Travelling Salesman Problem Solved ‘in materio’ by Evolved Carbon Nanotube Device

Composite structures of single walled carbon nanotubes (SWNTs) and poly(3-octylthiophene) polymer were tested as field emitters. The structures studied were formed on n+-Si by mixing the two materials after they had been dissolved in chloroform. Three different structures were tested: (a) a SWNT mat, (b) a SWNT mat on a SWNT (30 wt %)–polymer composite and (c) a SWNT mat on pure polymer. Although the conductivity of the composite is very much lower than that of the nanotube mat, experiments show that the field emission threshold is lower and the emission current higher from structure (b) compared to the pure SWNT mat on n+-Si. A comparison between the field enhancement factors and the expected aspect ratios shows that enhancement due to an additional field enhancement mechanism other than that due to the geometrical shape of the SWNTs must exist. We propose that the field due to the surface potential modification at the triple junction between SWNTs, polymer and vacuum is adequate to create additional field emission from such sites. This mechanism can also be used to explain previously reported field emission characteristics of CNx nanocomposite films.

Optical nanoscale technologies often implement covalent or noncovalent strategies for the modification of nanoparticles, whereby both functionalizations are leveraged for multimodal applications but can affect the intrinsic fluorescence of nanoparticles. Specifically, single‐walled carbon nanotubes (SWCNTs) can enable real‐time imaging and cellular delivery; however, the introduction of covalent SWCNT sidewall functionalizations often attenuates SWCNT fluorescence. Recent advances in SWCNT covalent functionalization chemistries preserve the SWCNT's pristine graphitic lattice and intrinsic fluorescence, and here, such covalently functionalized SWCNTs maintain intrinsic fluorescence‐based molecular recognition of neurotransmitter and protein analytes. The covalently modified SWCNT nanosensor preserves its fluorescence response towards its analyte for certain nanosensors, presumably dependent on the intermolecular interactions between SWCNTs or the steric hindrance introduced by the covalent functionalization that hinders noncovalent interactions with the SWCNT surface. These SWCNT nanosensors are further functionalized via their covalent handles with a targeting ligand, biotin, to self‐assemble on passivated microscopy slides, and these dual‐functionalized SWCNT materials are explored for future use in multiplexed sensing and imaging applications.

The traveling salesman problem (TSP) is a fundamental problem in combinatorial optimization. Several semidefinite programming relaxations have been proposed recently that exploit a variety of mathematical structures including, for example, algebraic connectivity, permutation matrices, and association schemes. The main results of this paper are twofold. First, de Klerk and Sotirov [de Klerk E, Sotirov R (2012) Improved semidefinite programming bounds for quadratic assignment problems with suitable symmetry. Math. Programming 133(1):75–91.] present a semidefinite program (SDP) based on permutation matrices and symmetry reduction; they show that it is incomparable to the subtour elimination linear program but generally dominates it on small instances. We provide a family of simplicial TSP instances that shows that the integrality gap of this SDP is unbounded. Second, we show that these simplicial TSP instances imply the unbounded integrality gap of every SDP relaxation of the TSP mentioned in the survey on SDP relaxations of the TSP in section 2 of Sotirov [Sotirov R (2012) SDP relaxations for some combinatorial optimization problems. Anjos MF, Lasserre JB, eds., Handbook on Semidefinite, Conic and Polynomial Optimization (Springer, New York), 795–819.]. In contrast, the subtour linear program performs perfectly on simplicial instances. The simplicial instances thus form a natural litmus test for future SDP relaxations of the TSP.

