Beyond Tobler’s Hiking Function

Goodchild, Michael F.

doi:10.1111/gean.12253

Cited by 57Transportation Planning and OptimizationUrban Transport and AccessibilityUrban Design and Spatial Analysis

The DOI matches its Crossref record; 18 of the 18 references it cites were found in a registry or an index.

Beyond Tobler’s Hiking Function

Goodchild, Michael F.·2020·Geographical Analysis

DOI 10.1111/gean.12253

Open this paper in CoChat — free account

Abstract

Waldo Tobler introduced his hiking function in a little‐known article in 1993, as a formal representation of the relationship between topographic gradient and the velocity of an average hiker, with parameters estimated from some previously collected data. Such functions are becoming more useful as apps for route guidance proliferate. Numerous practical issues are raised by any effort to validate these functions empirically. Hiking functions in general allow routes to be measured on various criteria, including travel time, travel distance, or energy consumption, yet, few efforts have been made to calibrate similar functions for other modes of travel, other traveler profiles, and other route criteria. Connected and autonomous vehicles raise the possibility that route choice may take on greater significance in the context of system‐wide goals, rather than the current individual self‐interest.

Integrity signals

Registry

Crossref · 10.1111/gean.12253

Cites

18 of 18 references verified0 citation errors · 0 not checkable

Statistics

Recomputing p-values needs the paper’s full text.

Claims the paper makes

This paper’s full text isn’t openly available, so its claims and self-check weren’t run. The registry and citation checks still apply.

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

Least-cost path modeling is among the most common applications of travel rate functions.
“Least-cost path modeling is among the most common applications of travel rate functions41,42, enabling the identification of routes that minimize travel time between two (or more) points on a landscape.”
From A singular, broadly-applicable model for estimating on- and off-path walking travel rates using airborne lidar data (2024) · cites this paper as [41]
Slope-controlled models estimate travel rates solely as a function of slope, which is most appropriate for on-path travel where vegetation density and surface roughness are low.
“These slopecontrolled models estimate travel rates solely as a function of slope, which is most appropriate for on-path travel (i.e. on a road or trail) where vegetation density and surface roughness are low.”
From Machine learning estimation of off-trail pedestrian travel rates using LiDAR-derived slope, vegetation, and surface roughness (2026) · cites this paper as Goodchild 2020

