Secondary log breakdown optimization with dynamic programming

The weighted m -d matching and m -set packing problems (m ≥ 3) are usually solved through approximation algorithms. In this paper, we define the parameterized versions of these problems and study their algorithms. For the weighted m -set packing problem, we develop a parameterized algorithm of running time O(12.8 mk n O(1)), which is based on the recently improved color-coding technology and dynamic programming. By refining the techniques, we also develop a more efficient parameterized algorithm of running time O(12.8(m − 1)k n O(1)) for the weighted m -d matching problem, which is a restricted version of the weighted m -set packing problem.

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. >

In this paper we propose an algorithm for the constrained two-dimensional cutting stock problem (TDC) in which a single stock sheet has to be cut into a set of small pieces, while maximizing the value of the pieces cut. The TDC problem is NP-hard in the strong sense and finds many practical applications in the cutting and packing area. The proposed algorithm is a hybrid approach in which a depth-first search using hill-climbing strategies and dynamic programming techniques are combined. The algorithm starts with an initial (feasible) lower bound computed by solving a series of single bounded knapsack problems. In order to enhance the first-level lower bound, we introduce an incremental procedure which is used within a top-down branch-and-bound procedure. We also propose some hill-climbing strategies in order to produce a good trade-off between the computational time and the solution quality. Extensive computational testing on problem instances from the literature shows the effectiveness of the proposed approach. The obtained results are compared to the results published by Alvarez-Valdes et al. (2002).

Multi-stage planning of clean resources and energy storage assets with hybrid uncertainty modeling for low-carbon resilient distribution systems

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.

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

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).

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.

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.

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.

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.

This work is concerned with stochastic optimal control for a running maximum cost. A direct approach based on dynamic programming techniques is studied leading to the characterization of the value function as the unique viscosity solution of a second order Hamilton–Jacobi–Bellman (HJB) equation with an oblique derivative boundary condition. A general numerical scheme is proposed and a convergence result is provided. Error estimates are obtained for the semi-Lagrangian scheme. These results can apply to the case of lookback options in finance. Moreover, optimal control problems with maximum cost arise in the characterization of the reachable sets for a system of controlled stochastic differential equations. Some numerical simulations on examples of reachable analysis are included to illustrate our approach.