A primogenitary linked quad tree approach for solution storage and retrieval in heuristic binary optimization

A data structure, called the primogenitary linked quad tree (PLQT), is used to store and retrieve solutions in heuristic solution procedures for binary optimization problems. Two ways are proposed to use integer vectors to represent solutions represented by binary vectors. One way is to encode binary vectors into integer vectors in a much lower dimension and the other is to use the sorted indices of binary variables with values equal to 0 or equal to 1. The integer vectors are used as composite keys to store and retrieve solutions in the PLQT. An algorithm processing trial solutions for insertion into or retrieval from the PLQT is developed. Examples are provided to demonstrate the way the algorithm works. Another algorithm traversing the PLQT is also developed. Computational results show that the PLQT approach takes only a very tiny portion of the CPU time taken by a linear list approach for the same purpose for any reasonable application. The CPU time taken by the PLQT managing trial solutions is negligible as compared to that taken by a heuristic procedure for any reasonably hard to solve binary optimization problem, as shown in a tabu search heuristic procedure for the capacitated facility location problem. Compared to the hashing approach, the PLQT approach takes the same or less amount of CPU time but much less memory space while completely eliminating collision.     

An exact algorithm for connected red–blue dominating set

In the Connected Red–Blue Dominating Set problem we are given a graph G whose vertex set is partitioned into two parts R and B (red and blue vertices), and we are asked to find a connected subgraph induced by a subset S of B such that each red vertex of G is adjacent to some vertex in S. The problem can be solved in O^?(²n−|B|) time by reduction to the Weighted Steiner Tree problem. Combining exhaustive enumeration when |B| is small with the Weighted Steiner Tree approach when |B| is large, solves the problem in O^?(n^1.4143). In this paper we present a first non-trivial exact algorithm whose running time is in O^?(n^1.3645). We use our algorithm to solve the Connected Dominating Set problem in O^?(n^1.8619). This improves the current best known algorithm, which used sophisticated run-time analysis via the measure and conquer technique to solve the problem in O^?(n^1.8966).     

Detection of refined olive oil adulteration with refined hazelnut oil by employing NMR spectroscopy and multivariate statistical analysis

NMR spectroscopy was employed for the detection of adulteration of refined olive oil with refined hazelnut oil. Fatty acids and iodine number were determined by ¹H NMR, whereas ³¹P NMR was used for the quantification of minor compounds including phenolic compounds, diacylglycerols, sterols, and free fatty acids (free acidity). Classification of the refined oils based on their fatty acids content and the concentration of their minor compounds was achieved by using the forward stepwise canonical discriminant analysis (CDA) and the classification binary trees (CBTs). Both methods provided good discrimination between the refined hazelnut and olive oils. Different admixtures of refined olive oils with refined hazelnut oils were prepared and analyzed by ¹H NMR and ³¹P NMR spectroscopy. Subsequent application of CDA to the NMR data allowed the detection of the presence of refined hazelnut oils in refined olive oils at percentages higher than 5%. Application of the non-linear classification method of the binary trees offered better possibilities of measuring adulteration of the refined olive oils at a lower limit of detection than that obtained by the CDA method.     

Synchronization of inventory and transportation under flexible vehicle constraint: A heuristics approach using sliding windows and hierarchical tree structure

This paper investigates the integrated inventory and transportation planning under flexible vehicle constraint. To offer better services at lower prices, more and more companies turn to outsource transportation functions to other professional service providers, namely 3rd party logistics companies. Under these vehicle rental arrangements, the number of vehicles is a decision variable instead of a fixed number, and the transportation cost includes not only the delivery cost but also the cost of vehicle rental that is proportional to the number of vehicles rented in a given planning horizon. In this paper, the problem is formulated as a mixed integer programming problem. A heuristic algorithm is developed, in which sliding windows are applied to approximate the problem by repeatedly solving a series of overlapping short-term subproblems, and a hierarchical tree structure is used to evaluate the closeness of different groups of retailers. Numerical experiments show that a better tradeoff between the inventory cost and transportation cost can be achieved through the proposed heuristic algorithm.     

树指标集马氏链的常返性

用鞅方法给出了在不限定根顶点O的条件下,树指标集马氏链常返性的充分条件,部分解决了Benjamin.I提出的问题.     

Stability of the phase transition of critical-field Ising model on Cayley trees under inhomogeneous external fields

We consider the ferromagnetic Ising model with spatially dependent external fields on a Cayley tree, and we investigate the conditions for the existence of the phase transition for a class of external fields, asymptotically approaching a homogeneous critical external field. Our results extend earlier results by Rozikov and Ganikhodjaev.     

Characterization of polysaccharides purified from Lacquer tree seed cakes and its antioxidant activity

Three polysaccharides, LTPS-1, LTPS-21 and LTPS-31 were isolated and purified from the seed cakes of lacquer tree using DEAE-52 cellulose and Sephadex G-200 column chromatography. The total sugar contents of LTPS-1, LTPS-21 and LTPS-31 were 931.8, 958.2 and 895.1 g kg^?1, respectively. LTPS-1 (3.48 kDa) was mainly composed of rhamnose, arabinose, glucose and galactose in a ratio of 35.36:5.06:1:2. LTPS-21 (11.4 kDa) was mainly composed of rhamnose, arabinose, mannose and galactose in a ratio of 41.93:21.8:1.01:9.24. LTPS-31 (19.49 kDa) was mainly composed of rhamnose, arabinose and mannose in a ratio of 38.31:16.44:1.1. IR analysis suggested they contained lower sulphuric acids, the LTPS-21 and LTPS-31 belonged to β-type polysaccharide. Among the three polysaccharides, LTPS-21 exhibited the strongest reducing power, scavenging activity on ABTS and hydroxyl radicals. These findings suggested that polysaccharides from the seed cakes could be potentially developed as natural functional ingredients in the food and cosmetic industry.     

Mining information from time series in the form of sentences of natural language

The goal of this paper is to provide a more detailed explanation of the principles how special formulas that characterize properties of trend of time series can be formed and how they are interpreted. Then we show how these formulas can be used in a tectogrammatical tree that construes special sentences of natural language, using which information on behavior of time series is provided. We also outline the principles of mining this information. The last part is devoted to application of the theory of intermediate quantifiers to mining summarized information on time series also in sentences of natural language.