Catálogo de publicaciones - libros

The restructuring of the gas industry did not so far generate the same modeling activity as in electricity. While the literature of activity in electricity market models is now abundant, it is still rather scant on the gas side. This paper surveys some of the existing models and attempts to take advantage of the wealth of knowledge available in electricity in order to develop relevant models of restructured gas markets. The presentation is in three parts. The first one gives a blueprint of the market architectures inherited from the European and North American gas legislation. It also introduces a prototype optimization model and its interpretation in terms of perfect competition between agents operating on the restructured market. The second part extends the model to the case where marketers have market power. The third part considers more complex issues related to regulation of access to the network and existence of market power with different types of agents. Equilibrium models are commonly formulated as complementarity problems and the same mathematical programming framework is adopted here. Many models are single stage, there are generally easy to formulate and well known computationally. But many phenomena require two stage models that are much more intricate and on which much less is known. The paper is thus also aimed at pinpointing possible avenues for mathematical programming research.

This paper deals with a hard nonlinear biobjective optimization problem: finding the optimal location and design for a new franchised facility within a region where facilities (both of the franchise and not) already exist and compete for the market. The franchisor and the new franchisee both want to maximise their own profit in the market, but these two objectives are in conflict. Customers patronize all the facilities, old and new, proportionally to their attraction to them. Both resulting objective functions are neither convex nor concave. An interval branch and bound method is proposed to obtain an outer approximation of the whole set of efficient solutions. Computational experiments highlight the different kinds of information provided by this method and by a variation of the lexicographic method.

In this paper we describe how robot trajectory planning, using cubic splines to generate the trajectory, can be formulated as standard semi-infinite programming (SIP) problems and efficiently solved by a discretization method. These formulated problems were coded in the publicly available SIPAMPL environment and to allow the codification of these problems a cubic splines dynamic library for AMPL was developed. The discretization method used to solve the formulated problems is implemented in the NSIPS solver and numerical results with four particular problems are shown.

MPCC can be solved with specific MPCC codes or in its nonlinear equivalent formulation (NLP) using NLP solvers. Two NLP solvers - NPSOL and the line search filter SQP - are used to solve a collection of test problems in AMPL. Both are based on SQP (Sequential Quadratic Programming) philosophy but the second one uses a line search filter scheme.

A new algorithm based on filter SQP with line search to solve nonlinear constrained optimization problems is presented. The filter replaces the merit function avoiding the penalty parameter estimation. This new concept works like an oracle estimating the trial approximation of the iterative SQP algorithm. A collection of AMPL test problems is solved by this new code as well as NPSOL and LOQO solvers. A comparative analysis is made - the filter SQP with line search presents good performance.

This paper describes the optimization of an activated sludge system which comprises an aeration tank and a secondary settler. This system is by far the most widely used biological process in wastewater treatment plants. The optimization process is represented as a smooth nonlinear problem with highly nonlinear equality constraints, some linear equality constraints, one inequality constraint and simple bounds, in which the objective is to minimize the total cost associated with the installation and operation of the biological process. We use the software LOQO to solve the problem. Several computational results show that the quality of the effluent, especially in terms of carbonaceous matter, influences directly the cost and the main contribution to the total cost is the air flow, due to the acquirement of the electromechanical equipment and spent energy.