This chapter presents an evolutionary approach for solving the traveling salesman problem (TSP) and the TSP with backhauls (TSPB). We propose two evolutionary algorithms for solving the difficult TSPs. Our focus is on developing evolutionary operators based on conventional heuristics. We rely on a set of detailed computational experiments and statistical tests for developing an effective algorithm.The chapter starts with a careful survey of the algorithms for the TSP and the TSPB, with a special emphasis on crossover and mutation operators and applications on benchmark test instances. The second part addresses our first evolutionary algorithm. We explore the use of two tour construction heuristics, nearest neighbor and greedy, in developing new crossover operators.We focus on preserving the edges in the union graph constructed by edges of the parent tours.We let the heuristics exploit the building blocks found in this graph. This way, new solutions can inherit good blocks from both parents. We also combine the two crossover operators together in generating offspring to explore the potential gain due to synergy. In addition, we make use of 2-edge exchange moves as the mutation operator to incorporate more problem specific information in the evolution process. Our reproduction strategy is based on the generational approach. Experimental results indicate that our operators are promising in terms of both solution quality and computation time.In the third part of the chapter, we present the second evolutionary algorithm developed. This part can be thought of as an enhancement of the first algorithm. A common practice with such algorithms is to generate one child or two children from two parents. In the second implementation, we investigate the preservation of good edges available in more than two parents and generate multiple children.We use the steady-state evolution as a reproduction strategy this time and test the replacement of the worst parent or the worst population member to find the better replacement strategy. Our two mutation operators try to eliminate the longest and randomly selected edges and a third operator makes use of the cheapest insertion heuristic. The algorithm is finalized after conducting a set of experiments for best parameter settings and testing on larger TSPLIB instances. The second evolutionary algorithm is also implemented for solving randomly generated instances of the TSPB. Our experiments reveal that the algorithm is significantly better than the competitors in the literature. The last part concludes the chapter.KeywordsNetworks-GraphsTraveling Salesman ProblemsEvolutionary AlgorithmsCrossover OperatorMutation OperatorHeuristics

The Traveling Salesman Problem (TSP) is an NP-hard graph search problem. Despite having numerous modifications of the original abstract problem, Time Dependent Traveling Salesman Problem (TD TSP) was one of the most realistic extensions under real traffic conditions. In TD TSP the edges between nodes are assigned higher costs (weights), if they were traveled during the rush hour periods, or crossed the traffic jam regions, such as the city center(s). In this paper we introduce an even more real-life motivated approach, the Intuitionistic Fuzzy Time Dependent Traveling Salesman Problem (IFTD TSP), which is a further extension of the TSP, and also of the classic TD TSP, with the additional notion of using intuitionistic fuzzy sets for the definition of uncertain costs, time, and space of the rush hour—traffic jam region affecting graph sections. In IFTD TSP we use fuzzy memberships and non-memberships sets for estimating the vague costs between nodes in order to quantify the behavior of traffic jam regions, and the rush hour periods. Since intuitionistic fuzzy sets are generalizations of classic fuzzy sets, our approach may be considered an extension and substitution of the original abstract TD TSP problem, even, of the (classic) Fuzzy TD TSP. Lastly, DBMEA (Discrete Bacterial Memetic Evolutionary Algorithm) was applied on the IFTD TSP model, the results of the simulation runs based on some extensions of the benchmarks generated from the original TD TSP data set showed quite good and promising preliminary results.

Removal of harmful chemicals from water is paramount to environmental cleanliness and safety. As such, need for materials that will serve this purpose is in the forefront of environmental research that pertains to water purification. Here we show that bundles of single walled carbon nanotubes (SWNTs), synthesized by direct thermal decomposition of ferrocene (Fe(C5H5)2), can remove emerging contaminants like benzoic acid from water with high efficiencies. Experimental adsorption isotherm studies indicate that the sorption capacity of benzoic acid on these carbon nanotubes (CNTs) can be as high as 375 mg/g, which is significantly higher (in some cases an order of magnitude) than those reported previously for other adsorbents of benzoic acid such as activated carbon cloth, modified bentonite and commercially available graphitized multiwall carbon nanotubes (MWNTs). Our Molecular Dynamics (MD) simulation studies of experimental scenarios provided major insights related to this process of adsorption. The MD simulations indicate that, high binding energy sites present in SWNT bundles are majorly responsible for their enhanced adsorptive behavior compared to isolated MWNTs. These findings indicate that SWNT materials can be developed as scalable materials for efficient removal of environmental contaminants as well as for other sorption-based applications.

: A covalent, amide-bond interconnection between functionalized single-wall carbon nanotubes (SWNTs) is reported. SWNTs covalently connected via an amide bond were prepared by coupling the carboxylic acid group from one SWNT with the amine group on a different SWNT using DMAP and DCC reagents. The SWNT material was characterized by ATR FT-IR, Ramen Spectroscopy and Thermogravimetric Analysis (TGA). The amide functionalized SWNTs have potential to make polymeric-like materials and have applications in high strength nanocomposites.

