Search results for: topological optimization

Authors: Kostas Metaxiotis

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Portfolio optimization is one of the most important topics in finance. This paper proposes a mean–variance–skewness (MVS) portfolio optimization model. Traditionally, the portfolio optimization problem is solved by using the mean–variance (MV) framework. In this study, we formulate the proposed model as a three-objective optimization problem, where the portfolio's expected return and skewness are maximized whereas the portfolio risk is minimized. For solving the proposed three-objective portfolio optimization model we apply an adapted version of the non-dominated sorting genetic algorithm (NSGAII). Finally, we use a real dataset from FTSE-100 for validating the proposed model.

Keywords: evolutionary algorithms, portfolio optimization, skewness, stock selection

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Authors: Shael Brown, Reza Farivar

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Persistence diagrams capture valuable topological features of datasets that other methods cannot uncover. Still, their adoption in data pipelines has been limited due to the lack of publicly available tools in R (and python) for analyzing groups of them with machine learning and statistical inference. In an easy-to-use and scalable R package called TDApplied, we implement several applied analysis methods tailored to groups of persistence diagrams. The two main contributions of our package are comprehensiveness (most functions do not have implementations elsewhere) and speed (shown through benchmarking against other R packages). We demonstrate applications of the tools on simulated data to illustrate how easily practical analyses of any dataset can be enhanced with topological information.

Keywords: machine learning, persistence diagrams, R, statistical inference

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Authors: Shai Sarussi

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Let S be an integral domain with field of fractions F and let A be an F-algebra. An S-subalgebra R of A is called S-nice if R∩F = S and the localization of R with respect to S \{0} is A. Denoting by W the set of all S-nice subalgebras of A, and defining a notion of open sets on W, one can view W as a T0-Alexandroff space. Thus, the algebraic structure of W can be viewed from the point of view of topology. It is shown that every nonempty open subset of W has a maximal element in it, which is also a maximal element of W. Moreover, a supremum of an irreducible subset of W always exists. As a notable connection with valuation theory, one considers the case in which S is a valuation domain and A is an algebraic field extension of F; if S is indecomposed in A, then W is an irreducible topological space, and W contains a greatest element.

Keywords: integral domains, Alexandroff topology, prime spectrum of a ring, valuation domains

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Authors: Serges Mendomo Meye, Li Guowei, Shen Zhenzhong, Gan Lei, Xu Liqun

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Given the limitations of the original whale optimization algorithm (WAO) in local optimum and low convergence accuracy in truss structure optimization problems, based on the fundamental whale algorithm, an improved whale optimization algorithm (SWAO) based on information entropy is proposed. The information entropy itself is an uncertain measure. It is used to control the range of whale searches in path selection. It can overcome the shortcomings of the basic whale optimization algorithm (WAO) and can improve the global convergence speed of the algorithm. Taking truss structure as the optimization research object, the mathematical model of truss structure optimization is established; the cross-sectional area of truss is taken as the design variable; the objective function is the weight of truss structure; and an improved whale optimization algorithm (SWAO) is used for optimization design, which provides a new idea and means for its application in large and complex engineering structure optimization design.

Keywords: information entropy, structural optimization, truss structure, whale algorithm

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Authors: Ramin Javadzadeh

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The particle swarm optimization are Meta heuristic optimization method, which are used for clustering and pattern recognition applications are abundantly. These algorithms in multimodal optimization problems are more efficient than genetic algorithms. A major drawback in these algorithms is their slow convergence to global optimum and their weak stability can be considered in various running of these algorithms. In this paper, improved Particle swarm optimization is introduced for the first time to overcome its problems. The fuzzy cellular automata is used for improving the algorithm efficiently. The credibility of the proposed approach is evaluated by simulations, and it is shown that the proposed approach achieves better results can be achieved compared to the Particle swarm optimization algorithms.

Keywords: cellular automata, cellular learning automata, local search, optimization, particle swarm optimization

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Authors: María L. Jalón, Feargal Brennan

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A non-stationary stochastic optimization methodology is applied to an OWC (oscillating water column) to find the design that maximizes the wave energy extraction. Different temporal cycles are considered to represent the long-term variability of the wave climate at the site in the optimization problem. The results of the non-stationary stochastic optimization problem are compared against those obtained by a stationary stochastic optimization problem. The comparative analysis reveals that the proposed non-stationary optimization provides designs with a better fit to reality. However, the stationarity assumption can be adequate when looking at averaged system response.

