Abstract
We address the problem of dynamically switching the topology of a formation of a number of undistinguishable agents. Given the current and the final topologies, each with n agents, there are n! possible allocations between the initial and final positions of the agents. Given the agents maximum velocities, there is still a degree of freedom in the trajectories that might be used in order to avoid collisions. We seek an allocation and corresponding agent trajectories minimizing the maximum time required by all agents to reach the final topology, avoiding collisions. Collision avoidance is guaranteed through an appropriate choice of trajectories, which might have consequences in the choice of an optimal permutation. We propose here a dynamic programming approach to optimally solve problems of small dimension. We report computational results for problems involving formations with up to 12 agents. © Springer Science+Business Media, LLC 2010.

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 to 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, from the comparisons made it can be concluded that the results produced improve upon some of the best known solutions.

Abstract
We propose a Hybrid Genetic Algorithm (HGA) for a combinatorial optimization problem, motivated by, and a simplification of, a TV Self-promotion Assignment Problem. Given the weekly self-promotion space (a set of TV breaks with known duration) and a set of products to promote, the problem consists of assigning the products to the breaks in the "best" possible way. The objective is to maximize contacts in the target audience for each product, whist satisfying all constraints. The HGA developed incorporates a greedy heuristic to initialize part of the population and uses a repair routine to guarantee feasibility of each member of the population. The HGA works on a simplified version of the problem that, nevertheless, maintains its essential features. The proposed simplified problem is a binary programming problem that has similarities with other known combinatorial optimization problems, such as the assignment problem or the multiple knapsack problem, but has some distinctive features that characterize it as a new problem. Although we are mainly interested in solving problems of large dimension (of about 200 breaks and 50 spots), the quality of the solution has been tested on smaller dimension problems for which we are able to find an exact global minimum using a branch-and-bound algorithm. For these smaller dimension problems we have obtained solutions, on average, within 1% of the optimal solution value.

Abstract
In this work we address the Singe-Source Uncapacitated Minimum Cost Network Flow Problem with concave cost functions. Given that this problem is of a combinatorial nature and also that the total costs are nonlinear, we propose a hybrid heuristic to solve it. In this type of algorithms one usually tries to manage two conflicting aspects of searching behaviour: exploration, the algorithm's ability to search broadly through the search space; and exploitation, the algorithm ability to search locally around good solutions that have been found previously. In our case, we use an Ant Colony Optimization algorithm to mainly deal with the exploration, and a Local Search algorithm to cope with the exploitation of the search space. Our method proves to be very efficient while solving both small and large size problem instances. The problems we have used to test the algorithm were previously solved by other authors using other population based heuristics and our algorithm was able to improve upon their results, both in terms of computing time and solution quality.

Abstract
The environmental concerns are having a significant impact on the operation of power systems. The traditional Unit Commitment problem, which to minimizes the fuel cost is inadequate when environmental emissions are also considered in the operation of power plants. This paper presents a Biased Random Key Genetic Algorithm (BRKGA) approach combined with non-dominated sorting procedure to find solutions for the unit commitment multiobjective optimization problem. In the first stage, the BRKGA solutions are encoded by using random keys, which are represented as vectors of real numbers in the interval [0,1]. In the subsequent stage, a non-dominated sorting procedure similar to NSGA II is employed to approximate the set of Pareto solution through an evolutionary optimization process. 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. Test results with the existent benchmark systems of 10 units and 24 hours scheduling horizon are presented. The comparison of the obtained results with those of other Unit Commitment (UC) multiobjective optimization methods reveal the effectiveness of the proposed method.

Abstract
In this article we address the problem of determining how a structured formation of autonomous undistinguishable agents can be reorganized into another, eventually non-rigid, formation based on changes in the environment, perhaps unforeseeable. The methodology can also be used to correctly position the agents into a particular formation from an initial set of random locations. Given the information on the agents current location and the final locations, there are n! possible permutations for the n agents. Among these, we seek one that minimizes a total relative measure, e.g. distance traveled by the agents during the switching. We propose a dynamic programming methodology to solve this problem to optimality. Possible applications can be found in surveillance, damage assessment, chemical or biological monitoring, among others, where the switching to another formation, not necessarily predefined, may be required due to changes in the environment.