A note on two problems in connexion with graphs
Dijkstra, E. (1959) · Numerische Mathematik · doi:10.1007/bf01386390 · Cited by 24,351
A Formal Basis for the Heuristic Determination of Minimum Cost Paths
Hart, P., Nilsson, N., & Raphael, B. (1968) · IEEE Transactions on Systems Science and Cybernetics · doi:10.1109/tssc.1968.300136 · Cited by 12,738
Learning to Think Spatially
National Research Council (2006) · National Academies Press eBooks · doi:10.17226/11019 · Cited by 653
Geographic Information Science and Systems
Longley, P., & Goodchild, M. F. (2019) · Elsevier eBooks · doi:10.1016/b978-0-08-102295-5.10557-8 · Cited by 319
Self-citation
Activity-Based Approaches to Travel Analysis
Ettema, D., & Timmermans, H. J. P. (1997) · Cited by 303
Bidimensional Regression
Tobler, W. (1994) · Geographical Analysis · doi:10.1111/j.1538-4632.1994.tb00320.x · Cited by 177
Mapping for Wheelchair Users: Route Navigation in Urban Spaces
Beale, L., Field, K. S., Briggs, D., Picton, P. D., & Matthews, H. (2006) · The Cartographic Journal · doi:10.1179/000870406x93517 · Cited by 162
THREE PRESENTATIONS ON GEOGRAPHICAL ANALYSIS AND MODELING
Modeling, N.-I., & Tobler, W. (1993) · Cited by 158
Walking speed of older people and pedestrian crossing time
Duim, E., Lebrão, M. L., & Antunes, J. L. F. (2017) · Journal of Transport & Health · doi:10.1016/j.jth.2017.02.001 · Cited by 102
Using crowdsourced fitness tracker data to model the relationship between slope and travel rates
Campbell, M. J., Dennison, P. E., Butler, B. W., & Page, W. G. (2019) · Applied Geography · doi:10.1016/j.apgeog.2019.03.008 · Cited by 87
Effects of Sexual Activity on Beard Growth in Man
ANON (1970) · Nature · doi:10.1038/226869a0 · Cited by 81
Modeling slope as a contributor to route selection in mountainous areas
Pingel, T. J. (2010) · Cartography and Geographic Information Science · doi:10.1559/152304010791232163 · Cited by 72
Measuring and modeling the speed of human navigation
Irmischer, I. J., & Clarke, K. C. (2018) · Cartography and Geographic Information Science · doi:10.1080/15230406.2017.1292150 · Cited by 62
An Evaluation of Lattice Solutions to the Problem of Corridor Location
Goodchild, M. F. (1977) · Environment and Planning A: Economy and Space · doi:10.1068/a090727 · Cited by 60
Self-citation
An Information Model for Pedestrian Routing and Navigation Databases Supporting Universal Accessibility
Laakso, M., Sarjakoski, T., Lehto, L., & Sarjakoski, L. T. (2013) · Cartographica The International Journal for Geographic Information and Geovisualization · doi:10.3138/carto.48.2.1837 · Cited by 23
Spatial Filtering for Identifying a Shortest Path Around Obstacles
Hong, I., Murray, A. T., & Wolf, L. J. (2015) · Geographical Analysis · doi:10.1111/gean.12086 · Cited by 10
Untitled work
(1984) · OpenGrey (Institut de l'Information Scientifique et Technique)
Paperback Picks
Harris, E. (2009) · New Scientist · doi:10.1016/s0262-4079(09)61132-5

Flagged first, then by citations

Research works printed but not linked: 3

Hood J., 2019, Monetizing Data in the Age of Connected Vehicles, Deloitte Insights
Lombard K., 1993, The Gateway Shortest Path Problem: Generating Alternative Routes for a Corridor Location Problem, Geographical Systems, 1, 25
Naismith W. W., 1892, Untitled, Scottish Mountaineering Club Journal, 2, 135

