Fast algorithm for the cutting angle method of global optimization

The cutting angle method for global optimization was proposed in 1999 by Andramonov et al. (Appl. Math. Lett. 12 (1999) 95). Computer implementation of the resulting algorithm indicates that running time could be improved with appropriate modifications to the underlying mathematical description. In this article, we describe the initial algorithm and introduce a new one which we prove is significantly faster at each stage. Results of numerical experiments performed on a Pentium III 750 Mhz processor are presented.

Predicting molecular structures: an application of the cutting angle method

The ability to predict molecular geometries has important applications in chemistry. Specific examples include the areas of protein space structure elucidation, the investigation of host–guest interactions, the understanding of properties of superconductors and of zeolites. This prediction of molecular geometries often depends on finding the global minimum or maximum of a function such as the potential energy. In this paper, we consider several well-known molecular conformation problems to which we apply a new method of deterministic global optimization called the cutting angle method. We demonstrate that this method is competitive with other global optimization techniques for these molecular conformation problems.

Geometry and combinatorics of the cutting angle method

Lower approximation of Lipschitz functions plays an important role in deterministic global optimization. This article examines in detail the lower piecewise linear approximation which arises in the cutting angle method. All its local minima can be explicitly enumerated, and a special data structure was designed to process them very efficiently, improving previous results by several orders of magnitude. Further, some geometrical properties of the lower approximation have been studied, and regions on which this function is linear have been identified explicitly. Connection to a special distance function and Voronoi diagrams was established. An application of these results is a black-box multivariate random number generator, based on acceptance-rejection approach.

Cutting angle method - a tool for constrained global optimization

Cutting angle method (CAM) is a deterministic global optimization technique applicable to Lipschitz functions f: Rn → R. The method builds a sequence of piecewise linear lower approximations to the objective function f. The sequence of solutions to these relaxed problems converges to the global minimum of f. This article adapts CAM to the case of linear constraints on the feasible domain. We show how the relaxed problems are modified, and how the numerical efficiency of solving these problems can be preserved. A number of numerical experiments confirms the improved numerical efficiency.

Efficient serial and parallel implementations of the cutting angle global optimisation technique

We examine efficient computer implementation of one method of deterministic global optimisation, the cutting angle method. In this method the objective function is approximated from values below the function with a piecewise linear auxiliary function. The global minimum of the objective function is approximated from the sequence of minima of this auxiliary function. Computing the minima of the auxiliary function is a combinatorial problem, and we show that it can be effectively parallelised. We discuss the improvements made to the serial implementation of the cutting angle method, and ways of distributing computations across multiple processors on parallel and cluster computers.

Where in the world is room N101? Engaging with first year education students' experiences of transition

National reports on students’ experiences in their first year of tertiary study suggest that many students, particularly those coming directly from  secondary schools, find the transition into university life particularly difficult. These reports suggest that while many students find the experience to be a challenging hurdle others feel disengaged and unconnected to academic life. Reports also note that many students enter university with the expectation that their university experience should 'fit into their lives' rather than vice-versa.

Additionally, research indicates that successful transitional experiences for undergraduate students are critical in promoting effective learning habits, positive attitudes and openness to new knowledge. Establishing positive practices in the early days of the undergraduate course can enable students to utilise these experiences and knowledge as a part of their life-long professional habits. However, in order for this to occur, connections must be made, and relationships built, between students and their new peer groups and with the wider academic community. Connections must also be made between students' prior experiences and their new knowledge.

In light of the findings of recent research and reports, Deakin University has instituted a First Year Initiative to assist students in their transitions. Alongside and complementary to this, the Faculty of Education has developed a new three year Education Studies Major program which began this year.

In this paper, we discuss the ways in which the first two units of this new educational program aim to address some of the issues that students face when making the transition into university life. We see the implementation of the first two units as a 'pilot study' and while at this stage, evaluation of these units is only beginning, here we will consider some of the pedagogical strategies, resources, organisational structures and 'grounded' experiences that are being trialled as means to help students make the connections and take the first successful steps in their journey to becoming professional educators. Ways in which these new approaches aim to build important relationships between students, with staff and, as well, help them connect their prior experiences with new knowledge, will be considered in light of the literature on first year student transitions.

