A nonlinear minimization approach to multiobjective and structured controls for discrete‐time systems

In this paper, a nonlinear minimization approach is proposed for multiobjective and structured controls for discrete‐time systems. The problem of finding multiobjective and structured controls for discrete‐time systems is represented as a quadratic matrix inequality problem. It is shown that the problem is reduced to a nonlinear minimization problem that has a concave objective function and linear matrix inequality constraints. An algorithm for the nonlinear minimization problem is proposed, which is easily implemented with existing semidefinite programming algorithms. The validity of the proposed algorithm is illustrated by comparisons with existing methods. In addition, applications of this work are demonstrated via numerical examples. Copyright © 2004 John Wiley & Sons, Ltd.     

A practical implementation of stochastic programming: an application to the evaluation of option contracts in supply chains

Stochastic programming is a powerful analytical method in order to solve sequential decision-making problems under uncertainty. We describe an approach to build such stochastic linear programming models. We show that algebraic modeling languages make it possible for non-specialist users to formulate complex problems and have solved them by powerful commercial solvers. We illustrate our point in the case of option contracts in supply chain management and propose a numerical analysis of performance. We propose easy-to-implement discretization procedures of the stochastic process in order to limit the size of the event tree in a multi-period environment.     

CP methods of higher order for Sturm-Liouville and Schrödinger equations

The algorithm upon which the code SLCPM12, described in Computer Physics Communications 118 (1999) 259-277, is based, is extended to higher order. The implementation of the original algorithm, which was of order {12,10} (meaning order 12 at low energies and order 10 at high energies), was more efficient than the well-established codes SL02F, SLEDGE and SLEIGN. In the new algorithm the orders {14,12}, {16,14} and {18,16} are introduced. Besides regular Sturm-Liouville and one-dimensional Schrödinger problems also radial Schrödinger equations are considered with potentials of the form V(r)=S(r)/r+R(r), where S(r) and R(r) are well behaved functions which tend to some (not necessarily equal) constants when r→0 and r→∞. Numerical illustrations are given showing the accuracy, the robustness and the CPU-time gain of the proposed algorithms.     

Further study of minimizing total tardiness for the worker assignment scheduling problem in the identical parallel-machine models

Minimizing total tardiness in the model of an identical parallel-machine with nonpreemptive jobs of the worker assignment scheduling problem is further studied in this paper. More complicated simulation processes are established for this purpose. The specific worker assignment scheduling problem is solved in two parts of job scheduling and worker assignment. The S_PT, E_DD, S_lack (SES) heuristic is used for the job scheduling part while the largest marginal contribution (LMC) procedure is used to for the worker assignment part and then minimizes the total tardiness. From the new simulations conducted, the heuristics developed have again shown very convincing results quite efficiently.     

Nonlinear programming approaches for an inverse problem in quasibrittle fracture

Characterization of the parameters describing the cohesive crack model is an important and difficult problem. Based on the availability of load-deflection data, obtained from such standard tests as the three-point bending and wedge splitting experiments, we formulate the required parameter identification as a special type of inverse problem. The formulation is in the form of a constrained optimization problem known as a mathematical program with equilibrium constraints characterized, in the present instance, by complementarity conditions involving the orthogonality of two sign-constrained vectors. Due to the difficulty of solving such a mathematical program directly, we investigate a number of numerical algorithms that are all based on solving a series of standard nonlinear programming problems. Computational results, using actual experimental data, are presented to compare the various schemes proposed.     

ROBUST CONTROL OF GAS TUNGSTEN ARC WELDING SYSTEM

The robust control law for gas tungsten arc welding dynamic process, which is a typical sampled-data system and full of uncertainties, is presented. By using the Lyapunov second method, the robust control and robust optimal control for a class of sampled-data systems whose underlying continuous-time systems are subjected to structured uncertainties are discussed in time-domain. As a result, some sufficient conditions of robust stability and the corresponding robust control laws are derived. All these results are designed by solving a class of linear matrix inequalities (LMIs) and a class of dynamic optimization problem with LMIs constraints respectively. An example adapted under some experimental conditions in the dynamic process of gas tungsten arc welding system in which the controlled variable is the backside width of weld pool and controlling variable pulse duty ratio, is worked out to illustrate the proposed results, it is shown that the sampling period is the crucial design parameter.     

A heuristic algorithm for the just-in-time single machine scheduling problem with setups: a comparison with simulated annealing

This paper addresses the single machine early/tardy problem with unrestricted common due date and sequence-dependent setup times. Two algorithms are introduced to reach near-optimum solutions: the SAPT, a heuristic tailored for the problem, and a simulated annealing (SA) algorithm. It will be shown that SA provides solutions with slightly better quality; however, SAPT requires much less computational time. SAPT-SA is a hybrid heuristic that combines both approaches to obtain high quality solutions with low computational cost. Solutions provided by the three algorithms were compared to optimal solutions for problems with up to 25 jobs and to each other for larger problems.     

随机森林算法在空气质量评价中的应用

为了更好地反映空气质量的变化趋势,加强大气污染的防治,开展城市环境空气质量评价的意义重大。有效的空气质量评价方法可以提高评价体系的科学性,督促各个城市环保工作的稳步推进,从而对大气污染治理做出贡献,而空气质量评价算法是空气质量评价的核心。根据影响空气质量的几个基本要素:二氧化硫年平均浓度、二氧化氮年平均浓度、可吸入颗粒物年平均浓度等,创新性地采用随机森林算法对我国113个重点城市的空气质量进行了评价。通过评价指标将模型的评价结果与其他分类算法进行比较,发现随机森林分类模型,无论是在二分类还是多分类中都能够对各个城市地区的空气质量作出较为准确的评估,并进一步得出空气中PM10、PM2.5和O3的浓度是影响各大城市空气质量好坏的主要因素。     

Solving the location-routing problem with simultaneous pickup and delivery by simulated annealing

The study concerns the location-routing problem with simultaneous pickup and delivery (LRPSPD) in which the pickup and delivery take place at the same time for each customer. The goal is to determine the facility locations and vehicle routes in order to minimise the total system cost as a sum of facility opening cost, vehicle fixed cost and vehicle travel cost. A simulated annealing (SA) heuristic is proposed for the problem and extensive computational experiments are conducted. The results show that the proposed SA effectively solves LRPSPD and outperforms existing exact approaches in terms of solution quality.     

Developing a dynamic neighborhood structure for an adaptive hybrid simulated annealing – tabu search algorithm to solve the symmetrical traveling salesman problem

This paper applies a hybrid simulated annealing – tabu search algorithm to solve the Traveling Salesman Problem (TSP). Fully considering the characteristics of the hybrid algorithm, we develop a dynamic neighborhood structure for the hybrid algorithm to improve search efficiency by reducing the randomness of the conventional 2-opt neighborhood. A circle-directed mutation is developed to achieve this dynamic neighborhood structure. Furthermore, we propose adaptive parameters that can be automatically adjusted by the algorithm based on context specific examples. This negates the need to frequently readjust algorithm parameters. We employ benchmarks obtained from TSPLIB (a library of sample instances for the TSP) to test our algorithm, and find that the proposed algorithm can obtain satisfactory solutions within a reasonable amount of time. The experimental results demonstrate that the proposed hybrid algorithm can overcome the disadvantages of traditional simulated annealing and tabu search methods. The results also show that the dynamic neighborhood structure is more efficient and accurate than the classical 2-opt. Also, adaptive parameters are appropriate for almost all of the numerical examples tested in this paper. Finally, the experimental results are compared with those of other algorithms, to demonstrate the improved accuracy and efficiency of the proposed algorithm.