Sorted by citations

The Hiking Optimization Algorithm: A novel human-based metaheuristic approach
Oladejo, S. O., Ekwe, S. O., & Mirjalili, S. (2024) · Knowledge-Based Systems · doi:10.1016/j.knosys.2024.111880 · Cited by 372
Predicting the variability in pedestrian travel rates and times using crowdsourced GPS data
Campbell, M. J., Dennison, P. E., & Thompson, M. P. (2022) · Computers, Environment and Urban Systems · doi:10.1016/j.compenvurbsys.2022.101866 · Cited by 26
Water-wall tube temperature prediction model for supercritical coal-fired boiler based on improved stochastic configuration network
Wang, Z., Yin, Y., Yao, G., Wang, D., Liu, Y., He, Z., Li, K., Tao, D., Zhu, H., Peng, X., et al. (2025) · Energy · doi:10.1016/j.energy.2025.136765 · Cited by 14
Hiking with Tobler: Tracking Movement and Calibrating a Cost Function for Personalized 3D Accessibility
Higgins, C. D. (2021) · Findings · doi:10.32866/001c.28107 · Cited by 14
Hiking-time formulas: a review
Prisner, E., & Sui, P. (2023) · Cartography and Geographic Information Science · doi:10.1080/15230406.2023.2197625 · Cited by 11
Binary hiking optimization for gene selection: Insights from HNSCC RNA-Seq data
Pashaei, E., Pashaei, E., & Mirjalili, S. (2025) · Expert Systems with Applications · doi:10.1016/j.eswa.2025.126404 · Cited by 10
Assessment of the 15-minute park accessibility accounting for fine-grained 3D pedestrian network and subjective quality perception among the public housing residents
Liu, D., Huang, J., Fang, D., Lee, J., Liu, Y., Wang, S., & Kan, Z. (2025) · Urban forestry & urban greening · doi:10.1016/j.ufug.2025.129165 · Cited by 8
A singular, broadly-applicable model for estimating on- and off-path walking travel rates using airborne lidar data
Campbell, M. J., Cutler, S. L., & Dennison, P. E. (2024) · Scientific Reports · doi:10.1038/s41598-024-71359-6 · Cited by 7
Enhanced Hiking Optimization Algorithm for Robust PID Control in Doubly‐Fed Induction Generator Systems for Wind Energy Applications
İzci, D., Artun, F., Ekinci, S., Bajaj, M., Blažek, V., & ЗАЙЦЕВ, Є. О. (2025) · IET Control Theory and Applications · doi:10.1049/cth2.70071 · Cited by 7
I walk an ancient road: A straightforward methodology for analyzing intra- and inter-regional connectivity systems along Roman Frontier Zones (c. 1st—5th century AD)
Hagmann, D. (2025) · Journal of Archaeological Science · doi:10.1016/j.jas.2024.106151 · Cited by 6
Binary Hiking Optimization Algorithm
Sağ, T. (2024) · Lecture notes in computer science · doi:10.1007/978-3-031-71552-5_19 · Cited by 6
Striking distance: Investigating the epigraphy and geography of a Late Classic Maya war
Carter, N. P., Krause, S., & Lozano, J. (2023) · Ancient Mesoamerica · doi:10.1017/s095653612300010x · Cited by 6
Shale oil production time series forecasting for multi-fractured horizontal wells with optimized artificial neural networks integrating multi-source data
Zhan, J., Jia, J., Ding, X., Zhang, Z., Cheng, J., Li, Y., Ma, X., Lin, J., & Chen, Z. (2025) · Physics of Fluids · doi:10.1063/5.0260766 · Cited by 5
Probabilistic forecasting of nonstationary monthly runoff series based on secondary modal decomposition and deep learning model: a case study on the Yellow River Basin, China
Zhao, F., Yi, P., Wan, X., Li, J., Shi, W., & He, Z. (2025) · Journal of Hydrology · doi:10.1016/j.jhydrol.2025.134054 · Cited by 4
Permanent Human Occupation of the Western Tibetan Plateau in the Early Holocene
Lü, H., & Li, Z. (2024) · Land · doi:10.3390/land13091484 · Cited by 4
The Utility of GIS for Identifying Areas of Recreation Conflict for Targeted Interpretive Messaging
Peterson, B. A., Sharp, R. L., Fefer, J. P., & Brunson, M. (2020) · Journal of Interpretation Research · doi:10.1177/10925872211019731 · Cited by 4
An Enhanced Hiking Optimization Algorithm With Attention Mechanism for a Practical Joint Replenishment and Delivery Problem
Peng, L., & Wang, L. (2025) · Expert Systems · doi:10.1111/exsy.70159 · Cited by 3
The application of Tobler's hiking function in data-driven traverse modelling for planetary exploration
Goodwin, A., Hammett, M., & Harris, M. (2024) · Acta Astronautica · doi:10.1016/j.actaastro.2024.12.005 · Cited by 3
Surfacic networks
Barthélemy, M., Boeing, G., Chiaradia, A. J. F., & Webster, C. J. (2024) · PNAS Nexus · doi:10.1093/pnasnexus/pgae585 · Cited by 2
