Search results for "combinatorial"

Linear Programming Based Methods for Solving Arc Routing Problems

2000

From the pioneering works of Dantzig, Edmonds and others, polyhedral (i.e. linear programming based) methods have been successfully applied to the resolution of many combinatorial optimization problems. See Junger, Reinelt & Rinaldi (1995) for an excellent survey on this topic. Roughly speaking, the method consists of trying to formulate the problem as a Linear Program and using the existing powerful methods of Linear Programming to solve it.

On Optimal Solutions for the Optimal Communication Spanning Tree Problem

2009

This paper presents an experimental investigation into the properties of the optimal communication spanning tree (OCST) problem. The OCST problem seeks a spanning tree that connects all the nodes and satisfies their communication requirements at a minimum total cost. The paper compares the properties of random trees to the properties of the best solutions for the OCST problem that are found using an evolutionary algorithm. The results show, on average, that the optimal solution and the minimum spanning tree (MST) share a higher number of links than the optimal solution and a random tree. Furthermore, optimal solutions for OCST problems with randomly chosen distance weights share a higher n…

Using penalties instead of rewards: Solving OCST problems with guided local search

2012

Abstract This paper considers the optimal communication spanning tree (OCST) problem. Previous work analyzed features of high-quality solutions and found that edges in optimal solutions have low weight and point towards the center of a tree. Consequently, integrating this problem-specific knowledge into a metaheuristic increases its performance for the OCST problem. In this paper, we present a guided local search (GLS) approach which dynamically changes the objective function to guide the search process into promising areas. In contrast to traditional approaches which reward promising solution features by favoring edges with low weights pointing towards the tree’s center, GLS penalizes low-…

A hybrid genetic algorithm with local search: I. Discrete variables: optimisation of complementary mobile phases

2001

Abstract A hybrid genetic algorithm was developed for a combinatorial optimisation problem. The assayed hybridation modifies the reproduction pattern of the genetic algorithm through the application of a local search method, which enhances each individual in each generation. The method is applied to the optimisation of the mobile phase composition in liquid chromatography, using two or more mobile phases of complementary behaviour. Each of these phases concerns the optimal separation of certain compounds in the analysed mixture, while the others can remain overlapped. This optimisation approach may be useful in situations where full resolution with a single mobile phase is unfeasible. The o…

Branch-and-Bound

2010

We now turn to the discussion of how to solve the linear ordering problem to (proven) optimality. In this chapter we start with the branch-and-bound method which is a general procedure for solving combinatorial optimization problems. In the subsequent chapters this approach will be realized in a special way leading to the so-called branch-and-cut method. There are further possibilities for solving the LOP exactly, e.g. by formulating it as dynamic program or as quadratic assignment problem, but these approaches did not lead to the implementation of practical algorithms and we will not elaborate on them here.

Combinatorial Gray codes for classes of pattern avoiding permutations

2007

The past decade has seen a flurry of research into pattern avoiding permutations but little of it is concerned with their exhaustive generation. Many applications call for exhaustive generation of permutations subject to various constraints or imposing a particular generating order. In this paper we present generating algorithms and combinatorial Gray codes for several families of pattern avoiding permutations. Among the families under consideration are those counted by Catalan, Schr\"oder, Pell, even index Fibonacci numbers and the central binomial coefficients. Consequently, this provides Gray codes for $\s_n(\tau)$ for all $\tau\in \s_3$ and the obtained Gray codes have distances 4 and 5.

Self-assembly of catalytically-active supramolecular coordination compounds within metal-organic frameworks

2019

[EN] Supramolecular coordination compounds (SCCs) represent the power of coordination chemistry methodologies to self-assemble discrete architectures with targeted properties. SCCs are generally synthesized in solution, with isolated fully coordinated metal atoms as structural nodes, thus severely limited as metal-based catalysts. Metal-organic frameworks (MOFs) show unique features to act as chemical nanoreactors for the in situ synthesis and stabilization of otherwise not accessible functional species. Here, we present the self-assembly of Pd-II SCCs within the confined space of a pre-formed MOF (SCCs@MOF) and its post-assembly metalation to give a Pd-II-Au-III supra molecular assembly, c…

1982

Unzipping Nucleoside Channels by Means of Alcohol Disassembly

2013

Gold nanoparticles capped with simple adenosine derivatives can form colloidal aggregates in nonpolar solvents. Theoretical calculations indicate the formation of organic channels by the supramolecular assembly of the nanoparticles by means of hydrogen bonds between the adenine moieties. The aggregates were only negligibly sensitive to nPrOH, iPrOH, and tBuOH, whereas some showed a similar response to MeOH and EtOH, and others showed high selectivity toward MeOH. DNA nucleoside derivatives (1-(2-deoxy-β-D-ribofuranosyl)-5-methyluracil and 2′,3′-O-isopropylideneadenosine) as well as thymine and other aromatic compounds such as pyrene derivatives (pyrene, 1-chloropyrene, 1-hydroxypyrene, (1-p…

Front Cover: The Scope of Application of Macrocyclic Polyamines Beyond Metal Chelation (Eur. J. Org. Chem. 36/2019)

2019

International audience