In this paper, we propose a hardware implementable two-level parallel computing algorithm for general minimum-time control. We first discretize and transform the minimum-time control problem for a continuous-time system into a parameter optimization problem which is large dimensional and nonseparable. Then, the proposed two-level algorithm decomposes this parameter optimization problem into a master-slave problem. The master problem can be easily solved by a one-dimensional gradient method, and the slave problem will be solved by the proposed parallel computing method which combines recursive quadratic programming with the dual method. Furthermore, we have proved the convergence of this iterative two-level parallel computing algorithm under some conditions. Based on the VLSI array processor technology, we present a dedicated hardware computing architecture to realize this algorithm. The corresponding time complexity is also analyzed. Finally, several practical problems including the minimum-time orbit transfer problem and the minimum-time robot control problem have been simulated. The results show that the algorithm is well-suited for real-time application of minimumtime control.
In this paper, we propose a modified parallel block scaled gradient method for solving block additive unconstrained optimization problems of large distributed systems. Our method makes two major modifications to the typical parallel block scaled gradient method: First, we include a pre‐processing step which reduces the computational time; second, we propose a decentralized Armijo‐type step‐size rule. This rule circumvents the difficulty of determining a step‐size in a distributed computing environment and enables the proposed parallel algorithm to execute in a distributed computer network with a limited amount of data transfer.
We have applied our method to the weighted‐least‐square problems of power system state estimation and demonstrated the convergence of our method by testing numerous examples on a PC network. The speedup ratio of the distributed version of our method tends to increase proportionally with the number of subsystems (or computers).
Probabilistic constrained simulation optimization problems (PCSOP) are concerned with allocating limited resources to achieve a stochastic objective function subject to a probabilistic inequality constraint. The PCSOP are NP-hard problems whose goal is to find optimal solutions using simulation in a large search space. An efficient “Ordinal Optimization (OO)” theory has been utilized to solve NP-hard problems for determining an outstanding solution in a reasonable amount of time. OO theory to solve NP-hard problems is an effective method, but the probabilistic inequality constraint will greatly decrease the effectiveness and efficiency. In this work, a method that embeds ordinal optimization (OO) into tree–seed algorithm (TSA) (OOTSA) is firstly proposed for solving the PCSOP. The OOTSA method consists of three modules: surrogate model, exploration and exploitation. Then, the proposed OOTSA approach is applied to minimize the expected lead time of semi-finished products in a pull-type production system, which is formulated as a PCSOP that comprises a well-defined search space. Test results obtained by the OOTSA are compared with the results obtained by three heuristic approaches. Simulation results demonstrate that the OOTSA method yields an outstanding solution of much higher computing efficiency with much higher quality than three heuristic approaches.
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