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
Energy policies in the European Union (EU) and its 27 member states respond to three main concerns namely energy security, economic development, and environmental sustainability. All the three "Es'' are pursued simultaneously with some slight differences in emphasizing the mutual importance of these, in particular the cost factors. The legislation of the EU (e. g., ETS-Emission Trading Scheme, directives) increasingly guides the member states' energy policies. However, energy policy directions are still made domestically, for example, on the support on renewable energy technologies. In this work, we look into distributed generation (DG), since it has been grown considerable in the past few years and can be used to partially fulfill renewable energy targets. The policy makers have to make decisions about regulation directives, more specifically they have to change the current regulation in order to incentive the increase in DG. However, these decisions have not only economic impacts but also technical impacts that must be accounted for. In this regard, a decision aid tool would help the policy makers in estimating producer economic impacts, as well as power network technical impacts, of various possible regulation directives. Here, we propose an interactive decision aid tool that models the aforementioned impacts and thus, can be used by policy makers to experiment with different regulation directives before deciding on the ones to set.

Abstract
We consider the. re-scaled PSI20 daily index positive returns r(t)(alpha) and negative returns (-r(t))(alpha) called, after normalization, the. positive and negative fluctuations, respectively. We use the Kolmogorov-Smirnov statistical test as a method to find the values of alpha that optimize the data collapse of the histogram of the. fluctuations with the truncated Bramwell-Holdsworth-Pinton (BHP) probability density function (pdf) fBHP and the truncated generalized log-normal pdf fLN that best approximates the truncated BHP pdf. The optimal parameters we found are alpha(+)(BHP) = 0.48, alpha(-)(BHP) = 0.46, alpha(+)(LN) = 0.50 and alpha(-)(LN) = 0.49. Using the optimal alpha's we compute the analytical approximations of the pdf of the normalized positive and negative PSI20 index daily returns r(t). Since the BHP probability density function appears in several other dissimilar phenomena, our result reveals a universal feature of the stock exchange markets.

Abstract
We provide an extension to Merton's famous continuous time model of optimal consumption and investment, in the spirit of previous works by Pliska and Ye, to allow for a wage earner to have a random lifetime and to use a portion of the income to purchase life insurance in order to provide for his estate, while investing his savings in a financial market consisting of one risk-free security and an arbitrary number of risky securities whose diffusive terms are driven by a multi-dimensional Brownian motion. The wage earner's problem is to find the optimal consumption, investment, and insurance purchase decisions in order to maximize expected utility of consumption and of the size of the estate in the event of premature death, and of the size of the estate at the time of retirement. Dynamic programming methods are used to obtain explicit solutions for the case of constant relative risk aversion utility functions, and new results are presented together with the corresponding economic interpretations.

Abstract
We present an infinite dimensional space of C1+ smooth conjugacy classes of circle diffeomorphisms that are C1+ fixed points of renormalization. We exhibit a one-to-one correspondence between these C1+ fixed points of renormalization and C1+ conjugacy classes of Anosov diffeomorphisms.