Search results for: simulation-based optimization

Authors: Rajesh Bera, Durbadal Mandal, Rajib Kar, Sakti P. Ghoshal

Abstract:

This paper describes optimal thinning of an Elliptical Cylindrical Array (ECA) of uniformly excited isotropic antennas which can generate directive beam with minimum relative Side Lobe Level (SLL). The Particle Swarm Optimization (PSO) method, which represents a new approach for optimization problems in electromagnetic, is used in the optimization process. The PSO is used to determine the optimal set of ‘ON-OFF’ elements that provides a radiation pattern with maximum SLL reduction. Optimization is done without prefixing the value of First Null Beam Width (FNBW). The variation of SLL with element spacing of thinned array is also reported. Simulation results show that the number of array elements can be reduced by more than 50% of the total number of elements in the array with a simultaneous reduction in SLL to less than -27dB.

Keywords: thinned array, Particle Swarm Optimization, Elliptical Cylindrical Array, Side Lobe Label.

Procedia PDF Downloads 443

Authors: Yassir AbdelRazig

Abstract:

Evolutionary optimization methods such as genetic algorithms have been used extensively for the construction site layout problem. More recently, ant colony optimization algorithms, which are evolutionary methods based on the foraging behavior of ants, have been successfully applied to benchmark combinatorial optimization problems. This paper proposes a formulation of the site layout problem in terms of a sequencing problem that is suitable for solution using an ant colony optimization algorithm. In the construction industry, site layout is a very important planning problem. The objective of site layout is to position temporary facilities both geographically and at the correct time such that the construction work can be performed satisfactorily with minimal costs and improved safety and working environment. During the last decade, evolutionary methods such as genetic algorithms have been used extensively for the construction site layout problem. This paper proposes an ant colony optimization model for construction site layout. A simple case study for a highway project is utilized to illustrate the application of the model.

Keywords: ant colony, construction site layout, optimization, genetic algorithms

Procedia PDF Downloads 382

Authors: Nima Khosravi

Abstract:

This paper describes an integrated optimization technique with concurrent use of sequential quadratic programming, genetic algorithm, and simulated annealing particle swarm optimization for the design and optimization of a beam column. In this research, the comparison between 4 different types of optimization methods. The comparison is done and it is found out that all the methods meet the required constraints and the lowest value of the objective function is achieved by SQP, which was also the fastest optimizer to produce the results. SQP is a gradient based optimizer hence its results are usually the same after every run. The only thing which affects the results is the initial conditions given. The initial conditions given in the various test run were very large as compared. Hence, the value converged at a different point. Rest of the methods is a heuristic method which provides different values for different runs even if every parameter is kept constant.

Keywords: beam column, genetic algorithm, particle swarm optimization, sequential quadratic programming, simulated annealing

Procedia PDF Downloads 386

Authors: Talha A. Taj, Talha A. Khan, M. Imran Khalid

Abstract:

Optimization techniques attract researchers to formulate a problem and determine its optimum solution. This paper presents an Enhanced Harmony Search (ENHS) algorithm for solving optimization problems. The proposed algorithm increases the convergence and is more efficient than the standard Harmony Search (HS) algorithm. The paper discusses the novel techniques in detail and also provides the strategy for tuning the decisive parameters that affects the efficiency of the ENHS algorithm. The algorithm is tested on various benchmark functions, a real world optimization problem and a constrained objective function. Also, the results of ENHS are compared to standard HS, and various other optimization algorithms. The ENHS algorithms prove to be significantly better and more efficient than other algorithms. The simulation and testing of the algorithms is performed in MATLAB.

Keywords: optimization, harmony search algorithm, MATLAB, electronic

Procedia PDF Downloads 463

Authors: Pushpendra S. Bharti

Abstract:

Process yield of electric discharge machining (EDM) is directly related to optimal combination(s) of process parameters. Optimization of process parameters of EDM is a multi-objective optimization problem owing to the contradictory behavior of performance measures. This paper employs Grey Relation Analysis (GRA) method as a multi-objective optimization technique for the optimal selection of process parameters combination. In GRA, multi-response optimization is converted into optimization of a single response grey relation grade which ultimately gives the optimal combination of process parameters. Experiments were carried out on die-sinking EDM by taking D2 steel as work piece and copper as electrode material. Taguchi's orthogonal array L36 was used for the design of experiments. On the experimental values, GRA was employed for the parametric optimization. A significant improvement has been observed and reported in the process yield by taking the parametric combination(s) obtained through GRA.

