We propose and analyze a simple new randomized algorithm, called ResolveSat, for finding satisfying assignments of Boolean formulas in conjunctive normal form. The algorithm consists of two stages: a preprocessing stage in which resolution is applied to enlarge the set of clauses of the formula, followed by a search stage that uses a simple randomized greedy procedure to look for a satisfying assignment. We show that, for each k, the running time of ResolveSat on a k--CNF formula is significantly better than 2 n , even in the worst case. In particular, we show that the algorithm finds a satisfying assignment of a general satisfiable 3--CNF in time O(2 :448n ) with high probability; where the best previous algorithm [13] has running time O(2 :562n ). We obtain a better upper bound of 2 (2 ln 2\Gamma1)n+o(n) = O(2 0:387n ) for 3CNF that have exactly one satisfying assignment (unique k-SAT). For each k, the bounds for general k-CNF are the best currently known for ...

Abstract. Inspired by a method by Jones et al. (1993), we present a global optimization algorithm based on multilevel coordinate search. It is guaranteed to converge if the function is continuous in the neighborhood of a global minimizer. By starting a local search from certain good points, an improved convergence result is obtained. We discuss implementation details and give some numerical results.

A numerical method has recently been presented to determine the noise thresholds of low density parity-check (LDPC) codes that employ the message passing decoding algorithm on the additive white Gaussian noise (AWGN) channel. In this paper, we extend this technique to the uncorrelated flat Rayleigh fading channel. Using a nonlinear code optimization technique, we optimized irregular LDPC codes for the uncorrelated Rayleigh fading channel. The thresholds of the optimized irregular LDPC codes are very close to the Shannon limit for this channel. For example, at rate one-half, the optimized irregular LDPC code has a threshold only 0.07dB away from the capacity of this channel. Furthermore, we compare simulated performance of the optimized irregular LDPC codes and turbo codes on a land mobile channel, and the results indicate that at a block size of 3072, irregular LDPC codes can outperform turbo codes over a wide range of mobile speeds. This work was sponsored by the National Science Fo...

We introduce a method that aims to find the global minimum of a continuous nonconvex function on a compact subset of R^d. It is assumed that function evaluations are expensive and that no additional information is available. Radial basis function interpolation is used to define a utility function. The maximizer of this function is the next point where the objective function is evaluated. We show that, for most types of radial basis functions that are considered in this paper, convergence can be achieved without further assumptions on the objective function. Besides, it turns out that our method is closely related to a statistical global optimization method, the P-algorithm. A general framework for both methods is presented. Finally, a few numerical examples show that on the set of Dixon-Szego test functions our method yields favourable results in comparison to other global optimization methods.

We design sequences of low-density parity check codes that provably perform at rates extremely close to the Shannon capacity. The codes are built from highly irregular bipartite graphs with carefully chosen degree patterns on both sides. Our theoretical analysis of the codes is based on [1]. Additionally, based on the assumption that the underlying communication channel is symmetric, we prove that the probability densities at the message nodes of the graph satisfy a certain symmetry. This enables us to derive a succinct description of the density evolution for the case of a belief propagation decoder. Furthermore, we prove a stability condition which implies an upper bound on the fraction of errors that a belief propagation decoder can correct when applied to a code induced from a bipartite graph with a given degree distribution. Our codes are found by optimizing the degree structure of the underlying graphs. We develop several strategies to perform this optimization. We also present s...

A hybrid particle swarm with differential evolution operator, termed DEPSO, which provide the bell-shaped mutations with consensus on the population diversity along with the evolution, while keeps the self-organized particle swarm dynamics, is proposed. Then it is applied to a set of benchmark functions, and the experimental results illustrate its efficiency.

We explore the combined effects of a climate threshold (a potential ocean thermohaline circulation collapse), parameter uncertainty, and learning in an optimal economic growth model. Our analysis shows that significantly reducing carbon dioxide ðCO2Þ emissions may be justified to avoid or delay even small (and arguably realistic) damages from an uncertain and irreversible climate change—even when future learning about the system is considered. Parameter uncertainty about the threshold specific damages and the CO2 level triggering a threshold can act to decrease near-term CO2 abatements that maximize expected utility.

This article discusses the stagnation of an evolutionary optimization algorithm called Differential Evolution. Stagnation problem refers to a situation in which the optimum seeking process stagnates before finding a globally optimal solution. Typically, stagnation occurs virtually without any obvious reason. The stagnation differs from the premature convergence so that the population remains diverse and unconverged after stagnation, but the optimization process does not progress anymore. The reasons for this problem have remained unknown so far. This article uncovers this problem describing the basic nature of stagnation phenomena, a mechanism behind it and some reasons for stagnation. Advices for reducing the risk of stagnation are concluded on basis of the new findings.

Abstract:- Initialization of the population in Evolutionary Computation algorithms is an issue of ongoing research. Proper initialization may help the algorithm to explore the search space more efficiently and detect better solutions. In this paper, the Nonlinear Simplex Method is used to initialize the swarm of the Particle Swarm technique. Experiments for several well-known benchmark problems imply that better convergence rates and success rates can be achieved by initializing the swarm this way.

Clustering aims at representing large datasets by a fewer number of prototypes or clusters. It brings simplicity in modeling data and thus plays a central role in the process of knowledge discovery and data mining. Data mining tasks, in these days, require fast and accurate partitioning of huge datasets, which may come with a variety of attributes or features. This, in turn, imposes severe computational requirements on the relevant clustering techniques. A family of bio-inspired algorithms, well-known as Swarm Intelligence (SI) has recently emerged that meets these requirements and has successfully been applied to a number of real world clustering problems. This chapter explores the role of SI in clustering different kinds of datasets. It finally describes a new SI technique for partitioning any dataset into an optimal number of groups through one run of optimization. Computer simulations undertaken in this research have also been provided to demonstrate the effectiveness of the proposed algorithm.