The probabilistic travelling salesman problem (PTSP) is an extension of the well-known travelling salesman problem (TSP), which has been extensively studied in the field of combinatorial optimization. The goal of the TSP is to find the minimum length of a tour to all customers, given the distances between all pairs of customers whereas the objective of the PTSP is to minimize the expected length of the a priori tour where each customer requires a visit only with a given probability (Bertsimas, 1988; Bertsimas et al., 1990; Jaillet, 1985). The main difference between the PTSP and the TSP is that in the PTSP the probability of each node being visited is between 0.0 and 1.0 while in TSP the probability of each node being visited is 1.0. Due to the fact that the element of uncertainty not only exists, but also significantly affects the system performance in many real-world transportation and logistics applications, the results from the PTSP can provide insights into research in other probabilistic combinatorial optimization problems. Moreover, the PTSP can also be used to model many real-world applications in logistical and transportation planning, such as daily pickup-delivery services with stochastic demand, job sequencing involving changeover cost, design of retrieval sequences in a warehouse or in a cargo terminal operations, meals on wheels in senior citizen services, trip-chaining activities, vehicle routing problem with stochastic demand, and home delivery service under e-commerce (Bartholdi et al., 1983; Bertsimas et al., 1995; Campbell, 2006; Jaillet, 1988; Tang & Miller-Hooks, 2004). Early PTSP computational studies, dating from 1985, adopted heuristic approaches that were modified from the TSP (e.g., nearest neighbor, savings approach, spacefilling curve, radial sorting, 1-shift, and 2-opt exchanges) (Bartholdi & Platzman, 1988; Bertsimas, 1988; Bertsimas & Howell, 1993; Jaillet, 1985, 1987; Rossi & Gavioli, 1987). With its less than satisfactory performance in yielding solution quality, researchers in the recent years switch to metaheuristic methods, such as ant colony optimization (Bianchi, 2006; Branke & Guntsch, 2004), evolutionary algorithm (Liu et al., 2007), simulated annealing (Bowler et al., 2003), threshold accepting (Tang & Miller-Hooks, 2004) and scatter search (Liu, 2006, 2007, 2008). Because the genetic algorithm (GA), a conceptual framework of the population-based metaheuristic method, has been shown to yield promising outcomes for solving various complicated optimization problems in the past three decades (Back et al., 1997; Davis, 1991; O pe n A cc es s D at ab as e w w w .ite ch on lin e. co m

This paper presents the performance evaluation for the simulation modeling approach of single-walled carbon nanotube (SWCNT) dipole antenna at THz and GHz frequency regimes. The equivalent nano-solid tube material (NSTM) modeling approach to the SWCNT is implemented into CST (MWS) software package. Where, the raw material of the NSTM model is derived from SWCNT material rather from other metal material. The comparison between NSTM modeling approach and related previous works is presented for the purpose of validation this model and investigate the behavior assessment of SWCNT dipole antenna. The results of this paper shows the good agreement between the NSTM dipole antenna and the SWCNT dipole antenna. This modeling approach will be utilized to estimate the SWCNT dipole antenna parameters, for instance, s11 parameters, radiation pattern and phase velocity. Finally, this modeling approach is presented to make possible to design and investigate different kinds of SWCNT antennas, which are significant in several area of applications.

We propose an evolutionary algorithm (EA) that applies to the traveling salesman problem (TSP). The EA uses edge assembly crossover (EAX), which is known to be efficient and effective for solving TSPs. Recently, a fast implementation of EAX and an effective technique for preserving population diversity were proposed. This makes it possible to compare the EA with EAX comparable to state-of-the-art TSP heuristics based on Lin-Karnighan heuristics. We further improved the performance of EAs with EAX, especially for large instances of more than 10,000 cities. Our method can find optimal solutions for instances of up to 24978 cities within a day using a single Itanium 2 1.3-GHz processor. Moreover, our EA found three new best tours for unsolved national TSP instances in a reasonable computation time.