The tortoise and the antilocaprid: adapting GPS tracking and terrain data to model wildlife walking functions
Chambers, S. N., von Nonn, J. W., Burgess, M. A., Brady, L. R., Bracewell, J., Guerra, D., & Villarreal, M. L. (2025) · Landscape Ecology · doi:10.1007/s10980-025-02092-2 · Cited by 2
Mhoa: multi-strategy Hiking Optimization Algorithm for solving engineering and numerical optimization problems
Zhang, J., & Liu, H. (2025) · Cluster Computing · doi:10.1007/s10586-025-05376-z · Cited by 2
Improved Hiking Optimization Algorithm for UAV-Assisted IoT Systems: Applications in Path Planning
Wang, B. (2025) · IEEE Transactions on Consumer Electronics · doi:10.1109/tce.2025.3648820 · Cited by 2
Online estimation of regional water-wall temperature fields in coal-fired boilers using a CFD-calibrated data-fusion framework
Ye, W., Hu, L., Zeng, H., Zhang, J., Zhang, Q., & Guo, S. (2026) · Case Studies in Thermal Engineering · doi:10.1016/j.csite.2026.108348 · Cited by 2
Analyse spatio-temporelle des mobilités de randonneurs dans le PNR du Massif des Bauges
Kerouanton, C. (2020) · HAL · doi:10.62437/cixz355cwvtgnjjlp-46096556 · Cited by 2
Measuring the Accessibility of the Railway Network with the Possibilities of Increasing the Attractiveness of Railway Transport
Vojtek, M., Štefancová, V., Široký, J., & Krbálková, M. (2024) · Transportation research procedia · doi:10.1016/j.trpro.2024.01.013 · Cited by 2
A Mobile Wireless Sensor Coverage Optimization Method for Bridge Monitoring
Mu, C., Yang, J., & Huo, J. (2025) · Sensors · doi:10.3390/s25092772 · Cited by 2
Revamped dynamic opposite learning the Hiking Optimization Algorithm for global optimization and engineering applications
Rajasekar, P., & Jayalakshmi, M. (2026) · OPSEARCH · doi:10.1007/s12597-026-01279-8 · Cited by 2
Examining trade routes through the Thai–Malay Peninsula: A simulation analysis
Koad, P., & Deesamutara, S. (2024) · The Journal of Island and Coastal Archaeology · doi:10.1080/15564894.2024.2335624 · Cited by 1
Short-term load forecasting based on successive variational mode decomposition and multi-band feature extraction
Ding, N., Li, M., Zhou, C., & Tie, R. (2025) · Evolving Systems · doi:10.1007/s12530-025-09771-0 · Cited by 1
Population Genomic Structure of Sorghum Landraces Across Landscape, Environment and Culture
Cerda, E. V., Bellis, E. S., Das, A., Slayton, E. R., Morris, G. P., & Lasky, J. R. (2026) · Molecular Ecology · doi:10.1111/mec.70287 · Cited by 1
An enhanced Hiking optimization algorithm for accurate and interpretable feature selection in medical data classification
Hegazy, A. E., Makhlouf, M. A. A., Salem, O. A. M., & Hafiz, B. (2026) · Cluster Computing · doi:10.1007/s10586-026-05946-9 · Cited by 1
How Walking-Speed Assumptions Shape 15-Minute City (15-MC) Accessibility Scores: A Case Study of Roanoke, Virginia
Rahman, F., Oliver, R., Crawford, T. W., Buehler, R., Lee, J., & Kim, J. (2026) · Future Transportation · doi:10.3390/futuretransp6040145 · Cited by 1
Geospatial mapping of a 16th century transport corridor for Southeast Europe
Kabadayı, M. E., Gerrits, P., & Boykov, G. (2021) · Digital Scholarship in the Humanities · doi:10.1093/llc/fqab084 · Cited by 1
Modeling potential environmental impacts of science activity in Antarctica
O'Sullivan, D., & Morgan, F. J. (2026) · Transactions in GIS · doi:10.1111/tgis.70369
Machine learning estimation of off-trail pedestrian travel rates using LiDAR-derived slope, vegetation, and surface roughness
Cutler, S. L., Campbell, M. J., Brewer, S. C., & Dennison, P. E. (2026) · GIScience & Remote Sensing · doi:10.1080/15481603.2026.2626632
Introduction to the Special Issue Commemorating Professor Waldo Tobler
Clarke, K., & Murray, A. T. (2020) · Geographical Analysis · doi:10.1111/gean.12261
Comité français de cartographie
Richard, H., Hofmann, C., Zanin, C., Habert, É., Noucher, M., Ferrand, M., Bachelet, P.-E., Vailly, M., Cagnasso, R., Shaalan, C., et al. (2023) · HAL
The Improved Conformable Fractional Grey Model Using ADMM and HOA Algorithm
Xu, H., Wang, D., & Wang, Y. (2025) · Highlights in Science Engineering and Technology · doi:10.54097/wkmz1s79
An optimized machine learning model for surface defect detection of heat sink based on hiking optimization algorithm
El-dosuky, M. A., Shehab, S. A., & Hassanien, A. E. (2025) · Signal Image and Video Processing · doi:10.1007/s11760-025-04927-6
Research On Twin Support Vector Regression by Hiker Optimization Algorithm