Keywords: non-stationary stochastic optimization, oscillating water, temporal variability, wave energy

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Authors: Liudmyla Koliechkina, Olena Dvirna

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The statement of the multi-objective optimization problem on combinatorial configurations is formulated, and the approach to its solution is proposed. The problem is of interest as a combinatorial optimization one with many criteria, which is a model of many applied tasks. The approach to solving the multi-objective optimization problem on combinatorial configurations consists of two stages; the first is the reduction of the multi-objective problem to the single criterion based on existing multi-objective optimization methods, the second stage solves the directly replaced single criterion combinatorial optimization problem by the horizontal combinatorial method. This approach provides the optimal solution to the multi-objective optimization problem on combinatorial configurations, taking into account additional restrictions for a finite number of steps.

Keywords: discrete set, linear combinatorial optimization, multi-objective optimization, Pareto solutions, partial permutation set, structural graph

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Authors: R. M. Rizk-Allah

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This paper presents co-evolutionary fruit fly optimization algorithm based on firefly algorithm (CFOA-FA) for solving unconstrained optimization problems. The proposed algorithm integrates the merits of fruit fly optimization algorithm (FOA), firefly algorithm (FA) and elite strategy to refine the performance of classical FOA. Moreover, co-evolutionary mechanism is performed by applying FA procedures to ensure the diversity of the swarm. Finally, the proposed algorithm CFOA- FA is tested on several benchmark problems from the usual literature and the numerical results have demonstrated the superiority of the proposed algorithm for finding the global optimal solution.

Keywords: firefly algorithm, fruit fly optimization algorithm, unconstrained optimization problems

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Authors: Ahmed Fradi

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In a digital world in perpetual evolution and acceleration, data more and more voluminous, rich and varied, the new software solutions emerged with the Big Data phenomenon offer new opportunities to the company enabling it not only to optimize its business and to evolve its production model, but also to reorganize itself to increase competitiveness and to identify new strategic axes. Design and manufacturing industrial companies, like the others, face these challenges, data represent a major asset, provided that they know how to capture, refine, combine and analyze them. The objective of our paper is to propose a solution allowing geometric and topological information extraction from 3D CAD model (precisely STEP files) databases, with specific algorithm based on the programming paradigm MapReduce. Our proposal is the first step of our future approach to 3D CAD object retrieval.

Keywords: Big Data, MapReduce, 3D object retrieval, CAD, STEP format

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Authors: Pham Van Nha, Le Cam Binh

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Particle swarm optimization (PSO) is a population-based stochastic optimization algorithm. PSO was inspired by the natural behavior of birds and fish in migration and foraging for food. PSO is considered as a multidisciplinary optimization model that can be applied in various optimization problems. PSO’s ideas are simple and easy to understand but PSO is only applied in simple model problems. We think that in order to expand the applicability of PSO in complex problems, PSO should be described more explicitly in the form of a mathematical model. In this paper, we represent PSO in a mathematical model and apply in the multivariate data classification. First, PSOs general mathematical model (MPSO) is analyzed as a universal optimization model. Then, Model of Optimal Centroids (MOC) is proposed for the multivariate data classification. Experiments were conducted on some benchmark data sets to prove the effectiveness of MOC compared with several proposed schemes.

Keywords: analysis of optimization, artificial intelligence based optimization, optimization for learning and data analysis, global optimization

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Authors: Nadia Ezzat Al-Kirbasee, Ahlam Hussein Hassan, Shatha Raheem Helal Alhimidi, Doaa Ezzat Al-Kirbasee, Muhsen Abood Muhsen Al-Ibadi

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Through DFT/QTAIM calculations, we have provided new insights into the nature of the M-M, M-H, M-O, and M-C bonds of the (Cp*Ru)n(Cp*Os)3−n(μ3-O)2(μ-H)(Cp* = η5-C5Me5, n= 3,2,1,0). The topological analysis of the electron density reveals important details of the chemical bonding interactions in the clusters. Calculations confirm the absence of bond critical points (BCP) and the corresponding bond paths (BP) between Ru-Ru, Ru-Os, and Os-Os. The position of bridging hydrides and Oxo atoms coordinated to Ru-Ru, Ru-Os, and Os-Os determines the distribution of the electron densities and which strongly affects the formation of the bonds between these transition metal atoms. On the other hand, the results confirm that the four clusters contain a 6c–12e and 4c–2e bonding interaction delocalized over M3(μ-H)(μ-O)2 and M3(μ-H), respectively, as revealed by the non-negligible delocalization indexes calculations. The small values for electron density ρ(b) above zero, together with the small values, again above zero, for laplacian ∇2ρ(b) and the small negative values for total energy density H(b) are shown by the Ru-H, Os-H, Ru-O, and Os-O bonds in the four clusters are typical of open shell interactions. Also, the topological data for the bonds between Ru and Os atoms with the C atoms of the pentamethylcyclopentadienyl (Cp*) ring ligands are basically similar and show properties very consistent with open shell interactions in the QTAIM classification.

