Discrete‐time sector based hands‐off control for nonlinear system

This article presents a hands‐off control design for discrete‐time nonlinear system with a special type of nonlinear sector termed as “discrete‐time sector.” The design method to define the boundary of a discrete‐time sector is done with control‐Lyapunov function. The generalization of nonlinear system is viewed in the perspective of a comparison function. By means of a proposed sector, a switching control is designed such that no control action is experienced inside the sector thus, saving unnecessary control efforts. However, to study the robustness for discrete‐time system, a hands‐off control is modified to ensure the monotonic decrease in the energy of the system. Finally, the proposed approach is verified with the simulation results.     

Probabilistic tree-based representation for solving minimum cost integer flow problems with nonlinear non-convex cost functions

The minimum cost flow problem (MCFP) is the most generic variation of the network flow problem which aims to transfer a commodity throughout the network to satisfy demands. The problem size (in terms of the number of nodes and arcs) and the shape of the cost function are the most critical factors when considering MCFPs. Existing mathematical programming techniques often assume the cost functions to be linear or convex. Unfortunately, the linearity and convexity assumptions are too restrictive for modelling many real-world scenarios. In addition, many real-world MCFPs are large-scale, with networks having a large number of nodes and arcs. In this paper, we propose a probabilistic tree-based genetic algorithm (PTbGA) for solving large-scale minimum cost integer flow problems with nonlinear non-convex cost functions. We first compare this probabilistic tree-based representation scheme with the priority-based representation scheme, which is the most commonly-used representation for solving MCFPs. We then compare the performance of PTbGA with that of the priority-based genetic algorithm (PrGA), and two state-of-the-art mathematical solvers on a set of MCFP instances. Our experimental results demonstrate the superiority and efficiency of PTbGA in dealing with large-sized MCFPs, as compared to the PrGA method and the mathematical solvers.     

某尾矿库调洪计算

调洪计算在尾矿库设计和运行管理中都是非常重要的，水量平衡是常用计算方法，涉及较多的插值计算与试算。为了提高计算效率和计算质量，在利用Excel强大数据处理功能的同时，采用VBA编程方法实现计算过程自动化。降低了人工插值和试算对计算结果的影响，提高了工作效率。计算过程清晰，通用性强。     

Complexity and performance of an Augmented Lagrangian algorithm

Algencan is a well established safeguarded Augmented Lagrangian algorithm introduced in [R. Andreani, E. G. Birgin, J. M. Martínez, and M. L. Schuverdt, On Augmented Lagrangian methods with general lower-level constraints, SIAM J. Optim. 18 (2008), pp. 1286–1309]. Complexity results that report its worst-case behaviour in terms of iterations and evaluations of functions and derivatives that are necessary to obtain suitable stopping criteria are presented in this work. In addition, its computational performance considering all problems from the CUTEst collection is presented, which shows that it is a useful tool for solving large-scale constrained optimization problems.     

p-Median and p-dispersion problems: A bi-criteria analysis

Given a collection of n locations and a symmetric measure of distance (difference) between each pair of locations, we seek to identify (select) a subset of p locations so as to achieve two distinct objectives. The first objective is to use the selected locations as centers (medians) of p groups that would partition the entire collection and minimize the total distance between the locations and their respective group medians. The second objective is to maximize the minimum distance (diversity) among the selected locations themselves. We study this problem as a multi-objective optimization problem and propose an iterative algorithm to obtain its non-dominated frontier. At each iteration we construct and solve a 0–1 integer programming problem. Through a computational experiment we show that this algorithm is computationally effective for small to medium size instances of the problem. We also propose a Lagrangian heuristic algorithm for solving larger instances of this problem.     

