Sensitivity Analysis of Partially Deployed Slowdown Warning Mechanisms for Vehicle Platoons

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).

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

Optimal consumption and portfolio policies when asset prices follow a diffusion process

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).

We model the situation where the productivity of members of a group, such as a salesforce, is periodically evaluated; those whose performance is sub-par are dismissed and replaced by new members. Individual productivity is modeled as a random variable, the distribution of which is a function of an unknown parameter. This parameter varies across the members of the group and is specified by a prior distribution. In this manner, the heterogeneity in the group is explicitly accounted for. We model the situation as a parameter adaptive Bayesian stochastic control problem, and use dynamic programming techniques and the appropriate optimality equations to obtain solutions. We prove the existence of an optimal policy in the general case. Further, for the case when the sales process can be characterized by a Beta-Binomial or a Gamma-Poisson distribution, we show that the optimal policy is of the threshold type at each evaluation period, depending only on the accumulated performance up to a given period. We present a computational procedure to solve for the optimal thresholds. Results of computational experiments show that an increase in the heterogeneity of the group can lead to more stringent levels of minimal acceptable performance.

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.

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.

We consider the problem of synthesizing optimal linear feedback policies subject to arbitrary convex constraints on the feedback matrix. This is known to be a hard problem in the usual formulations (ℋ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ;ℋ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> ;LQR) and previous works have focussed on characterizing classes of structural constraints that allow efficient solution through convex optimization or dynamic programming techniques. In this paper, we propose a new control objective based on eigenvalues of the covariance matrix of trajectories of the system and show that this formulation makes the problem of computing optimal linear feedback matrices convex under arbitrary convex constraints on the feedback matrix. This allows us to solve problems in distributed control (sparsity in the feedback matrices), control with delays and variable impedance control. Although the control objective is nonstandard, we present theoretical and empirical evidence that it agrees well with standard notions of control. We numerically validate the our approach on problems arising in power systems and simple mechanical systems.

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.