Keywords: metal-metal and metal-ligand interactions, organometallic complexes, topological analysis, DFT and QTAIM analyses

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Authors: Vishaal Subramanian, Annuatha Vinod Kumar, Santosh Kumar Budankayala, M. Senthil Kumar

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This paper discusses the aerodynamic and structural design, simulation and optimization of a mini-High Altitude Long Endurance (HALE) UAV. The applications of this mini HALE UAV vary from aerial topological surveys, quick first aid supply, emergency medical blood transport, search and relief activates to border patrol, surveillance and estimation of forest fire progression. Although classified as a mini UAV according to UVS International, our design is an amalgamation of the features of ‘mini’ and ‘HALE’ categories, combining the light weight of the ‘mini’ and the high altitude ceiling and endurance of the HALE. Designed with the idea of implementation in India, it is in strict compliance with the UAS rules proposed by the office of the Director General of Civil Aviation. The plane can be completely automated or have partial override control and is equipped with an Infra-Red camera and a multi coloured camera with on-board storage or live telemetry, GPS system with Geo Fencing and fail safe measures. An additional of 1.5 kg payload can be attached to three major hard points on the aircraft and can comprise of delicate equipment or releasable payloads. The paper details the design, optimization process and the simulations performed using various software such as Design Foil, XFLR5, Solidworks and Ansys.

Keywords: aircraft, endurance, HALE, high altitude, long range, UAV, unmanned aerial vehicle

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Authors: Sait Ali Uymaz, Gülay Tezel

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This paper presents the comparison results on the performance of the Cuckoo Search (CS) algorithm for constrained optimization problems. For constraint handling, CS algorithm uses penalty method. CS algorithm is tested on thirteen well-known test problems and the results obtained are compared to Particle Swarm Optimization (PSO) algorithm. Mean, best, median and worst values were employed for the analyses of performance.

Keywords: cuckoo search, particle swarm optimization, constrained optimization problems, penalty method

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Authors: Takahiro Hino, Michiharu Maeda

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Particle swarm optimization (PSO) is an optimization approach that achieves the social model of bird flocking and fish schooling. PSO works in continuous space and can solve continuous optimization problem with high quality. Set-based particle swarm optimization (SPSO) functions in discrete space by using a set. SPSO can solve combinatorial optimization problem with high quality and is successful to apply to the large-scale problem. In this paper, we present an algorithm of SPSO with status memory to decide the position based on the previous position for solving traveling salesman problem (TSP). In order to show the effectiveness of our approach. We examine SPSOSM for TSP compared to the existing algorithms.

Keywords: combinatorial optimization problems, particle swarm optimization, set-based particle swarm optimization, traveling salesman problem

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Authors: Sanja Podunavac-Kuzmanović, Strahinja Kovačević, Lidija Jevrić, Evgenija Djurendić, Jovana Ajduković

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In the present study, the molecular modeling of a series of 24 17-picolyl and 17-picolinylidene androstane derivatives whit significant anticancer activity was carried out. Modelling of studied compounds was performed by CS ChemBioDraw Ultra v12.0 program for drawing 2D molecular structures and CS ChemBio3D Ultra v12.0 for 3D molecular modelling. The obtained 3D structures were subjected to energy minimization using molecular mechanics force field method (MM2). The cutoff for structure optimization was set at a gradient of 0.1 kcal/Åmol. Full geometry optimization was done by the Austin Model 1 (AM1) until the root mean square (RMS) gradient reached a value smaller than 0.0001 kcal/Åmol using Molecular Orbital Package (MOPAC) program. The obtained physicochemical, lipophilicity and topological descriptors were used for analysis of molecular similarities and dissimilarities applying suitable chemometric methods (principal component analysis and cluster analysis). These results are the part of the project No. 114-451-347/2015-02, financially supported by the Provincial Secretariat for Science and Technological Development of Vojvodina and CMST COST Action CM1306.

