On the sub-permutations of pattern avoiding permutations

There is a deep connection between permutations and trees. Certain sub-structures of permutations, called sub-permutations, bijectively map to sub-trees of binary increasing trees. This opens a powerful tool set to study enumerative and probabilistic properties of sub-permutations and to investigate the relationships between 'local' and 'global' features using the concept of pattern avoidance. First, given a pattern {\mu}, we study how the avoidance of {\mu} in a permutation {\pi} affects the presence of other patterns in the sub-permutations of {\pi}. More precisely, considering patterns of length 3, we solve instances of the following problem: given a class of permutations K and a pattern {\mu}, we ask for the number of permutations $\pi \in Av_n(\mu)$ whose sub-permutations in K satisfy certain additional constraints on their size. Second, we study the probability for a generic pattern to be contained in a random permutation {\pi} of size n without being present in the sub-permutations of {\pi} generated by the entry $1 \leq k \leq n$. These theoretical results can be useful to define efficient randomized pattern-search procedures based on classical algorithms of pattern-recognition, while the general problem of pattern-search is NP-complete

Pattern Search algorithm for the Maximum Power Point Tracking in Photovoltaic System

The aim of this paper is to present an intelligent control method for the maximum power point tracking (MPPT) of photovoltaic system under different climatic conditions with regard to temperature and irradiation. A Pattern Search algorithm (PS) is suggested to be combined with the maximum power point tracker as a strategic optimization for the photovoltaic panel. The voltaic system is composed of a solar panel and PS MPP tracker and it is simulated and evaluated. The system has shown a better performance as well as the effectiveness of PS MPP in terms of getting maximum energy production despite the changing climate conditions

Pattern Search algorithm for the Maximum Power Point Tracking in Photovoltaic System

The aim of this paper is to present an intelligent control method for the maximum power point tracking (MPPT) of photovoltaic system under different climatic conditions with regard to temperature and irradiation. A Pattern Search algorithm (PS) is suggested to be combined with the maximum power point tracker as a strategic optimization for the photovoltaic panel. The voltaic system is composed of a solar panel and PS MPP tracker and it is simulated and evaluated. The system has shown a better performance as well as the effectiveness of PS MPP in terms of getting maximum energy production despite the changing climate conditions

Improving Hit-and-Run for global optimization

Improving Hit-and-Run is a random search algorithm for global optimization that at each iteration generates a candidate point for improvement that is uniformly distributed along a randomly chosen direction within the feasible region. The candidate point is accepted as the next iterate if it offers an improvement over the current iterate. We show that for positive definite quadratic programs, the expected number of function evaluations needed to arbitrarily well approximate the optimal solution is at most O(n 5/2 ) where n is the dimension of the problem. Improving Hit-and-Run when applied to global optimization problems can therefore be expected to converge polynomially fast as it approaches the global optimum.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44932/1/10898_2005_Article_BF01096737.pd

An improved exploratory search technique for pure integer linear programming problems

The development is documented of a heuristic method for the solution of pure integer linear programming problems. The procedure draws its methodology from the ideas of Hooke and Jeeves type 1 and 2 exploratory searches, greedy procedures, and neighborhood searches. It uses an efficient rounding method to obtain its first feasible integer point from the optimal continuous solution obtained via the simplex method. Since this method is based entirely on simple addition or subtraction of one to each variable of a point in n-space and the subsequent comparison of candidate solutions to a given set of constraints, it facilitates significant complexity improvements over existing techniques. It also obtains the same optimal solution found by the branch-and-bound technique in 44 of 45 small to moderate size test problems. Two example problems are worked in detail to show the inner workings of the method. Furthermore, using an established weighted scheme for comparing computational effort involved in an algorithm, a comparison of this algorithm is made to the more established and rigorous branch-and-bound method. A computer implementation of the procedure, in PC compatible Pascal, is also presented and discussed