An Improved Search Algorithm For Solving Mixed-integer Non Linear Programming Problem

The special nonlinear mathematical programming problem which isaddressed in this paper has a structure characterized by a subset ofvariables restricted to assume discrete values, which are linear andseperable from the continuous variables. The strategy of releasingnonbasic variables from their bounds, combined with the "activeconshaint" method and the notion of superbasics, has been developedfor efficiently tackling such a problem by ignoring the integralityrequirements, this strategy is used to force the appropriate non-integerbasic variables to move to their neighbourhood integer points. A studyof criteria for choosing a nonbasic variable to work with in theintegerizing shategy has also been made. Successful implementation ofthese algorithms was achieved on various test problems. The resultshow that the proposed integerizing strategy is promosing in tacklingcertain classes of mixed integer programming problems

An improved local search algorithm for 3-SAT

We slightly improve the pruning technique presented in Dantsin et. al. (2002) to obtain an $\mathcal{O}^*\left(1.473^n\right)$ algorithm for 3-SAT

An Improved Search Algorithm for Optimal Multiple-Sequence Alignment

Multiple sequence alignment (MSA) is a ubiquitous problem in computational biology. Although it is NP-hard to find an optimal solution for an arbitrary number of sequences, due to the importance of this problem researchers are trying to push the limits of exact algorithms further. Since MSA can be cast as a classical path finding problem, it is attracting a growing number of AI researchers interested in heuristic search algorithms as a challenge with actual practical relevance. In this paper, we first review two previous, complementary lines of research. Based on Hirschbergs algorithm, Dynamic Programming needs O(kN^(k-1)) space to store both the search frontier and the nodes needed to reconstruct the solution path, for k sequences of length N. Best first search, on the other hand, has the advantage of bounding the search space that has to be explored using a heuristic. However, it is necessary to maintain all explored nodes up to the final solution in order to prevent the search from re-expanding them at higher cost. Earlier approaches to reduce the Closed list are either incompatible with pruning methods for the Open list, or must retain at least the boundary of the Closed list. In this article, we present an algorithm that attempts at combining the respective advantages; like A* it uses a heuristic for pruning the search space, but reduces both the maximum Open and Closed size to O(kN^(k-1)), as in Dynamic Programming. The underlying idea is to conduct a series of searches with successively increasing upper bounds, but using the DP ordering as the key for the Open priority queue. With a suitable choice of thresholds, in practice, a running time below four times that of A* can be expected. In our experiments we show that our algorithm outperforms one of the currently most successful algorithms for optimal multiple sequence alignments, Partial Expansion A*, both in time and memory. Moreover, we apply a refined heuristic based on optimal alignments not only of pairs of sequences, but of larger subsets. This idea is not new; however, to make it practically relevant we show that it is equally important to bound the heuristic computation appropriately, or the overhead can obliterate any possible gain. Furthermore, we discuss a number of improvements in time and space efficiency with regard to practical implementations. Our algorithm, used in conjunction with higher-dimensional heuristics, is able to calculate for the first time the optimal alignment for almost all of the problems in Reference 1 of the benchmark database BAliBASE

An Improved Memetic Algorithm for Web Search

AbstractIn order to search a relevant data from World Wide Web, user use to submit query to search engine. Search engine returns combination of relevant and irrelevant results. This paper proposes a novel method based on Memetic Algorithm (MA) for searching the most relevant snippets in case of complex queries. The improved memetic algorithm (IMA) uses a hybrid-selection strategy to enhance the search result. Classical local search operators are combined for improvement in final output. Besides, the same chromosomes are modified to be different so that the population diversity is preserved and the algorithm kept from premature convergence. The performance of IMA is tested by comparing the result of search engine, basic Memetic and Improved Memetic Algorithm. Experimental results show that IMA could obtain superior solutions to the counterparts

Nested quantum search and NP-complete problems

A quantum algorithm is known that solves an unstructured search problem in a number of iterations of order $\sqrt{d}$, where $d$ is the dimension of the search space, whereas any classical algorithm necessarily scales as $O(d)$. It is shown here that an improved quantum search algorithm can be devised that exploits the structure of a tree search problem by nesting this standard search algorithm. The number of iterations required to find the solution of an average instance of a constraint satisfaction problem scales as $\sqrt{d^\alpha}$, with a constant $\alpha<1$ depending on the nesting depth and the problem considered. When applying a single nesting level to a problem with constraints of size 2 such as the graph coloring problem, this constant $\alpha$ is estimated to be around 0.62 for average instances of maximum difficulty. This corresponds to a square-root speedup over a classical nested search algorithm, of which our presented algorithm is the quantum counterpart.Comment: 18 pages RevTeX, 3 Postscript figure