Keywords: androstane derivatives, anticancer activity, chemometrics, molecular descriptors

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Authors: D. Li

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Optical thin films are used in a wide variety of optical components and there are many software tools programmed for advancing multilayer thin film design. The available software packages for designing the thin film structure may not provide optimum designs. Normally, almost all current software programs obtain their final designs either from optimizing a starting guess or by technique, which may or may not involve a pseudorandom process, that give different answers every time, depending upon the initial conditions. With the increasing power of personal computers, functional methods in optimization and synthesis of optical multilayer systems have been developed such as DGL Optimization, Simulated Annealing, Genetic Algorithms, Needle Optimization, Inductive Optimization and Flip-Flop Optimization. Among these, DGL Optimization has proved its efficiency in optical thin film designs. The application of the DGL optimization technique to the design of optical coating is presented. A DGL optimization technique is provided, and its main features are discussed. Guidelines on the application of the DGL optimization technique to various types of design problems are given. The innovative global optimization strategies used in a software tool, OnlyFilm, to optimize multilayer thin film designs through different filter designs are outlined. OnlyFilm is a powerful, versatile, and user-friendly thin film software on the market, which combines optimization and synthesis design capabilities with powerful analytical tools for optical thin film designers. It is also the only thin film design software that offers a true global optimization function.

Keywords: optical coatings, optimization, design software, thin film design

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Authors: O. Mohamed Amine, A. Khireddine

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Telecoms operators are always looking to meet their share of the other customers, they try to gain optimum utilization of the deployed equipment and network optimization has become essential. This project consists of optimizing UMTS network, and the study area is an urban area situated in the center of Algiers. It was initially questions to become familiar with the different communication systems (3G) and the optimization technique, its main components, and its fundamental characteristics radios were introduced.

Keywords: UMTS, UTRAN, WCDMA, optimization

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Authors: Francisco Bulnes

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Through the Fukaya conjecture and the wrapped Floer cohomology, the correspondences between paths in a loop space and states of a wrapping space of states in a Hamiltonian space (the ramification of field in this case is the connection to the operator that goes from TM to T*M) are demonstrated where these last states are corresponding to bosonic extensions of a spectrum of the space-time or direct image of the functor Spec, on space-time. This establishes a distinguished diffeomorphism defined by the mapping from the corresponding loops space to wrapping category of the Floer cohomology complex which furthermore relates in certain proportion D-branes (certain D-modules) with strings. This also gives to place to certain conjecture that establishes equivalences between moduli spaces that can be consigned in a moduli identity taking as space-time the Hitchin moduli space on G, whose dual can be expressed by a factor of a bosonic moduli spaces.

Keywords: Floer cohomology, Fukaya conjecture, Lagrangian submanifolds, quantum topological diffeomorphism

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Authors: Wu Qinglong, Zhou Qicai, Xiong Xiaolei, Zhang Richeng

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In order to achieve the layout and size optimization of the web members of tower crane boom, a truss topology and cross section size optimization method based on continuum is proposed considering three typical working conditions. Firstly, the optimization model is established by replacing web members with web plates. And the web plates are divided into several sub-domains so that periodic soft kill option (SKO) method can be carried out for topology optimization of the slender boom. After getting the optimized topology of web plates, the optimized layout of web members is formed through extracting the principal stress distribution. Finally, using the web member radius as design variable, the boom compliance as objective and the material volume of the boom as constraint, the cross section size optimization mathematical model is established. The size optimization criterion is deduced from the mathematical model by Lagrange multiplier method and Kuhn-Tucker condition. By comparing the original boom with the optimal boom, it is identified that this optimization method can effectively lighten the boom and improve its performance.

Keywords: tower crane boom, topology optimization, size optimization, periodic, SKO, optimization criterion

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Authors: Mengxiao Li, Johnson Zhang

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Currently, topology optimization technique is widely used to define the layout design of structures that are presented as truss-like topologies. However, due to the difficulty in combining optimization technique with more realistic material models where their nonlinear properties should be considered, the achieved optimized topologies are commonly unable to apply straight towards the practical design problems. This study presented an optimization procedure of composite structures where different elastic stiffness, yield criteria, and hardening models are assumed for the candidate materials. From the results, it can be concluded that a more explicit modeling has the significant influence on the resulting topologies. Also, the isotropic or kinematic hardening is important for elastoplastic structural optimization design. The capability of the proposed optimization procedure is shown through several cases.

