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- 저자 : Kazakovtsev, Lev A. (검색결과 3 건)
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ALGORITHM FOR WEBER PROBLEM WITH A METRIC BASED ON THE INITIAL FARE
Kazakovtsev, Lev A.,Stanimirovic, Predrag S. The Korean Society for Computational and Applied M 2015 Journal of applied mathematics & informatics Vol.33 No.1
We introduce a non-Euclidean metric for transportation systems with a defined minimum transportation cost (initial fare) and investigate the continuous single-facility Weber location problem based on this metric. The proposed algorithm uses the results for solving the Weber problem with Euclidean metric by Weiszfeld procedure as the initial point for a special local search procedure. The results of local search are then checked for optimality by calculating directional derivative of modified objective functions in finite number of directions. If the local search result is not optimal then algorithm solves constrained Weber problems with Euclidean metric to obtain the final result. An illustrative example is presented.
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Algorithm for Weber problem with a metric based on the initial fare
Lev A. Kazakovtsev,Predrag S. Stanimirovic 한국전산응용수학회 2015 Journal of applied mathematics & informatics Vol.33 No.1
We introduce a non-Euclidean metric for transportation systems with a defined minimum transportation cost (initial fare) and investigatethe continuous single-facility Weber location problem based on this metric. The proposed algorithm uses the results for solving the Weber problem with Euclidean metric by Weiszfeld procedure as the initial point fora special local search procedure. The results of local search are then checked for optimality by calculating directional derivative ofmodified objective functions in finite number of directions. If the local search result is not optimal then algorithm solves constrainedWeber problems with Euclidean metric to obtain the final result. An illustrative example is presented.
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Automatic Classification Models and Algorithms Based on the Minimum Sum-of-Squared Errors Model
Guzel Shkaberina,Lev Kazakovtsev 대한산업공학회 2020 Industrial Engineeering & Management Systems Vol.19 No.4
We propose new models and algorithms for automatic classification of objects (clustering) based on the minimum sum-of-squared errors clustering (MSSC) model. Our approach was aimed at improving the accuracy and stability of the result in solving practical problems, such as identifying homogeneous batches of industrial products. We examined the application of the MSSC model and k-means algorithm with various distance measures: Euclidean, Manhattan, Mahalanobis for the problem of automatic classification of objects in a multi-dimensional space of measured parameters (features). For such problems, we present a new model (Mahalanobis Minimum Sum-of-Squared Error Clustering, MMSSC) for solving problems of automatic classification based on the MSSC model with Mahalanobis distance. In addition, we present a new algorithm for automatic classification of objects based on the MMSSC optimization model with the Mahalanobis distance measure and the weighted average covariance matrix calculated from the training sample (pre-labeled data). This algorithm allows us to reduce the number of errors (increasing the Rand index) when identifying homogeneous production batches based on the results of quality control tests. A new approach in the development of evolutionary algorithms for the MSSC problem is presented using a greedy agglomerative heuristic procedure contained in several genetic operators. The use of this approach enables a statistically significant increase in the accuracy of the result (the achieved value of the objective function within the chosen MMSSC mathematical model), as well as its stability, in a fixed time, in comparison with the known algorithms. Thus, in this work, an increase in the accuracy of solving the problem of automatic classification is achieved both by increasing the adequacy of the model (according to the Rand index) and by improving the algorithm that allows us to achieve the best objective function values of within the framework of the chosen model.
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