Evolutionary algorithms and other metaheuristics in water resources: Current status, research challenges and future directions

The development and application of evolutionary algorithms (EAs) and other metaheuristics for the optimisation of water resources systems has been an active research field for over two decades. Research to date has emphasized algorithmic improvements and individual applications in specific areas (e.g. model calibration, water distribution systems, groundwater management, river-basin planning and management, etc.). However, there has been limited synthesis between shared problem traits, common EA challenges, and needed advances across major applications. This paper clarifies the current status and future research directions for better solving key water resources problems using EAs. Advances in understanding fitness landscape properties and their effects on algorithm performance are critical. Future EA-based applications to real-world problems require a fundamental shift of focus towards improving problem formulations, understanding general theoretic frameworks for problem decompositions, major advances in EA computational efficiency, and most importantly aiding real decision-making in complex, uncertain application contexts.

[1]  George Kuczera,et al.  Multiobjective optimization of urban water resources: Moving toward more practical solutions , 2012 .

[2]  Andrea Castelletti,et al.  Emulation techniques for the reduction and sensitivity analysis of complex environmental models , 2012, Environ. Model. Softw..

[3]  Mohammad Hadi Afshar,et al.  Improving the efficiency of ant algorithms using adaptive refinement: Application to storm water network design , 2006 .

[4]  A. Castelletti,et al.  Tree‐based iterative input variable selection for hydrological modeling , 2013 .

[5]  Tim Jones Evolutionary Algorithms, Fitness Landscapes and Search , 1995 .

[6]  D. Savić,et al.  Multiobjective design of water distribution systems under uncertainty , 2005 .

[7]  Andries Petrus Engelbrecht,et al.  A survey of techniques for characterising fitness landscapes and some possible ways forward , 2013, Inf. Sci..

[8]  Angela Marchi,et al.  Methodology for Comparing Evolutionary Algorithms for Optimization of Water Distribution Systems , 2014 .

[9]  Dumitru Roman,et al.  Model as a Service (MaaS) , 2008 .

[10]  Meghna Babbar-Sebens,et al.  Standard Interactive Genetic Algorithm—Comprehensive Optimization Framework for Groundwater Monitoring Design , 2008 .

[11]  Lothar Thiele,et al.  A Preference-Based Evolutionary Algorithm for Multi-Objective Optimization , 2009, Evolutionary Computation.

[12]  Riccardo Poli,et al.  Topological Interpretation of Crossover , 2004, GECCO.

[13]  Angus R. Simpson,et al.  A decomposition and multistage optimization approach applied to the optimization of water distribution systems with multiple supply sources , 2013 .

[14]  Holger R. Maier,et al.  A multiobjective ant colony optimization approach for scheduling environmental flow management alternatives with application to the River Murray, Australia , 2013 .

[15]  Holger R. Maier,et al.  Reliability-Based Approach to Multicriteria Decision Analysis for Water Resources , 2004 .

[16]  Miguel A. Carreira-Perpinan,et al.  Dimensionality Reduction , 2011 .

[17]  Meghna Babbar-Sebens,et al.  Interactive Genetic Algorithm with Mixed Initiative Interaction for multi-criteria ground water monitoring design , 2012, Appl. Soft Comput..

[18]  Vladan Babovic,et al.  A Real Options Approach to the Design and Architecture of Water Supply Systems Using Innovative Water Technologies Under Uncertainty , 2012 .

[19]  Maarten Keijzer,et al.  Evolving Objects: A General Purpose Evolutionary Computation Library , 2001, Artificial Evolution.

[20]  George Kuczera,et al.  Bayesian analysis of input uncertainty in hydrological modeling: 2. Application , 2006 .

[21]  Joshua D. Knowles,et al.  ParEGO: a hybrid algorithm with on-line landscape approximation for expensive multiobjective optimization problems , 2006, IEEE Transactions on Evolutionary Computation.

[22]  Meghna Babbar-Sebens,et al.  User Modelling for Interactive Optimization Using Neural Network , 2013, 2013 IEEE International Conference on Systems, Man, and Cybernetics.

[23]  Pierre Collet,et al.  Massively Parallel Evolutionary Computation on GPGPUs , 2013, Natural Computing Series.

