Abstract

Abstract
We address the problem of dynamically switching the geometry of a formation of a number of undistinguishable agents. Given the current and the final desired geometries, there are several possible allocations between the initial and final positions of the agents as well as several combinations for each agent velocity. However, not all are of interest since collision avoidance is enforced. Collision avoidance is guaranteed through an appropriate choice of agent paths and agent velocities. Therefore, given the agent set of possible velocities and initial positions, we wish to find their final positions and traveling velocities such that agent trajectories are apart, by a specified value, at all times. Among all the possibilities we are interested in choosing the one that minimizes a predefined performance criteria, e.g. minimizes the maximum time required by all agents to reach the final geometry. We propose here a dynamic programming approach to solve optimally such problems. © Springer Science+Business Media New York 2012.

Abstract
We propose a two-layer scheme to control a set of vehicles moving in a formation. The first; layer, file trajectory controller, is a nonlinear controller since most vehicles are nonholonomic systems and require a nonlinear, even discontinuous, feedback to stabilize them. The trajectory controller, a model predictive controller, computes centrally a bang-bang control law and only a small set of parameters need to be transmitted to each vehicle at each iteration. The second layer, the formation controller, aims to compensate for small changes around a nominal trajectory maintaining the relative positions between vehicles. We argue that; the formation control call be, in most; cases, adequately carried out, by a linear model predictive controller accommodating input, and state constraints. This has the advantage that the control laws for each vehicle are simple piecewise affine feedback laws that, call be pre-computed off-line and implemented in a, distributed way in each vehicle. Although several optimization problems have to be solved, the control strategy proposed results in a simple and efficient; implementation where no optimization problem needs to be solved in real-time at each vehicle.

Abstract
A Biased Random Key Genetic Algorithm (BRKGA) is proposed to find solutions for the unit commitment problem. In this problem, one wishes to schedule energy production on a given set of thermal generation units in order to meet energy demands at minimum cost, while satisfying a set of technological and spinning reserve constraints. In the BRKGA, solutions are encoded by using random keys, which are represented as vectors of real numbers in the interval [0, 1]. The GA proposed is a variant of the random key genetic algorithm, since bias is introduced in the parent selection procedure, as well as in the crossover strategy. Tests have been performed on benchmark large-scale power systems of up 100 units for a 24 hours period. The results obtained have shown the proposed methodology to be an effective and efficient tool for finding solutions to large-scale unit commitment problems. Furthermore, form the comparisons made it can be concluded that the results produced improve upon the best known solutions.

Abstract
We report on the development of a Genetic Algorithm (GA), which has been integrated into a Decision Support System to plan the best assignment of the weekly self-promotion space for a TV station. The problem addressed consists on deciding which shows to advertise and when such that the number of viewers, of an intended group or target, is maximized. The GA proposed incorporates a greedy heuristic to find good initial solutions. These solutions, as well as the solutions later obtained through the use of the GA, go then through a repair procedure. This is used with two objectives, which are addressed in turn. Firstly, it checks the solution feasibility and if unfeasible it is fixed by removing some shows. Secondly, it tries to improve the solution by adding some extra shows. Since the problem faced by the commercial TV station is too big and has too many features it cannot be solved exactly. Therefore, in order to test the quality of the solutions provided by the proposed GA we have randomly generated some smaller problem instances. For these problems we have obtained solutions on average within 1% of the optimal solution value.

Abstract
We report on the development of a Decision Support System (DSS) to plan the best assignment for the weekly promotion space of a TV station. Each product to promote has a given target audience that is best reached at specific time periods during the week. The DSS aims to maximize the total viewing for each product within its target audience while fulfilling a set of constraints defined by the user. The purpose of this paper is to describe the development and successful implementation of a heuristic-based scheduling software system that has been developed for a major Portuguese TV station.