A Multiobjective Approach for the Heuristic Optimization of Compactness and Homogeneity in the Optimal Zoning

Abstract

This paper presents a multiobjective methodology for optimal zoning design (OZ), based on the grouping of geographic data with characteristics of territorial aggregation. The two objectives considered are the minimization of the geometric compactness on the geographical location of the data and the homogeneity of any of the descriptive variables. Since this problem is NP hard [1], our proposal provides an approximate solution taking into account properties of partitioning algorithms and design restrictions for territorial space. Approximate solutions are generated through the set of optimum values (Maxima) and the corresponding minimals (dual Minima) [2] of the bi-objective function using Variable Neighborhood Search (VNS) [3] and the Pareto order defined over this set of values. The results obtained by our proposed approach constitute good solutions and are generated in a reasonably low computational time.

Design of robust optimal regulator considering state and control nonlinearities

“…Then the optimal control of the SDRE has been investigated by Cloutier, D'Souza, and Mracek (1996), Khaloozadeh and Abdollahi (2002). Over the past two decades, SDRE has been used more extensively in optimizing the control of nonlinear systems (Abbaszadeh & Marquez, 2012;Aliyu, 2000;Amato, 2006;Amato, Colacino, Cosentino, & Merola, 2014;Amato, Cosentino, & Merola, 2010;Banks, Kwon, Toivanen, & Tran, 2006;Bernábe-Loranca, Coello-Coello, & Osorio-Lama, 2012;Bouzaouache & Braiek, 2008;Elloumi & Braiek, 2012;Mohan & Miller, 2008;Shamma & Cloutier, 2003;Strano & Terzo, 2015;Won & Biswas, 2007). The SDRE method can be used to control and stabilize a wide range of systems, such as satellites (Cyril, Jaar, & Misra, 1995;Flores-Abad & Ma, 2012;Inaba, Oda, & Asano, 2006;Tarabini et al, 2007), spacecraft (Kaiser, Sjöberg, Delcura, & Eilertsen, 2008;Xin & Pan, 2011), helicopter (Bogdanov CONTACT Mohammad Ali Nekoui manekoui@eetd.kntu.ac.ir et al, 2003;Dimitrov & Yoshida, 2004;Liu, Wu, & Lu, 2007;Yoshida, Dimitrov, & Nakanishi, 2006), robots (Abiko & Hirzinger, 2007;Huang, Wang, Meng, & Liu, 2015;Huang, Wang, Meng, Zhang, & Liu, 2016), chaotic system (Choi, 2012;Sinha, Henrichs, & Ravindra, 2000;Yuan, Liu, Lin, Hu, & Gong, 2017) and more.…”

Multi-Objective Feature Subset Selection using Non-dominated Sorting Genetic Algorithm

“…A solution x is said to dominate the other solution y if the solution x is no worse than y in all objectives and the solution x is strictly better than y in at least one objective [14]. There are other approaches using neural network [20], evolutionary multi agent system [21], evolutionary algorithm [22,25], a hybrid of evolutionary algorithm and neural network [23], approaches using genetic algorithm with particle swarm optimization [24], hybrid evolutionary algorithm [26], and using multi-objective approaches for heuristic optimization [27] for optimization and classification problems. The evolutionary based technique has been used as it works well for the problems with large dimensions, it is known to be a robust technique and it works well with all types of problems because it does not make any assumptions about underlying fitness landscape.…”

On Feedback Control Techniques of Nonlinear Analytic Systems

“…However, and despite recent advances, many unresolved problems are steel subsisting, so that practitioners often complain about the inapplicability of contemporary theories. For example, most of the developed techniques have very limited applicability because of the strong conditions imposed on the system [29,40,41,42,43]. This has led to many methods being proposed in the literature for ways to obtain a suboptimal feedback control for general nonlinear dynamical systems.…”