Keywords: electric discharge machining, grey relation analysis, material removal rate, optimization

Procedia PDF Downloads 409

Authors: Mustafa Ural, Can Bayseferogulari

Abstract:

In this work, radio frequency (RF) coupling between two HF antennas on a shipboard platform is minimized by determining an optimal antenna placement. Unlike the other works, the coupling is minimized not only at single frequency but over the whole frequency band of operation. Similarly, GAO and PSO, are used in order to determine optimal antenna placement. Throughout this work, outputs of two optimization techniques are compared with each other in terms of antenna placements and coupling results. At the end of the work, far-field radiation pattern performances of the antennas at their optimal places are analyzed in terms of directivity and coverage in order to see that.

Keywords: electromagnetic compatibility, antenna placement, optimization, genetic algorithm optimization, particle swarm optimization

Procedia PDF Downloads 236

Authors: Houda Abadlia, Nadia Smairi, Khaled Ghedira

Abstract:

Multiobjective Particle Swarm Optimization (MOPSO) has shown an effective performance for solving test functions and real-world optimization problems. However, this method has a premature convergence problem, which may lead to lack of diversity. In order to improve its performance, this paper presents a hybrid approach which embedded the MOPSO into the island model and integrated a local search technique, Variable Neighborhood Search, to enhance the diversity into the swarm. Experiments on two series of test functions have shown the effectiveness of the proposed approach. A comparison with other evolutionary algorithms shows that the proposed approach presented a good performance in solving multiobjective optimization problems.

Keywords: particle swarm optimization, migration, variable neighborhood search, multiobjective optimization

Procedia PDF Downloads 167

Authors: Manas Shah

Abstract:

Black Scholes option pricing model is one of the most important concepts in modern world of computational finance. However, its practical use can be challenging as one of the input parameters must be estimated; implied volatility of the underlying security. The more precisely these values are estimated, the more accurate their corresponding estimates of theoretical option prices would be. Here, we present a novel model based on Cuckoo Search Optimization (CS) which finds more precise estimates of implied volatility than Particle Swarm Optimization (PSO) and Genetic Algorithm (GA).

Keywords: black scholes model, cuckoo search optimization, particle swarm optimization, genetic algorithm

Procedia PDF Downloads 453

Authors: D. K. Lee, S. M. Shin, J. H. Lee

Abstract:

Topology optimization technique utilizes constant element densities as design parameters. Finally, optimal distribution contours of the material densities between voids (0) and solids (1) in design domain represent the determination of topology. It means that regions with element density values become occupied by solids in design domain, while there are only void phases in regions where no density values exist. Therefore the void regions of topology optimization results provide design information to decide appropriate depositions of web-opening in structure. Contrary to the basic objective of the topology optimization technique which is to obtain optimal topology of structures, this present study proposes a new idea that topology optimization results can be also utilized for decision of proper web-opening’s position. Numerical examples of linear elastostatic structures demonstrate efficiency of methodological design processes using topology optimization in order to determinate the proper deposition of web-openings.

Keywords: topology optimization, web-opening, structure, element density, material

Procedia PDF Downloads 472

Authors: Mohammadhadi Mirmohammadi, Reza Safian, Hossein Haddad

Abstract:

This paper presents an innovative solution for complex multi-objective optimization problem which is a part of efforts toward maximizing rolling mill throughput and minimizing processing costs in tandem cold rolling. This computational intelligence based optimization has been applied to the rolling schedules of tandem cold rolling mill. This method involves the combination of two derivative-free optimization procedures in the form of nested loops. The first optimization loop is based on Improving Hit and Run method which focus on balance of power, force and reduction distribution in rolling schedules. The second loop is a real-coded genetic algorithm based optimization procedure which optimizes energy consumption and productivity. An experimental result of application to five stand tandem cold rolling mill is presented.