[24]  D. Levine,et al.  Experiences with the PGAPack Parallel Genetic Algorithm Library , 1999 .

[25]  Joseph R. Kasprzyk,et al.  Many objective robust decision making for complex environmental systems undergoing change , 2012, Environ. Model. Softw..

[26]  Holger R. Maier,et al.  A genetic algorithm calibration method based on convergence due to genetic drift , 2008, Inf. Sci..

[27]  Angus R. Simpson,et al.  Genetic algorithms compared to other techniques for pipe optimization , 1994 .

[28]  Bryan A. Tolson,et al.  A benchmarking framework for simulation-based optimization of environmental models , 2012, Environ. Model. Softw..

[29]  Leon Basdekas Is Multiobjective Optimization Ready for Water Resources Practitioners? Utility’s Drought Policy Investigation , 2014 .

[30]  Jery R. Stedinger,et al.  SOCRATES: A system for scheduling hydroelectric generation under uncertainty , 1995, Ann. Oper. Res..

[31]  Holger R. Maier,et al.  Comparison of genetic algorithm parameter setting methods for chlorine injection optimization. , 2010 .

[32]  R. P. Oliveira,et al.  Operating rules for multireservoir systems , 1997 .

[33]  Kalyanmoy Deb,et al.  Running performance metrics for evolutionary multi-objective optimizations , 2002 .

[34]  G. K. Young Finding Reservoir Operating Rules , 1967 .

[35]  Marco Laumanns,et al.  Combining Convergence and Diversity in Evolutionary Multiobjective Optimization , 2002, Evolutionary Computation.

[36]  Wenyan Wu,et al.  Multiobjective optimization of water distribution systems accounting for economic cost, hydraulic reliability, and greenhouse gas emissions , 2013 .

[37]  Robert W. Blanning,et al.  The construction and implementation of metamodels , 1975 .

[38]  Ganapati Panda,et al.  A survey on nature inspired metaheuristic algorithms for partitional clustering , 2014, Swarm Evol. Comput..

[39]  L. Shawn Matott,et al.  Evaluating uncertainty in integrated environmental models: A review of concepts and tools , 2009 .

[40]  D. McKinney,et al.  Genetic algorithm solution of groundwater management models , 1994 .

[41]  Patrick M. Reed,et al.  A Framework for Visually Interactive Decision-Making and Design Using Evolutionary Multiobjective Optimization (VIDEO) , 2007 .

[42]  Feifei Zheng,et al.  An efficient decomposition and dual-stage multi-objective optimization method for water distribution systems with multiple supply sources , 2014, Environ. Model. Softw..

[43]  David H. Wolpert,et al.  No free lunch theorems for optimization , 1997, IEEE Trans. Evol. Comput..

[44]  Eckart Zitzler,et al.  Evolutionary algorithms for multiobjective optimization: methods and applications , 1999 .

[45]  Saguiv A. Hadari Value Trade-off , 1988, The Journal of Politics.

[46]  Patrick M. Reed,et al.  Borg: An Auto-Adaptive Many-Objective Evolutionary Computing Framework , 2013, Evolutionary Computation.

[47]  Jon C. Liebman,et al.  Some Simple-Minded Observations on the Role of Optimization in Public Systems Decision-Making , 1976 .

[48]  David E. Goldberg,et al.  Designing a competent simple genetic algorithm for search and optimization , 2000 .

[49]  Dr.-Ing. Hartmut Pohlheim Genetic and Evolutionary Algorithm Toolbox for Matlab , 2000 .

[50]  Soon-Thiam Khu,et al.  An Investigation on Preference Order Ranking Scheme for Multiobjective Evolutionary Optimization , 2007, IEEE Transactions on Evolutionary Computation.

[51]  Zoran Kapelan,et al.  Fuzzy probabilistic design of water distribution networks , 2011 .

[52]  Meghna Babbar-Sebens,et al.  A Case-Based Micro Interactive Genetic Algorithm (CBMIGA) for interactive learning and search: Methodology and application to groundwater monitoring design , 2010, Environ. Model. Softw..

[53]  Marcin Studniarski Stopping Criteria for Genetic Algorithms with Application to Multiobjective Optimization , 2010, PPSN.