Su, L. (2025) · Highlights in Science Engineering and Technology · doi:10.54097/bq1ekh26
Distributed Photovoltaic Interval Prediction Based on the Optimal HA-KDE Model
Ma, Y., Huang, Y., Yuan, Y., & Shi, W. (2025) · International Conference on Power System Technology (POWERCON) · doi:10.1109/powercon66300.2025.11294174
Ensemble Prediction of China Consumer Price Index Based on MLP and BiLSTM
Song, Z., Gu, C., Zhang, C., & Zhao, S. (2025) · Journal of big data and computing. · doi:10.62517/jbdc.202501414
Self-calibration and real-time prediction of regional water-wall temperature fields in coal-fired boilers using a CFD-calibrated data-fusion frameworkPreprint
Ye, W., Hu, L., Zeng, H., Zhang, J., Zhang, Q., & Guo, S. (2026) · SSRN Electronic Journal · doi:10.2139/ssrn.6521039
Two-stage spatio-temporal optimization framework for transport-integrated multi-energy systems with bidirectional energy and hydrogen logistics
Taghavi, A., Niknam, T., Parsa, N., & Shojaeiyan, S. (2026) · Energy Conversion and Management X · doi:10.1016/j.ecmx.2026.101872
Self-calibration and real-time prediction of regional water-wall temperature fields in coal-fired boilers using a CFD-calibrated data-fusion frameworkPreprint
Ye, W., Hu, L., Zeng, H., Zhang, J., Zhang, Q., & Guo, S. (2026) · SSRN Electronic Journal · doi:10.2139/ssrn.6663706
GIS-Based Evaluation of Green Space Accessibility (GSA) in Earthquake-Prone Urban Areas: a Case Study of Istanbul, Türkiye
Zengin, E. (2026) · Remote Sensing in Earth Systems Sciences · doi:10.1007/s41976-026-00287-y
Senderos de montaña periurbanos del Cusco, Perú: una propuesta de análisis multicriterio para evaluar su aptitud ecoturística
Bellota, E., García-Leiva, B., & Chuquimaco, I. H. (2026) · Revista Kawsaypacha Sociedad y Medio Ambiente · doi:10.18800/kawsaypacha.202601.a006
Modeling hiking speed via interpretable machine learning: Uncovering nonlinear impacts of multidimensional environmental factors
Huang, H., Jin Yeu, T. S. O. U., Zheng, H., Ma, R., Shi, H., & Zhang, B. (2026) · Applied Geography · doi:10.1016/j.apgeog.2026.104052
Automatic recognition of sonar targets based on group classifier with majority voting weighted by the Hiking optimization algorithm
Saffari, A., Moghaddam, M. J., & Ghanbari, N. (2025) · Marine Engineering · doi:10.66224/marineeng.21.47.7
HOA-IAPF: a hiking optimization algorithm and improved artificial potential field for formation path planning for multi-mobile robots
Liu, C., Zhang, J., Geng, N., Sun, H., & Song, B. (2026) · Intelligent Service Robotics · doi:10.1007/s11370-026-00717-2
Speed, slope, and synchrony: Empirical insights into SAR searcher behavior
Hashimoto, A., Aung, E., Koester, R., & Abaid, N. (2026) · PLoS ONE · doi:10.1371/journal.pone.0339541
A Comparative Analysis of the Applicability of New Generation Metaheuristic Algorithms to Engineering Optimization Problems
Elmas, Y., Arslan, S., Yalçın, E., & Aydemı̇r, S. B. (2026) · Sakarya University Journal of Computer and Information Sciences · doi:10.35377/saucis...1759726
SMART15: AN OPEN-SOURCE SPATIAL DECISION SUPPORT SYSTEM INTEGRATING INTERPRETABLE AI, TOPOGRAPHIC IMPEDANCE, AND ENVIRONMENTAL EXPOSURE FOR ACCESSIBILITY-BASED PLANNING IN THE 15-MINUTE CITYPreprint
da Costa, A. T., da Silva, T. O., Rodrigues, K. H. D. P., Gregorio, L. S., Gregorio, F. D. S., Nunes, D. M., Duarte, D. C. D. O., & Lopes, E. C. (2026) · SSRN Electronic Journal · doi:10.2139/ssrn.7404827
Neural sentinels: A Quasi-Quantum hiking optimization based deep feature selection system for robust IoT-metaverse intrusion detection
Askr, H., Abdel-Salam, M., & Hassanien, A. E. (2026) · Knowledge-Based Systems · doi:10.1016/j.knosys.2026.117103
Band Selection of Hyperspectral Images Based on Improved Hiking Optimization Combined With Fuzzy Clustering
Zhang, Y., Feng, C., & Lin, N. (2026) · Concurrency and Computation Practice and Experience · doi:10.1002/cpe.70966
Coordinated optimal planning and operational scheduling of WT–BESS systems in distribution networks using corrected Hiking Optimization Algorithm
Singh, P., Singh, B., Tejani, G. G., & Kumar, P. (2026) · Energy Nexus · doi:10.1016/j.nexus.2026.100855
A dual branch deep learning framework with trend gating for nonstationary monthly runoff prediction
Ma, H., Zhang, X., Zhang, Y., Zhao, T., & Huang, Y. (2026) · Journal of Hydrology Regional Studies · doi:10.1016/j.ejrh.2026.104185

