The non-smooth and bi-objective team orienteering problem with soft constraints
- Authors: Estrada-Moreno, Alejandro , Ferrer, Albert , Juan, Angel , Panadero, Javier , Bagirov, Adil
- Date: 2020
- Type: Text , Journal article
- Relation: Mathematics Vol. 8, no. 9 (2020), p.
- Full Text:
- Reviewed:
- Description: In the classical team orienteering problem (TOP), a fixed fleet of vehicles is employed, each of them with a limited driving range. The manager has to decide about the subset of customers to visit, as well as the visiting order (routes). Each customer offers a different reward, which is gathered the first time that it is visited. The goal is then to maximize the total reward collected without exceeding the driving range constraint. This paper analyzes a more realistic version of the TOP in which the driving range limitation is considered as a soft constraint: every time that this range is exceeded, a penalty cost is triggered. This cost is modeled as a piece-wise function, which depends on factors such as the distance of the vehicle to the destination depot. As a result, the traditional reward-maximization objective becomes a non-smooth function. In addition, a second objective, regarding the design of balanced routing plans, is considered as well. A mathematical model for this non-smooth and bi-objective TOP is provided, and a biased-randomized algorithm is proposed as a solving approach. © 2020 by the authors.
- Description: This work has been partially supported by the Spanish Ministry of Economy and Competitiveness & FEDER (SEV-2015-0563), the Spanish Ministry of Science (PID2019-111100RB-C21, RED2018-102642-T), and the Erasmus+ Program (2019-I-ES01-KA103-062602).
Non-smooth optimization methods for computation of the conditional value-at-risk and portfolio optimization
- Authors: Beliakov, Gleb , Bagirov, Adil
- Date: 2006
- Type: Text , Journal article
- Relation: Optimization Vol. 55, no. 5-6 (2006), p. 459-479
- Full Text:
- Reviewed:
- Description: We examine numerical performance of various methods of calculation of the Conditional Value-at-risk (CVaR), and portfolio optimization with respect to this risk measure. We concentrate on the method proposed by Rockafellar and Uryasev in (Rockafellar, R.T. and Uryasev, S., 2000, Optimization of conditional value-at-risk. Journal of Risk, 2, 21-41), which converts this problem to that of convex optimization. We compare the use of linear programming techniques against a non-smooth optimization method of the discrete gradient, and establish the supremacy of the latter. We show that non-smooth optimization can be used efficiently for large portfolio optimization, and also examine parallel execution of this method on computer clusters. © 2006 Taylor & Francis.
- Description: C1
- Description: 2003002156
An algorithm for clustering based on non-smooth optimization techniques
- Authors: Bagirov, Adil , Rubinov, Alex , Sukhorukova, Nadezda , Yearwood, John
- Date: 2003
- Type: Text , Journal article
- Relation: International Transactions in Operational Research Vol. 10, no. 6 (2003), p. 611-617
- Full Text: false
- Reviewed:
- Description: The problem of cluster analysis is formulated as a problem of non-smooth, non-convex optimization, and an algorithm for solving the cluster analysis problem based on non-smooth optimization techniques is developed. We discuss applications of this algorithm in large databases. Results of numerical experiments are presented to demonstrate the effectiveness of this algorithm.
- Description: C1
- Description: 2003000422
Derivative-free optimization and neural networks for robust regression
- Authors: Beliakov, Gleb , Kelarev, Andrei , Yearwood, John
- Date: 2012
- Type: Text , Journal article
- Relation: Optimization Vol. 61, no. 12 (2012), p. 1467-1490
- Full Text:
- Reviewed:
- Description: Large outliers break down linear and nonlinear regression models. Robust regression methods allow one to filter out the outliers when building a model. By replacing the traditional least squares criterion with the least trimmed squares (LTS) criterion, in which half of data is treated as potential outliers, one can fit accurate regression models to strongly contaminated data. High-breakdown methods have become very well established in linear regression, but have started being applied for non-linear regression only recently. In this work, we examine the problem of fitting artificial neural networks (ANNs) to contaminated data using LTS criterion. We introduce a penalized LTS criterion which prevents unnecessary removal of valid data. Training of ANNs leads to a challenging non-smooth global optimization problem. We compare the efficiency of several derivative-free optimization methods in solving it, and show that our approach identifies the outliers correctly when ANNs are used for nonlinear regression. © 2012 Copyright Taylor and Francis Group, LLC.
Nonsmooth DC programming approach to the minimum sum-of-squares clustering problems
- Authors: Bagirov, Adil , Taheri, Sona , Ugon, Julien
- Date: 2016
- Type: Text , Journal article
- Relation: Pattern Recognition Vol. 53, no. (2016), p. 12-24
- Relation: http://purl.org/au-research/grants/arc/DP140103213
- Full Text: false
- Reviewed:
- Description: This paper introduces an algorithm for solving the minimum sum-of-squares clustering problems using their difference of convex representations. A non-smooth non-convex optimization formulation of the clustering problem is used to design the algorithm. Characterizations of critical points, stationary points in the sense of generalized gradients and inf-stationary points of the clustering problem are given. The proposed algorithm is tested and compared with other clustering algorithms using large real world data sets. © 2015 Elsevier Ltd. All rights reserved.
A sharp augmented Lagrangian-based method in constrained non-convex optimization
- Authors: Bagirov, Adil , Ozturk, Gurkan , Kasimbeyli, Refail
- Date: 2019
- Type: Text , Journal article
- Relation: Optimization Methods and Software Vol. 34, no. 3 (2019), p. 462-488
- Full Text: false
- Reviewed:
- Description: In this paper, a novel sharp Augmented Lagrangian-based global optimization method is developed for solving constrained non-convex optimization problems. The algorithm consists of outer and inner loops. At each inner iteration, the discrete gradient method is applied to minimize the sharp augmented Lagrangian function. Depending on the solution found the algorithm stops or updates the dual variables in the inner loop, or updates the upper or lower bounds by going to the outer loop. The convergence results for the proposed method are presented. The performance of the method is demonstrated using a wide range of nonlinear smooth and non-smooth constrained optimization test problems from the literature.