A new method for locating the global optimum : application of the cutting angle method to molecular structure prediction

Many problems in chemistry depend on the ability to identify the global minimum or maximum of a function. Examples include applications in chemometrics, optimization of reaction or operating conditions, and non-linear least-squares analysis. This paper presents the results of the application of a new method of deterministic global optimization, called the cutting angle method (CAM), as applied to the prediction of molecular geometries. CAM is shown to be competitive with other global optimization techniques for several benchmark molecular conformation problem. CAM is a general method that can also be applied to other computational problems involving global minima, global maxima or finding the roots of nonlinear equations.

A scale-model room as a practical teaching experiment

A practical experiment is described which was used to help university students increase their understanding of the effect of construction methods and window design on passive solar heating and electrical heating. A number of one tenth scale model rooms were constructed by students and sited out-of-doors in the late autumn. The models were fabricated to mimic available commercial construction techniques with careful consideration being given to window size and placement for solar access. Each model had a thermostatically controlled electric heating element. The temperatures and electricity use of the models were recorded using data-loggers over a two week period. The performances of the models based on energy consumption and internal temperature were compared with each other and with predictions based upon thermal mass and R-values. Examples of questions used by students to facilitate this process are included. The effect of scaling on thermal properties was analysed using Buckingham’s p-theorem.

Room-temperature insertion of elemental tellurium into the Cspł-Br and -I bonds of α-bromo-and α-iodopinacolone

Pinacolyltellurium(IV) dihalides, (t-BuCOCH₂)₂TeX₂ (X ) Br (1b), I (1c)) and Ar(t-BuCOCH₂)TeCl₂ (Ar == 1-C₁₀H₇ (Np) (2a), 2,4,6-Me₃C₆H₂ (Mes) (3a)), are readily prepared at room temperature by the oxidative insertion of elemental tellurium into the C_sp³-Br or -I bond of the α-halopinacolone and by the reaction of ArTeCl₃ with the pinacolone t-BuCOCH₃. The bromides Np(t-BuCOCH₂)TeBr₂ (2b) and Mes(t-BuCOCH₂)TeBr₂ (3b) can be prepared by the addition of bromine to the telluride Ar(t-BuCOCH₂)-Te or of α-bromopinacolone to ArTeBr. Variable-temperature ¹H and ¹³C NMR of the separate signals for the o-Me groups in 3a,b indicate a very high barrier to rotation about the Te-C(aryl) bond. Crystal diffraction data for 1c, 2a-c, and 3b show that intramolecular 1,4-Te …O(C) secondary bonding interactions (SBIs) are retained even in the presence of bulky aryl groups and intermolecular Te …X SBIs are subject to electronic population and steric congestion around the Te(IV) center in the solid state.

New cutting-planes for the time-and/or precedence-constrained ATSP and directed VRP

In this paper, we introduce five classes of new valid cutting planes for the precedence-constrained (PC) and/or time-window-constrained (TW) Asymmetric Travelling Salesman Problems (ATSPs) and directed Vehicle Routing Problems (VRPs). We show that all five classes of new inequalities are facet-defining for the directed VRP-TW, under reasonable conditions and the assumption that vehicles are identical. Similar proofs can be developed for the VRP-PC. As ATSP-TW and PC-ATSP can be formulated as directed identical-vehicle VRP-TW and PC-VRP, respectively, this provides a link to study the polyhedral combinatorics for the ATSP-TW and PC-ATSP. The first four classes of these new cutting planes are cycle-breaking inequalities that are lifted from the well-known D^-_k and D⁺_k inequalities (see Grötschel and Padberg in Polyhedral theory. The traveling salesman problem: a guided tour of combinatorial optimization, Wiley, New York, 1985). The last class of new cutting planes, the TW ₂ inequalities, are infeasible-path elimination inequalities. Separation of these constraints will also be discussed. We also present prelimanry numerical results to demonstrate the strengh of these new cutting planes.