, but either they do not ensure the achievement of the globally optimal solution, or they have not been demonstrated on robots of practical relevance. In this communication, recent advances in dynamic programming redundancy resolution, so far only demonstrated on simple planar robots, are extended to be used with generic kinematic structures. This is done by expanding the Robot Operating System (ROS) and proposing a novel architecture meeting the requirements of maintainability, re-usability, modularity and flexibility that are usually required to robotic software libraries. The proposed ROS extension integrates seamlessly with the other software components of the ROS ecosystem, so as to encourage the reuse of the available visualization and analysis tools. The new architecture is demonstrated on a 7-DOF robot with a six-dimensional task, and topological analyses are carried out on both its state space and resulting joint-space solution.

The standard model of Markov decision processes implicitly relies on a preference structure induced by the existence of scalar and additive costs and the use of a certain criterion for policy evaluation (total, discounted, average...). This preference structure imposes strict hypotheses allowing the use of dynamic programming. We are interested here in Markov decision processes whose preference structure is non-classic and we give simple and sufficient properties on theses preferences for the use of methods based on dynamic programming. So these properties define a larger class of Markov decision processes solvable with dynamic programming techniques.

Dynamic programming and bicubic spline interpolation

The relationship between efficient quantum gate synthesis and control theory has been a topic of recent interest in the quantum computing literature. Motivated by this work, we describe how the dynamic programming technique from optimal control may be used in principle to determine gate complexity and for the optimal synthesis of quantum circuits. We illustrate the dynamic programming methodology using a simple example on the Lie group SU(2).

Dynamic Programming (DP) technique is an effective algorithm to find the global optimum. However when applying DP for finite state problems, if the state variables are discretized, it increases the cumulative errors and leads to suboptimal results. In this paper we develop and present a new DP algorithm that overcomes the above problem by eliminating the need to discretize the state space by the use of sets. We show that the proposed DP leads to a globally optimal solution for a discrete time system by minimizing a cost function at each time step. To show the efficacy of the proposed DP, we apply it to optimize the fuel economy of the series and parallel Hybrid Electric Vehicle (HEV) architectures and the case study of Chevrolet Volt 2012 and the Honda Civic 2012 for the series and parallel HEV’s respectively are considered. Simulations are performed over predefined drive cycles and the results of the proposed DP are compared to previous DP algorithm (DPdis). The proposed DP showed an average improvement of 2.45% and 21.29% over the DPdis algorithm for the series and the parallel HEV case respectively over the drive cycles considered. We also propose a real time control strategy (RTCS) for online implementation based on the concept of Preview Control. The RTCS proposed is applied for the series and parallel HEV’s over the drive cycles and the results obtained are discussed.

Coordinated navigation to a single perfectly known target by multiple cooperating sensor-equipped agents in a partially known static environment is investigated. Original results on the spatial distribution of the agents under an optimal policy are derived using dynamic programming and neurodynamic programming techniques. Extension of the framework to counter the curse of dimensionality via multilevel path planning is outlined. Practical implications are discussed.

In this paper, a model-free approximate dynamic programming (ADP) technique for continuous-time linear systems is proposed to solve the infinite horizon optimal regulator problems with input derivative constraints. By the fact that the input coupling matrix B is not shown in the explicit formula of the solution to the input-derivative-constrained optimal regulator problem, the assumption of the known B matrix is relaxed. And then, partially model-free ADP technique given in [13] is employed to this regulator problem in order to develop the model-free approximate dynamic programming technique. Moreover, using the inherent property of the input-derivative-constrained optimal regulator problem, we extend the proposed model-free ADP technique to the more general linear systems which include constant matching disturbances. The proposed technique can be considered an adaptive optimal controller since it updates the parameters in the controller in a way that the parameters converge to the optimal ones. The simulation is executed to verify the applicability of the proposed method.

Economic dispatch is considered as one of the critical advancement errand and operational choice which gives a financial condition to control framework. The principle emphasis of economic dispatch is the means by which a power system network can be arranged with the goal that we have minimum cost of electric generation to take care of the load demand, while meeting all the balance and imbalance constraints. Economic load dispatch arrangements are found by explaining the customary techniques, for example lambda iteration technique, gradient search technique, linear programming technique, dynamic programming technique and so on. Out of every single traditional technique the convergence rate of lambda iteration method is very fast and it gives accurate results and precise outcomes. This work has been made by utilizing MiPower version9 programming to distinguish the best scheduling of generator. Lambda iteration method is utilized to take care of economic dispatch issue for 6 generating unit framework with and without transmission losses.

State space relaxation for set covering problems related to bus driver scheduling

Modern GPUs (Graphics Processing Units) can be used for general purpose parallel computation. Users can develop parallel programs running on GPUs using programming architecture called CUDA (Compute Unified Device Architecture). The Matrix Chain Product Problem is an optimization problem for finding parentheses of the matrix chain that gives the minimum total number of multiplications necessary to compute the product of the matrix chain. It is well known that this problem can be solved using the dynamic programming technique in O(n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ) time using tables of size O(n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ). The main contribution of this paper is to present an efficient parallel implementation of this O(n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> )-time algorithm on the GPU. In our implementation, we have considered the architecture and programming issues of the GPU system. The experimental results show that, for a chain of 16384 matrices generated at random, our implementation in the Nvidia GeForce GTX 480 achieves a speedup factor of 40 over a conventional CPU implementation.

Log breakdown can be viewed as a two-stage process with logs sawn into slabs of wood known as flitches during the primary stage and flitches further processed during the secondary stage to produce edged (cut lengthwise) and trimmed (cut widthwise) pieces. This paper addresses the secondary problem and describes some procedures for determining the optimal cutting of flitches into graded dimensional boards. The problem is formulated as a set packing problem with the objective being to maximise total value. Extensions to the basic formulation include constraints which restrict the number of saws and which disallow waste between adjacent edged pieces. The problem is solved using dynamic programming techniques and the algorithms incorporated into a sawing simulation system. Comparisons with existing edging and trimming procedures show that substantial reductions in solution time (to as little as 1/25th of the time required for an enumerative search) can be achieved.

In this chapter we use the dynamic programming techniques as applied to the various problems and arrive at the structure of the solutions of the second order equations without solving them. The variation diminishing properties of the Green’s functin, the unimodal nature of the solutions of the Sturm- Liouville equations are derived in Sections 1 and 2. In Section 3, variational equations for the characteristic functions and characteristic values are obtained, treating one of the limits of the interval of integration as the imbedding parameter.