Keywords: derivative-free optimization, Improving Hit and Run method, real-coded genetic algorithm, rolling schedules of tandem cold rolling mill

Procedia PDF Downloads 696

Authors: Angga S. Fajar, A. Aminullah, J. Kiyono, R. A. Safitri

Abstract:

This paper discusses about the application of ANN for optimizing of bridge structure design. ANN has been applied in various field of science concerning prediction and optimization. The structural optimization has several benefit including accelerate structural design process, saving the structural material, and minimize self-weight and mass of structure. In this paper, there are three types of bridge structure that being optimized including PSC I-girder superstructure, composite steel-concrete girder superstructure, and RC bridge pier. The different optimization strategy on each bridge structure implement back propagation method of ANN is conducted in this research. The optimal weight and easier design process of bridge structure with satisfied error are achieved.

Keywords: bridge structures, ANN, optimization, back propagation

Procedia PDF Downloads 372

Authors: David Lindström

Abstract:

We evaluate the performance of a numerical method for global optimization of expensive functions. The method is using a response surface to guide the search for the global optimum. This metamodel could be based on radial basis functions, kriging, or a combination of different models. We discuss how to set the cycling parameters of the optimization method to get a balance between local and global search. We also discuss the eventual problem with Runge oscillations in the response surface.

Keywords: expensive function, infill sampling criterion, kriging, global optimization, response surface, Runge phenomenon

Procedia PDF Downloads 578

Authors: Romisaa Ali

Abstract:

The Policy Gradient approach is one of the deep reinforcement learning families that combines deep neural networks (DNN) with reinforcement learning RL to discover the optimum of the control problem through experience gained from the interaction between the robot and its surroundings. In contrast to earlier policy gradient algorithms, which were unable to handle these two types of error because of over-or under-estimation introduced by the deep neural network model, this article will discuss the state-of-the-art SOTA policy gradient technique, trust region policy optimization (TRPO), by applying this method in various environments compared to another policy gradient method, the Proximal Policy Optimization (PPO), to explain their robust optimization, using this SOTA to gather experience data during various training phases after observing the impact of hyper-parameters on neural network performance.

Keywords: deep neural networks, deep reinforcement learning, proximal policy optimization, state-of-the-art, trust region policy optimization

Procedia PDF Downloads 169

Authors: Jong-Yeon Kim, Kwang-Bok Shin, Tae-Hwan Ko

Abstract:

The purpose of this paper is to suggest a weight-reduction design method for the aluminum extrusion carbody structure of a double deck high-speed train using size optimization method. The size optimization method was used to optimize thicknesses of skin and rib of the aluminum extrusion for the carbody structure. Thicknesses of 1st underframe, 2nd underframe, solebar and roof frame were selected by design variables in order to conduct size optimization. The results of the size optimization analysis showed that the weight of the aluminum extrusion could be reduced by 0.61 tons (5.60%) compared to the weight of the original carbody structure.

Keywords: double deck high-speed train, size optimization, weigh-reduction, aluminum extrusion

Procedia PDF Downloads 290

Authors: Syed Auon Raza, Tahir Mahmood, Syed Basit Ali Bukhari

Abstract:

In power system properly coordinated protection scheme is designed to make sure that only the faulty part of the system will be isolated when abnormal operating condition of the system will reach. The complexity of the system as well as the increased user demand and the deregulated environment enforce the utilities to improve system reliability by using a properly coordinated protection scheme. This paper presents overview of over current relay coordination techniques. Different techniques such as Deterministic Techniques, Meta Heuristic Optimization techniques, Hybrid Optimization Techniques, and Trial and Error Optimization Techniques have been reviewed in terms of method of their implementation, operation modes, nature of distribution system, and finally their advantages as well as the disadvantages.

Keywords: distribution system, relay coordination, optimization, Plug Setting Multiplier (PSM)

Procedia PDF Downloads 399

Authors: William Anderson, Kyle Kobold, Oleg Yakimenko

Abstract:

Green microgrids using mostly renewable energy (RE) for generation, are complex systems with inherent nonlinear dynamics. Among a variety of different optimization tools there are only a few ones that adequately consider this complexity. This paper evaluates applicability of two somewhat similar optimization tools tailored for standalone RE microgrids and also assesses a machine learning tool for performance prediction that can enhance the reliability of any chosen optimization tool. It shows that one of these microgrid optimization tools has certain advantages over another and presents a detailed routine of preparing input data to simulate RE microgrid behavior. The paper also shows how neural-network-based predictive modeling can be used to validate and forecast solar power generation based on weather time series data, which improves the overall quality of standalone RE microgrid analysis.