Authors: Goodchild, M. F.
Affiliations: Department of Geography University of California Santa Barbara CA USA
Venue: Geographical Analysis
Publisher: Wiley
Published: 2020-08
Volume: 52
Issue: 4
Pages: 558-569
ISSN: 0016-7363 (ISSN-L)
1538-4632
DOI: 10.1111/gean.12253
OpenAlex: W3046297283
Cited by: 57
References: 16
Citations by year: 2026: 21 · 2025: 19 · 2024: 8 · 2023: 3 · 2022: 1 · 2021: 2 · 2020: 3
FWCI: 1.36
Type: journal article
Language: en
Open access: closed
Licence: onlinelibrary.wiley.com/termsAndConditions#vor (vor)
Locations: Geographical Analysis (publishedVersion)
Topics: Social Sciences › Transportation › Transportation Planning and Optimization
Social Sciences › Transportation › Urban Transport and Accessibility
Social Sciences › Urban Studies › Urban Design and Spatial Analysis
Keywords: travel time functions, topographic gradient, travel distance, energy consumption, connected and autonomous vehicles, route choice, travel time estimation

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review

Beyond Tobler’s Hiking Function

Abstract

Overview

Integrity signals

Verification

Claims the paper makes

Claims other papers make about this one

Citations

Cites

Cited by

Related

Metadata

Record

About these checks