In view of Traveling Salesman Problem (TSP) is a NP hard problem, Lion Swarm Optimization (LSO) Algorithm is a new swarm intelligence optimization algorithm. Therefore, in this paper, it uses improved hybrid LSO algorithm to solve TSP. Because the basic LSO algorithm is mainly used to solve the continuous problem, and the TSP is a discrete combinatorial optimization problem, this paper improves the LSO algorithm, introduces the greedy strategy, and combines with the Population Competitive Search (PCS) algorithm in the later stage of the search. As a result, the convergence speed is accelerated and the search efficiency is improved. The classic TSP example is tested, and the simulation results show that the algorithm proposed in this paper has strong stability and is an effective method for solving TSP.

Recent work applying deep reinforcement learning (DRL) to solve traveling salesman problems (TSP) has shown that DRL-based solvers can be fast and competitive with TSP heuristics for small instances, but do not generalize well to larger instances. In this work, we propose a novel approach named MAGIC that includes a deep learning architecture and a DRL training method. Our architecture, which integrates a multilayer perceptron, a graph neural network, and an attention model, defines a stochastic policy that sequentially generates a TSP solution. Our training method includes several innovations: (1) we interleave DRL policy gradient updates with local search (using a new local search technique), (2) we use a novel simple baseline, and (3) we apply curriculum learning. Finally, we empirically demonstrate that MAGIC is superior to other DRL-based methods on random TSP instances, both in terms of performance and generalizability. Moreover, our method compares favorably against TSP heuristics and other state-of-the-art approach in terms of performance and computational time.

A unique feature of single-wall carbon nanotube (SWCNT) material is its structure diversity: within the same rolled-up graphene sheet structure framework one finds SWCNTs of different electronic bandgaps: metals with zero bandgap, quasi-metals with meV bandgap and semiconductors with ~ 1 eV bandgap. However, making use of SWCNT structure diversity requires a method to obtain SWCNTs of defined structures. In this contribution, we present our current state of DNA-based sorting of SWCNTs. In particular, we show our ability to put any DNA sequence on any SWCNT species, enabling DNA-based assembly of high-density SWCNT devices. In the end, we discuss the design of a device we call Photon Perceptron Array (PPA). PPA is an array of micron-sized spectrometer units that can measure the spectrum of incoming photon in the wavelength range of 200 nm to 2000 nm (and possibly going all the way to THz), with a spatial resolution comparable to the size of a single spectrometer unit. Each spectrometer unit is composed of a set of distinct photodetectors made of SWCNTs of defined atomic structures, placed in parallel with tube-to-tube separations controlled at nanometer precision by DNA origami technology. A high-density array of identical spectrometers can be constructed by placing DNA origami/carbon nanotube complexes in photolithographically-defined locations. PPA may be used for spectral imaging in many fields of science and technology.

As the traditional evolutionary algorithms for large-scale TSP(Traveling Salesman Problem) produce so huge amount of paths vectors with random that the slow and premature convergence is nearly inevitable,this paper presents a novel evolutional algorithm based on hybrid probability distribution(EABHPD) with area partition strategy. The fundamental idea is to use evolutionary algorithm twice.Firstly the large-scale TSP is divided into several small-scale TSP, then each sub-TSP can be solved with EABHPD.With EABHPD, the rules of mutation are the combination of Gaussian probability distribution,Cauchy probability distribution and t probability distribution. This designed algorithm can get a good compromise of the desired pricision and computation cost, it also can avoid the premature convergence problem of the common evolutionary algorithms.Besides,the efficiency of our approach is manifested by the preliminary simulation experiment .

In a traveling salesman problem (TSP), the contribution of a variable to fitness depends on the state of other variables. This characteristic can be referred to as entire linkage, utilizing which evolutionary algorithms can significantly enhance performance, especially in cases of large scale problems. In this paper, a construction graph-based evolutionary algorithm (CGEA) to learn variable interactions in TSP is presented. The proposed method employs real adjacency matrix-coding based on construction graph to make population individuals as carriers of variable interaction degrees through evolution. Iteratively, variable interactions are discovered by a parameterless search scheme, called matrix recombination-difference. In order to explore features of CGEA, an entire linkage index (ELI) is proposed to measure the entire linkage level of TSP. The experimental results show CGEA is promising for TSP, especially with a high entire linkage level.