Keywords: microgrid, renewable energy, complex systems, optimization, predictive modeling, neural networks

Procedia PDF Downloads 282

Authors: Ali Rabah

Abstract:

This research received no grant or financial support from any public, commercial, or none governmental agency. The author conducted this work as part of his normal research activities as a professor of Chemical Engineering at the University of Khartoum, Sudan. Abstract While fossil oil reserves have been receding, the demand for diesel and gasoline has been growing. In recent years, syngas of biomass origin has been emerging as a viable feedstock for Fischer-Tropsch (FT) synthesis, a process for manufacturing synthetic gasoline and diesel. This paper reports the optimization of syngas quality to match FT synthesis requirements. The optimization model maximizes the thermal efficiency under the constraint of H2/CO≥2.0 and operating conditions of equivalent ratio (0 ≤ ER ≤ 1.0), steam to biomass ratio (0 ≤ SB ≤ 5), and gasification temperature (500 °C ≤ Tg ≤ 1300 °C). The optimization model is executed using the optimization section of the Model Analysis Tools of the Aspen Plus simulator. The model is tested using eleven (11) types of MSW. The optimum operating conditions under which the objective function and the constraint are satisfied are ER=0, SB=0.66-1.22, and Tg=679 - 763°C. Under the optimum operating conditions, the syngas quality is H2=52.38 - 58.67-mole percent, LHV=12.55 - 17.15 MJ/kg, N2=0.38 - 2.33-mole percent, and H2/CO≥2.15. The generalized optimization model reported could be extended to any other type of biomass and coal. Keywords: MSW, Syngas, Optimization, Fischer-Tropsch.

Keywords: syngas, MSW, optimization, Fisher-Tropsh

Procedia PDF Downloads 80

Authors: Peng Liu

Abstract:

Deep Q networks (DQNs) represent a significant advancement in reinforcement learning, utilizing neural networks to approximate the optimal Q-value for guiding sequential decision processes. This paper presents a comprehensive introduction to reinforcement learning principles, delves into the mechanics of DQNs, and explores its application in portfolio optimization. By evaluating the performance of DQNs against traditional benchmark portfolios, we demonstrate its potential to enhance investment strategies. Our results underscore the advantages of DQNs in dynamically adjusting asset allocations, offering a robust portfolio management framework.

Keywords: deep reinforcement learning, deep Q networks, portfolio optimization, multi-period optimization

Procedia PDF Downloads 32

Authors: Inayat Ur Rehman, Georgia Sakellari

Abstract:

Cloud computing has evolved into a vital technology for businesses, offering scalability, flexibility, and cost-effectiveness. However, maintaining high availability and optimal performance in the cloud is crucial for reliable services. This paper explores the significance of cloud monitoring and performance optimization in sustaining the high availability of cloud-based systems. It discusses diverse monitoring tools, techniques, and best practices for continually assessing the health and performance of cloud resources. The paper also delves into performance optimization strategies, including resource allocation, load balancing, and auto-scaling, to ensure efficient resource utilization and responsiveness. Addressing potential challenges in cloud monitoring and optimization, the paper offers insights into data security and privacy considerations. Through this thorough analysis, the paper aims to underscore the importance of cloud monitoring and performance optimization for ensuring a seamless and highly available cloud computing environment.

Keywords: cloud computing, cloud monitoring, performance optimization, high availability

Procedia PDF Downloads 65

Authors: Mehrdad Rezaei, Reza Haghmaram, Nima Amjadi

Abstract:

This paper proposes an operating and cost optimization model for micro-grid (MG). This model takes into account emission costs of NOx, SO2, and CO2, together with the operation and maintenance costs. Wind turbines (WT), photovoltaic (PV) arrays, micro turbines (MT), fuel cells (FC), diesel engine generators (DEG) with different capacities are considered in this model. The aim of the optimization is minimizing operation cost according to constraints, supply demand and safety of the system. The proposed genetic algorithm (GA), with the ability to fine-tune its own settings, is used to optimize the micro-grid operation.