Keywords: topology optimization, material composition, nonlinear modeling, hardening rules

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Authors: Akintayo E. Akinsunmade

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The digestion optimization algorithm is a novel biological-inspired metaheuristic method for solving complex optimization problems. The algorithm development was inspired by studying the human digestive system. The algorithm mimics the process of food ingestion, breakdown, absorption, and elimination to effectively and efficiently search for optimal solutions. This algorithm was tested for optimal solutions on seven different types of optimization benchmark functions. The algorithm produced optimal solutions with standard errors, which were compared with the exact solution of the test functions.

Keywords: bio-inspired algorithm, benchmark optimization functions, digestive system in human, algorithm development

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Authors: S. Adhirai, R. P. Mahapatra, Paramjit Singh

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Optimization is an important tool in making decisions and in analysing physical systems. In mathematical terms, an optimization problem is the problem of finding the best solution from among the set of all feasible solutions. The paper discusses the Whale Optimization Algorithm (WOA), and its applications in different fields. The algorithm is tested using MATLAB because of its unique and powerful features. The benchmark functions used in WOA algorithm are grouped as: unimodal (F1-F7), multimodal (F8-F13), and fixed-dimension multimodal (F14-F23). Out of these benchmark functions, we show the experimental results for F7, F11, and F19 for different number of iterations. The search space and objective space for the selected function are drawn, and finally, the best solution as well as the best optimal value of the objective function found by WOA is presented. The algorithmic results demonstrate that the WOA performs better than the state-of-the-art meta-heuristic and conventional algorithms.

Keywords: optimization, optimal value, objective function, optimization problems, meta-heuristic optimization algorithms, Whale Optimization Algorithm, implementation, MATLAB

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Authors: Mazura Mokhtar, Adibah Shuib, Daud Mohamad

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Portfolio optimization problem has received a lot of attention from both researchers and practitioners over the last six decades. This paper provides an overview of the current state of research in portfolio optimization with the support of mathematical programming techniques. On top of that, this paper also surveys the solution algorithms for solving portfolio optimization models classifying them according to their nature in heuristic and exact methods. To serve these purposes, 40 related articles appearing in the international journal from 2003 to 2013 have been gathered and analyzed. Based on the literature review, it has been observed that stochastic programming and goal programming constitute the highest number of mathematical programming techniques employed to tackle the portfolio optimization problem. It is hoped that the paper can meet the needs of researchers and practitioners for easy references of portfolio optimization.

Keywords: portfolio optimization, mathematical programming, multi-objective programming, solution approaches

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Authors: Masoud Charkhabi

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We examine trade theory with this motivation. The full set of World Trade Organization data are organized into country-year pairs, each treated as a different entity. Topological Data Analysis reveals that among the 16 region and 240 region-year pairs there exists in fact a distinguishable group of region-period pairs. The generally accepted periods of shifts from dissimilar-dissimilar to similar-similar trade in goods among regions are examined from this new perspective. The period breaks are treated as cumulative and are flexible. This type of all-subsets analysis is motivated from computer science and is made possible with Lossy Compression and Graph Theory. The results question many patterns in similar-similar to dissimilar-dissimilar trade. They also show indications of economic shifts that only later become evident in other economic metrics.

Keywords: econometrics, globalization, network science, topological data, analysis, trade theory, visualization, world trade

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Authors: Elham Kazemi

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Quadratic Assignment Problem (QAP) is one the combinatorial optimization problems about which research has been done in many companies for allocating some facilities to some locations. The issue of particular importance in this process is the costs of this allocation and the attempt in this problem is to minimize this group of costs. Since the QAP’s are from NP-hard problem, they cannot be solved by exact solution methods. Cuckoo Optimization Algorithm is a Meta-heuristicmethod which has higher capability to find the global optimal points. It is an algorithm which is basically raised to search a continuous space. The Quadratic Assignment Problem is the issue which can be solved in the discrete space, thus the standard arithmetic operators of Cuckoo Optimization Algorithm need to be redefined on the discrete space in order to apply the Cuckoo Optimization Algorithm on the discrete searching space. This paper represents the way of discretizing the Cuckoo optimization algorithm for solving the quadratic assignment problem.

