Finding Multiple Solutions in Nonlinear Integer Programming with Algebraic Test-Sets

We explain how to compute all the solutions of a nonlinear integer problem using the algebraic test-sets associated to a suitable linear subproblem. These test-sets are obtained using Gröbner bases. The main advantage of this method, compared to other available alternatives, is its exactness within a quite good efficiency.Ministerio de Economía y Competitividad MTM2016-75024-PMinisterio de Economía y Competitividad MTM2016-74983-C2- 1-RJunta de Andalucía P12-FQM-269

Development of an in-field tree imaging system : a thesis presented in partial fulfilment of the requirements for the degree of Master of Technology at Massey University

Quality inventory information is essential for optimal resource utilisation in the forestry industry. In-field tree imaging is a method which has been proposed to improve the preharvest inventor assessment of standing trees. It involves the application of digital imaging technology to this task. The method described generates a three dimensional model of each tree through the capture of two orthogonal images from ground level. The images are captured and analysed using the "TreeScan" in-field tree imaging system. This thesis describes the design, development, and evaluation of the TreeScan system. The thesis can also be used as a technical reference for the system and as such contains appropriate technical and design detail. The TreeScan system consists of a portable computer, a custom designed high resolution scanner with integral microcontroller, a calibration rod, and custom designed processing software. Images of trees are captured using the scanner which contains a CCD line scan camera and a precision scanning mechanism. Captured images are analysed on the portable computer using customised image processing software to estimate real world tree dimensions and shape. The TreeScan system provides quantitative estimates of five tree parameters; height, sweep, stem diameter, branch diameter, and feature separation such as internodal distance. In addition to these estimates a three dimensional model is generated which can be further processed to determine the optimal stem breakdown into logs

Reformulation and decomposition of integer programs

In this survey we examine ways to reformulate integer and mixed integer programs. Typically, but not exclusively, one reformulates so as to obtain stronger linear programming relaxations, and hence better bounds for use in a branch-and-bound based algorithm. First we cover in detail reformulations based on decomposition, such as Lagrangean relaxation, Dantzig-Wolfe column generation and the resulting branch-and-price algorithms. This is followed by an examination of Benders’ type algorithms based on projection. Finally we discuss in detail extended formulations involving additional variables that are based on problem structure. These can often be used to provide strengthened a priori formulations. Reformulations obtained by adding cutting planes in the original variables are not treated here.Integer program, Lagrangean relaxation, column generation, branch-and-price, extended formulation, Benders' algorithm

High-level Counterexamples for Probabilistic Automata

Providing compact and understandable counterexamples for violated system properties is an essential task in model checking. Existing works on counterexamples for probabilistic systems so far computed either a large set of system runs or a subset of the system's states, both of which are of limited use in manual debugging. Many probabilistic systems are described in a guarded command language like the one used by the popular model checker PRISM. In this paper we describe how a smallest possible subset of the commands can be identified which together make the system erroneous. We additionally show how the selected commands can be further simplified to obtain a well-understandable counterexample