Two stage stochastic bilevel programming model of a pre-established timberlands supply chain with biorefinery investment interests

This work studies the supply allocation problem, using a Stackelberg game, for an established timberlands supply chain with an additional decision of new biorefinery investments. In a timberlands system, harvester and manufacturer decision makers have separate objectives to maximize their respective profits. This interaction is represented with a turn based Stackelberg game. The harvesters decide first on the quantity harvested, and the manufacturers decide on how much to utilize. This game is modeled with a bilevel mathematical program. The novel feature of this paper's bilevel formulation is the inclusion of parametric uncertainty in a two stage model. The first stage problem involves logistical decisions around biorefinery investments, such as location and capacity, while the second stage problem involves a bilevel timberlands model with parameter uncertainty. Studying this problem formulation revealed interesting insights for solving multiperiod problems with bilevel stages as well as the decision maker's behavior for the timberlands model.     

Optimal scheduling of single stage batch plants with direct heat integration

This paper addresses the multi-objective optimization problem arising in the operation of heat integrated batch plants, where makespan and utility consumption are the two conflicting objectives. A new continuous-time MILP formulation with general precedence variables is proposed to simultaneously handle decisions related to timing, product sequencing, heat exchanger matches (selected from a two-stage superstructure) and their heat loads. It features a complex set of timing constraints to synchronize heating and cooling tasks, derived from Generalized Disjunctive Programming. Through the solution of an industrial case study from a vegetable oil refinery, we show that major savings in utilities can be achieved while generating the set of Pareto optimal solutions through the ɛ-constraint method.     

Programming assistance tools to support the learning of IT programming in South African secondary schools

Novice programmers struggle to understand introductory programming concepts and this difficulty, associated with learning to program, contributes mainly to the lack of interest in the field of Computer Science at tertiary level. Programming assistance tools have been used to assist novice programmers extensively at education institutions. A programming assistance tool (PAT) is a software program that can be used by novice programmers to learn how to program and/or improve their understanding of programming concepts.This research proposes that novice programmers, specifically Information Technology (IT) scholars in South African secondary schools, could be supported by PATs. The main objective of this research was to determine whether the use of a PAT impacted IT scholars' understanding of programming concepts and their motivation towards programming in general. Criteria for the selection of PATs were derived from the programming difficulties identified in literature and from surveys to IT teachers and scholars. The selection criteria were grouped into programming knowledge and programming skills categories. Existing PATs were evaluated using the selection criteria and three PATs, namely, RoboMind, Scratch and B#, were selected for evaluation in this research study. A convenience sample of schools participated in the study. The three PATs provided different approaches while being able to support the Delphi programming language used in schools that participated in the study.The findings of this research indicated that, although scholars perceived the PATs to be useful in the explanation of certain of the programming concepts, there was no conclusive evidence that IT scholars who used a PAT had a significantly better understanding of programming concepts and motivation towards programming than scholars who did not use a PAT. Participant feedback was used to identify the strengths and shortcomings of the three PATs and to provide recommendations for the development of future PATs specifically designed to support IT scholars.     

Impulse controls and uncertainty in economics: Method and application

We develop a stochastic optimal control framework to address an important class of economic problems where there are discontinuities and a decision maker is able to undertake impulse controls in response to unexpected disturbances. Our contribution is two fold: (1) to develop a linear programming algorithm that produces a consistent approximation of the maximum value and optimal policy functions in the context of stochastic impulse controls; and (2) to illustrate the economic benefits of impulse controls optimized, using our framework, and calibrated to the population dynamics of a marine fishery. We contend that the framework has wide applicability and offers the possibility of higher economic pay-off for a wide-range of policy problems in the presence of discontinuities and adverse shocks.     

Integer programming methods for large-scale practical classroom assignment problems

In this paper we present an integer programming method for solving the Classroom Assignment Problem in University Course Timetabling. We introduce a novel formulation of the problem which generalises existing models and maintains tractability even for large instances. The model is validated through computational results based on our experiences at the University of Auckland, and on instances from the 2007 International Timetabling Competition. We also expand upon existing results into the computational difficulty of room assignment problems.