Project Scheduling with Multiple Modes: A Genetic Algorithm

In this paper we consider the resource-constrained project scheduling problem with multiple execution modes for each activity and makespan minimization as objective. We present a new genetic algorithm approach to solve this problem. The genetic encoding is based on a precedence feasible list of activities and a mode assignment. After defining the related crossover, mutation, and selection operators, we describe a local search extension which is employed to improve the schedules found by the basic genetic algorithm. Finally, we present the results of our thorough computational study. We determine the best among several different variants of our genetic algorithm and compare it to four other heuristics that have recently been proposed in the literature. The results that have been obtained using a standard set of instances show that the new genetic algorithm outperforms the other heuristic procedures with regard to a lower average deviation from the optimal makespan.     

On the numerical solution of the linear complementarity problem

The well-known linear complementarity problem with definite matrices is considered. It is proposed to solve it using a global optimization algorithm in which one of the basic stages is a special local search. The proposed global search algorithm is tested using a variety of randomly generated problems; a detailed analysis of the computational experiment is given.     

Lower bounds on the pathwidth of some grid-like graphs

We present proofs of lower bounds on the node search number of some grid-like graphs including two-dimensional grids, cylinders, tori and a variation we call “orb-webs”. Node search number is equivalent to pathwidth and vertex separation, which are all important graph parameters. Since matching upper bounds are not difficult to obtain, this implies that the pathwidth of these graphs is easily computed, because the bounds are simple functions of the graph dimensions. We also show matching upper and lower bounds on the node search number of equidimensional tori which are one less than the obvious upper bound.     

Effects of initial states on the quantum correlations in the generalized Grover search algorithm

We investigate the correlations between two qubits in the Grover search algorithm with arbitrary initial states by numerical simulation. Using a set of suitable bases, we construct the reduced density matrix and give the numerical expression of correlations relating to the iterations. For different initial states, we obtain the concurrence and quantum discord compared with the success probability in the algorithm. The results show that the initial states affect the correlations and the limit point of the correlations in the searching process. However, the initial states do not influence the whole cyclical trend.     

A UNIVERSAL APPROACH FOR CONTINUOUS OR DISCRETE NONLINEAR PROGRAMMINGS WITH MULTIPLE VARIABLES AND CONSTRAINTS

IntroductionExtensive research works have been published for solving nonlinear mathematicprogramming problems.Nonetheless,it is still difficult to find an effective and universalapproach for general programming problems with multiple design variables and …     

SKATE: A docking program that decouples systematic sampling from scoring

SKATE is a docking prototype that decouples systematic sampling from scoring. This novel approach removes any interdependence between sampling and scoring functions to achieve better sampling and, thus, improves docking accuracy. SKATE systematically samples a ligand's conformational, rotational and translational degrees of freedom, as constrained by a receptor pocket, to find sterically allowed poses. Efficient systematic sampling is achieved by pruning the combinatorial tree using aggregate assembly, discriminant analysis, adaptive sampling, radial sampling, and clustering. Because systematic sampling is decoupled from scoring, the poses generated by SKATE can be ranked by any published, or in‐house, scoring function. To test the performance of SKATE, ligands from the Asetex/CDCC set, the Surflex set, and the Vertex set, a total of 266 complexes, were redocked to their respective receptors. The results show that SKATE was able to sample poses within 2 Å RMSD of the native structure for 98, 95, and 98% of the cases in the Astex/CDCC, Surflex, and Vertex sets, respectively. Cross‐docking accuracy of SKATE was also assessed by docking 10 ligands to thymidine kinase and 73 ligands to cyclin‐dependent kinase. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Precise and global identification of phospholipid molecular species by an Orbitrap mass spectrometer and automated search engine Lipid Search

In the present research, we have established a new lipidomics approach for the comprehensive and precise identification of molecular species in a crude lipid mixture using a LTQ Orbitrap mass spectrometer (MS) and reverse-phase liquid chromatography (RPLC) combination with our newly developed lipid search engine “Lipid Search”. LTQ Orbitrap provides high mass accuracy MS spectra by Fourier-transform (FT) mass spectrometer mode and can perform rapid MSⁿ by ion trap (IT) mass spectrometer mode. In this study, the negative ion mode was selected to detect fragment ions from phospholipids, such as fatty acid anions, by MS2 or MS3. We selected the specific detection approach by neutral loss survey-dependent MS3, for the identification of molecular species of phosphatidylcholine, sphingomyelin and phosphatidylserine. Identification of molecular species was performed by using both the high mass accuracy of the mass spectrometric data obtained from FT mode and structural data obtained from fragments in IT mode. Some alkylacyl and alkenylacyl species have the same m/z value as molecular-related ions and fragment ions, thus, direct acid hydrolysis analysis was performed to identify alkylacyl and alkenylacyl species, and then the RPLC–LTQ Orbitrap method was applied. As a result, 290 species from mouse liver and 248 species from mouse brain were identified within six different classes of phospholipid, only those in manually detected and confirmed. Most of all manually detected mass peaks were also automatically detected by “Lipid Search”. Adding to differences in molecular species in different classes of phospholipids, many characteristic differences in molecular species were detected in mouse liver and brain. More variable number of saturated and monounsaturated fatty acid-containing molecular species were detected in mouse brain than liver.     

On the expected longest length probe sequence for hashing with separate chaining

Hashing is a widely used technique for data organization. Hash tables enable a fast search of the stored data and are used in a variety of applications ranging from software to network equipment and computer hardware. One of the main issues associated with hashing are collisions that cause an increase in the search time. A number of alternatives have been proposed to deal with collisions. One of them is separate chaining, in which for each hash value an independent list of the elements that have that value is stored. In this scenario, the worst case search time is given by the maximum length of that list across all hash values. This worst case is often referred to as Longest Length Probe Sequence (llps) in the literature. Approximations for the expected longest length probe sequence when the hash table is large have been proposed and an exact analytical solution has also been presented in terms of a set of recurring equations. In this paper, a novel analytical formulation of the expected longest length probe sequence is introduced. The new formulation does not require a recursive computation and can be easily implemented in a symbolic computation tool.     

Experimental implementation of a fixed-point duality quantum search algorithm in the nuclear magnetic resonance quantum system

In this work, we demonstrated a fixed-point quantum search algorithm in the nuclear magnetic resonance (NMR) system. We constructed the pulse sequences for the pivotal operations in the quantum search protocol. The experimental results agree well with the theoretical predictions. The generalization of the scheme to the arbitrary number of qubits has also been given.