Flying elephants: a general method for solving non-differentiable problems

Abstract

Flying Elephants (FE) is a generalization and a new interpretation of the Hyperbolic Smoothing approach. The article introduces the fundamental smoothing procedures. It contains a general overview of successful applications of the approach for solving a select set of five important problems, namely: distance geometry, covering, clustering, Fermat-Weber and hub location. For each problem the original nonsmooth formulation and the succedaneous completely differentiable one are presented. Computational experiments for all related problems obtained results that exhibited a high level of performance according to all criteria: consistency, robustness and efficiency. For each problem some results to illustrate the performance of FE are also presented.

An exhaustive review of the metaheuristic algorithms for search and optimization: taxonomy, applications, and open challenges

“…( 2006 ) 206 Flow Direction Algorithm (FDA) Karami et al. ( 2021 ) 207 Flow Regime Algorithm (FRA) Tahani and Babayan ( 2019 ) 208 Flower Pollination Algorithm (FPA) Yang ( 2012 ) 209 Flying Elephant Algorithm (FEA) Xavier and Xavier ( 2016 ) 210 Football Game Algorithm (FGA) Fadakar and Ebrahimi ( 2016 ) 211 Forensic Based Investigation (FBI) Chou and Nguyen ( 2020 ) 212 Forest Optimization Algorithm (FOA) Ghaemi and Feizi-Derakhshi ( 2014 ) 213 Fox Optimizer (FOX) Mohammed and Rashid ( 2022 ) 214 Fractal-Based Algorithm (FA) Kaedi ( 2017 ) 215 Frog Call Inspired Algorithm (FCA) Mutazono et al. ( 2009 ) 216 Fruit Fly Optimization Algorithm (FOA) Pan ( 2012 ) 217 Gaining Sharing Knowledge Based Algorithm (GSK) Mohamed et al.…”

NOAH as an Innovative Tool for Modeling the Use of Suburban Railways

“…Canca et al, 2017 [1] Line planning O Yan et al, 2019 [2] MILP Hickish et al, 2020 [3] Network optimization GA Schlechte et al, 2011 [4] NH Weik et al, 2020 [5] Nodes (location, classification) NH Ahmed et al, 2020 [6] Station location GA Dong et al, 2020 [7] O Qiannan et al, 2022 [8] NH Binder et al, 2021 [9] Timetable creation and rescheduling SA Jamili and Pourseyed Aghaee, 2015 [10] SA Shang et al, 2018 [11] NH Wang et al, 2018 [12] MILP Jensen et al, 2016 [13] NH Yin et al, 2021 [14] O Zhang et al, 2018 [15] O Zhang et al, 2019a [16] MILP Zhang et al, 2019b [17] NH Zhang et al, 2022 [18] O Zhao et al, 2021 [19] MILP Whitbrook et al, 2018 [20] MS Zheng et al, 2014 [21] BBO Satoshi et al, 2011 [22] Operations (delay management, train routing) TS Sama et al, 2017 [23] SI Oneto et al, 2017 [24] O Xiao et al, 2018 [25] Demand side of the transport system NH Shen et al, 2016 [26] O Wu et al, 2013 [27] O Liu et al, 2019 [28] ANN Hansson et al, 2021 [30] Bus systems and networks NH Wei et al, 2021 [31] NH Ngo et al, 2021 [32] Ride-hailing services NH Behrends, 2017 [33] Nodes, coordination NH Stead et al, 2019 [34] NH Yang et al, 2020 [35] GA Lianhua and Xingfang, 2022 [36] SA Chen et al, 2020 [37] Autonomous Vehicles O Lopez and Farooq, 2020 [39] Smart mobility data-markets BC Xavier and Xavier, 2016 [44] Not related to transport systems O Martinelli and Teng, 1996…”

“…New developments in "metaheuristics" and their applications are presented by Lau et al [43]. They evoke, among others, a new method called "flying elephants" (Xavier and Xavier [44]), which shows interesting and intriguing assumptions and solutions. Some studies include more than one tool, including Yang et al [35], who compared the effectiveness of GA and MINLP.…”

“…Sources [38,39] show directions for future research, and sources [40][41][42][43] contain important definitions (they were not added to the table). In [44][45][46][47][48][49][50][51][52][53], authors present different tools used to solve some problems (partially not as transportation problems, but with methodologies inspiring the method presented here). The tools are discussed in Section 2.…”

New developments in metaheuristics and their applications

“…The article Xavier and Xavier (2014) "Flying elephants: a general method for solving non-differentiable problems" by Adilson Elias Xavier and Vinicius Layter Xavier, proposes a generalization of the Hyperbolic Smoothing approach. Computational experiments on distance geometry, covering, clustering, Fermat-Weber and hub location problems indiacte that the proposed method has good performance and robustness.…”