Keywords: micro-grid, optimization, genetic algorithm, MG

Procedia PDF Downloads 511

Authors: Sofia Ayouche, Rachid Ellaia, Rajae Aboulaich

Abstract:

Today, insurers may use the yield curve as an indicator evaluation of the profit or the performance of their portfolios; therefore, they modeled it by one class of model that has the ability to fit and forecast the future term structure of interest rates. This class of model is the Nelson-Siegel-Svensson model. Unfortunately, many authors have reported a lot of difficulties when they want to calibrate the model because the optimization problem is not convex and has multiple local optima. In this context, we implement a hybrid Particle Swarm optimization and Nelder Mead algorithm in order to minimize by least squares method, the difference between the zero-coupon curve and the NSS curve.

Keywords: optimization, zero-coupon curve, Nelson-Siegel-Svensson, particle swarm optimization, Nelder-Mead algorithm

Procedia PDF Downloads 430

Authors: Rahul Paul, Kedar Nath Das

Abstract:

The field of machine learning (ML) is experiencing rapid development, resulting in a multitude of theoretical advancements and extensive practical implementations across various disciplines. The objective of ML is to facilitate the ability of machines to perform cognitive tasks by leveraging knowledge gained from prior experiences and effectively addressing complex problems, even in situations that deviate from previously encountered instances. Reinforcement Learning (RL) has emerged as a prominent subfield within ML and has gained considerable attention in recent times from researchers. This surge in interest can be attributed to the practical applications of RL, the increasing availability of data, and the rapid advancements in computing power. At the same time, optimization algorithms play a pivotal role in the field of ML and have attracted considerable interest from researchers. A multitude of proposals have been put forth to address optimization problems or improve optimization techniques within the domain of ML. The necessity of a thorough examination and implementation of optimization algorithms within the context of ML is of utmost importance in order to provide guidance for the advancement of research in both optimization and ML. This article provides a comprehensive overview of the application of metaheuristic evolutionary optimization algorithms in conjunction with RL to address a diverse range of scientific challenges. Furthermore, this article delves into the various challenges and unresolved issues pertaining to the optimization of RL models.

Keywords: machine learning, reinforcement learning, loss function, evolutionary optimization techniques

Procedia PDF Downloads 74

Authors: Arslan Ellahi, Syed Amjad Hussain, Fawaz Saleem Bokhari

Abstract:

Optimization of software architecture can be done with respect to a quality attributes (QA). In this paper, there is an analysis of multiple research papers from different dimensions that have been used to classify those attributes. We have proposed a technique of swarm intelligence Meta heuristic ant colony optimization algorithm as a contribution to solve this critical optimization problem of software architecture. We have ranked quality attributes and run our algorithm on every QA, and then we will rank those on the basis of accuracy. At the end, we have selected the most accurate quality attributes. Ant colony algorithm is an effective algorithm and will perform best in optimizing the QA’s and ranking them.

Keywords: complexity, rapid evolution, swarm intelligence, dimensions

Procedia PDF Downloads 261

Authors: Saeed Kamarian, Mahmoud Shakeri

Abstract:

Sandwich structures are used in a variety of engineering applications including aircraft, construction and transportation where strong, stiff and light structures are required. In this paper, frequency maximization of Functionally Graded Sandwich (FGS) beams resting on Pasternak foundations is investigated. A generalized power-law distribution with four parameters is considered for material distribution through the thicknesses of face layers. Since the search space is large, the optimization processes becomes so complicated and too much time consuming. Thus a novel meta–heuristic called Imperialist Competitive Algorithm (ICA) which is a socio-politically motivated global search strategy is implemented to improve the speed of optimization process. Results show the success of applying ICA for engineering problems especially for design optimization of FGM sandwich beams.

Keywords: sandwich beam, functionally graded materials, optimization, imperialist competitive algorithm

Procedia PDF Downloads 569

Authors: Li Ni, Pen ManMan, Li KenLi

Abstract:

Clustering is an intensive research for some years because of its multifaceted applications, such as biology, information retrieval, medicine, business and so on. The expectation maximization (EM) is a kind of algorithm framework in clustering methods, one of the ten algorithms of machine learning. Traditionally, optimization of objective function has been the standard approach in EM. Hence, research has investigated the utility of evolutionary computing and related techniques in the regard. Chemical Reaction Optimization (CRO) is a recently established method. So the property embedded in CRO is used to solve optimization problems. This paper presents an algorithm framework (EM-CRO) with modified CRO operators based on EM cluster problems. The hybrid algorithm is mainly to solve the problem of initial value sensitivity of the objective function optimization clustering algorithm. Our experiments mainly take the EM classic algorithm:k-means and fuzzy k-means as an example, through the CRO algorithm to optimize its initial value, get K-means-CRO and FKM-CRO algorithm. The experimental results of them show that there is improved efficiency for solving objective function optimization clustering problems.