Keywords: Quadratic Assignment Problem (QAP), Discrete Cuckoo Optimization Algorithm (DCOA), meta-heuristic algorithms, optimization algorithms

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Authors: Liubov Magerramova, Mikhail Petrov, Vladimir Isakov, Liana Shcherbinina, Suren Gukasyan, Daniil Povalyukhin, Olga Klimova-Korsmik, Darya Volosevich

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Aircraft engines are developing along the path of increasing resource, strength, reliability, and safety. The building of gas turbine engine body parts is a complex design and technological task. Particularly complex in the design and manufacturing are the casings of the input stages of helicopter gearboxes and central drives of aircraft engines. Traditional technologies, such as precision casting or isothermal forging, are characterized by significant limitations in parts production. For parts like housing, additive technologies guarantee spatial freedom and limitless or flexible design. This article presents the results of computational and experimental studies. These investigations justify the applicability of additive technologies (AT) to reduce the weight of aircraft housing gearbox parts by up to 32%. This is possible due to geometrical optimization compared to the classical, less flexible manufacturing methods and as-casted aircraft parts with over-insured values of safety factors. Using an example of the body of the input stage of an aircraft gearbox, visualization of the layer-by-layer manufacturing of a part based on thermal deformation was demonstrated.

Keywords: additive technologies, gas turbine engines, topological optimization, synthesis process

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Authors: Felipe Haro, Soheila Antar

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This paper introduces a custom optimization experiment developed in AnyLogic, based on genetic algorithms, designed to ensure reliable optimization results by incorporating Montecarlo simulations and achieving a specified confidence level. To validate the custom experiment, we compared its performance with AnyLogic's built-in OptQuest optimization method across three distinct problems. Statistical analyses, including Welch's t-test, were conducted to assess the differences in performance. The results demonstrate that while the custom experiment shows advantages in certain scenarios, both methods perform comparably in others, confirming the custom approach as a reliable and effective tool for optimization under uncertainty.

Keywords: optimization, confidence intervals, Montecarlo simulation, optQuest, AnyLogic

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Authors: Orhun Aydin, Mark V. Janikas, Rodrigo Alves, Renato Assuncao

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In this paper, a tree-based perturbation methodology for regionalization inference is presented. Regionalization is a constrained optimization problem that aims to create groups with similar attributes while satisfying spatial contiguity constraints. Similar to any constrained optimization problem, the spatial constraint may hinder convergence to some global minima, resulting in spatially contiguous members of a group with dissimilar attributes. This paper presents a general methodology for rigorously perturbing spatial constraints through the use of random spanning trees. The general framework presented can be used to quantify the effect of the spatial constraints in the overall regionalization result. We compare several types of stochastic spanning trees used in inference problems such as fuzzy regionalization and determining the number of regions. Performance of stochastic spanning trees is juxtaposed against the traditional permutation-based hypothesis testing frequently used in spatial statistics. Inference results for fuzzy regionalization and determining the number of regions is presented on the Local Area Personal Incomes for Texas Counties provided by the Bureau of Economic Analysis.

Keywords: regionalization, constrained clustering, probabilistic inference, fuzzy clustering

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Authors: Mohammad Saeed Bahramy

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Transition metal dichalcogenides have experienced a resurgence of interest in the past few years owing to their rich properties, ranging from metals and superconductors to strongly spin-orbit-coupled semiconductors and charge-density-wave systems. In all these cases, the transition metal d-electrons mainly determine the ground state properties. This presentation focuses on the chalcogen-derived states. Combining density-functional theory calculations with spin- and angle-resolved photoemission, it is shown that these states generically host a coexistence of type I and type II three-dimensional bulk Dirac fermions as well as ladders of topological surface states and surface resonances. It will be discussed how these naturally arise within a single p-orbital manifold as a general consequence of a trigonal crystal field, and as such can be expected across many compounds. Our finding opens a new route to design topological materials with advanced functionalities.

Keywords: topology, electronic structure, Dirac semimetals, transition metal dichalcogenides

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Authors: Sourabh Joshi, Tarun Sharma, Anurag Sharma

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Ant Colony Optimization is heuristic Algorithm which has been proven a successful technique applied on number of combinatorial optimization problems. Two variants of Ant Colony Optimization algorithm named Ant System and Max-Min Ant System are implemented in MATLAB to solve travelling Salesman Problem and the results are compared. In, this paper both systems are analyzed by solving the some Travelling Salesman Problem and depict which system solve the problem better in term of cost and time.

Keywords: Ant Colony Optimization, Travelling Salesman Problem, Ant System, Max-Min Ant System

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