Keywords: chemical reaction optimization, expection maimization, initia, objective function clustering

Procedia PDF Downloads 713

Authors: Tomasz Robert Kuczerski

Abstract:

The high complexity of the algorithm of the autonomous tandem detonator system creates an optimization problem due to the parallel operation of several machine states of the system. Many years of experience and classic analyses have led to a partially optimized model. Limitations on the energy resources of this class of autonomous systems make it necessary to search for more effective methods of optimisation. The use of the Quantum Approximate Optimization Algorithm (QAOA) in these studies shows the most promising results. With the help of multiple evaluations of several qubit quantum circuits, proper results of variable parameter optimization were obtained. In addition, it was observed that the increase in the number of assessments does not result in further efficient growth due to the increasing complexity of optimising variables. The tests confirmed the effectiveness of the QAOA optimization method.

Keywords: algorithm analysis, autonomous system, quantum optimization, tandem detonator

Procedia PDF Downloads 92

Authors: M. Farhaoui, M. Derraz

Abstract:

In the drinking water treatment processes, the optimization of the treatment is an issue of particular concern. In general, the process consists of many units as settling, coagulation, flocculation, sedimentation, filtration and disinfection. The optimization of the process consists of some measures to decrease the managing and monitoring expenses and improve the quality of the produced water. The objective of this study is to provide water treatment operators with methods and practices that enable to attain the most effective use of the facility and, in consequence, optimize the of the cubic meter price of the treated water. This paper proposes a review on optimization of drinking water treatment process by analyzing all of the water treatment units and gives some solutions in order to maximize the water treatment performances without compromising the water quality standards. Some solutions and methods are performed in the water treatment plant located in the middle of Morocco (Meknes).

Keywords: coagulation process, optimization, turbidity removal, water treatment

Procedia PDF Downloads 422

Authors: Riffi Mohammed Amine

Abstract:

A cloud is made up of small particles of liquid water or ice suspended in the atmosphere, which generally do not reach the ground. Various methods are used to classify clouds. This article focuses specifically on a technique known as particle swarm optimization (PSO), an AI approach inspired by the collective behaviors of animals living in groups, such as schools of fish and flocks of birds, and a method used to solve complex classification and optimization problems with approximate solutions. The proposed technique was evaluated using a series of second-generation METOSAT images taken by the MSG satellite. The acquired results indicate that the proposed method gave acceptable results.

Keywords: remote sensing, particle swarm optimization, clouds, meteorological image

Procedia PDF Downloads 15

Authors: K. Y. Tseng, C. Y. Wu

Abstract:

This paper employs a heuristic algorithm to solve engineering problems including truss structure optimization and optimal chiller loading (OCL) problems. Two different type algorithms, real-valued differential evolution (DE) and modified binary differential evolution (MBDE), are successfully integrated and then can obtain better performance in solving engineering problems. In order to demonstrate the performance of the proposed algorithm, this study adopts each one testing case of truss structure optimization and OCL problems to compare the results of other heuristic optimization methods. The result indicates that the proposed algorithm can obtain similar or better solution in comparing with previous studies.

Keywords: differential evolution, Truss structure optimization, optimal chiller loading, modified binary differential evolution

Procedia PDF Downloads 168

Authors: Aman Sharma, Sonali Sengupta

Abstract:

The study explores the utility of Bayesian optimization in tuning the physical and chemical parameters of reactions in an offline experimental setup. A comparative analysis of the influence of the acquisition function on the optimization performance is also studied. For proxy first and second-order reactions, the results are indifferent to the acquisition function used, whereas, while studying the parameters for oxidative desulphurization of thiophene in an offline setup, upper confidence bound (UCB) provides faster convergence along with a marginal trade-off in the maximum conversion achieved. The work also demarcates the critical number of independent parameters and input observations required for both sequential and offline reaction setups to yield tangible results.

Keywords: acquisition function, Bayesian optimization, desulfurization, kinetics, thiophene

Procedia PDF Downloads 182