[54]  Gary B. Lamont,et al.  Multiobjective evolutionary algorithms: classifications, analyses, and new innovations , 1999 .

[55]  John Doherty,et al.  Addendum to the PEST Manual , 2014 .

[56]  Zoran Kapelan,et al.  Flexible Water Distribution System Design under Future Demand Uncertainty , 2015 .

[57]  James Kennedy,et al.  Defining a Standard for Particle Swarm Optimization , 2007, 2007 IEEE Swarm Intelligence Symposium.

[58]  Barbara S. Minsker,et al.  Multiscale island injection genetic algorithms for groundwater remediation , 2007 .

[59]  Barbara S. Minsker,et al.  Applying Dynamic Surrogate Models in Noisy Genetic Algorithms to Optimize Groundwater Remediation Designs , 2011 .

[60]  Gary B. Lamont,et al.  Evolutionary algorithms for solving multi-objective problems, Second Edition , 2007, Genetic and evolutionary computation series.

[61]  Holger R. Maier,et al.  Relationship between problem characteristics and the optimal number of genetic algorithm generations , 2011 .

[62]  Marco Laumanns,et al.  Performance assessment of multiobjective optimizers: an analysis and review , 2003, IEEE Trans. Evol. Comput..

[63]  Kalyanmoy Deb,et al.  Muiltiobjective Optimization Using Nondominated Sorting in Genetic Algorithms , 1994, Evolutionary Computation.

[64]  Holger R. Maier,et al.  Non-linear variable selection for artificial neural networks using partial mutual information , 2008, Environ. Model. Softw..

[65]  Velimir V. Vesselinov,et al.  Adaptive hybrid optimization strategy for calibration and parameter estimation of physical process models , 2011, Comput. Geosci..

[66]  Victor J. Rayward-Smith,et al.  Fitness Distance Correlation and Ridge Functions , 1998, PPSN.

[67]  Patrick M. Reed,et al.  A framework for Visually Interactive Decision-making and Design using Evolutionary Multi-objective Optimization (VIDEO) , 2007, Environ. Model. Softw..

[68]  Mahmood Ali,et al.  A decision support system for ERP implementation in small and medium-sized enterprises , 2013 .

[69]  Thomas Stützle,et al.  An experimental analysis of design choices of multi-objective ant colony optimization algorithms , 2012, Swarm Intelligence.

[70]  Mauro Birattari,et al.  Towards a theory of practice in metaheuristics design: A machine learning perspective , 2006, RAIRO Theor. Informatics Appl..

[71]  Aaron C. Zecchin,et al.  Coupled Binary Linear Programming–Differential Evolution Algorithm Approach for Water Distribution System Optimization , 2014 .

[72]  Kalyanmoy Deb,et al.  Introducing Robustness in Multi-Objective Optimization , 2006, Evolutionary Computation.

[73]  John W. Labadie,et al.  Optimal Operational Analysis of the Colorado-Big Thompson Project , 1989 .

[74]  Rainer Laur,et al.  Stopping Criteria for Single-Objective Optimization , 2005 .

[75]  Kay Chen Tan,et al.  Evolutionary Multi-objective Optimization in Uncertain Environments - Issues and Algorithms , 2009, Studies in Computational Intelligence.

[76]  Holger R. Maier,et al.  Optimal sequencing of water supply options at the regional scale incorporating alternative water supply sources and multiple objectives , 2014, Environ. Model. Softw..

[77]  Jesús García,et al.  A cumulative evidential stopping criterion for multiobjective optimization evolutionary algorithms , 2007, GECCO '07.

[78]  P. Bhave,et al.  Optimal Design of Water Networks Using a Modified Genetic Algorithm with Reduction in Search Space , 2008 .

[79]  M. Franssen Arrow’s theorem, multi-criteria decision problems and multi-attribute preferences in engineering design , 2005 .

[80]  Holger R. Maier,et al.  Water Distribution System Optimization Using Metamodels , 2005 .

[81]  Shin Ta Liu,et al.  Risk Modeling, Assessment, and Management , 1999, Technometrics.

[82]  B. Minsker,et al.  Groundwater Remediation Design Using Multiscale Genetic Algorithms , 2006 .

[83]  Colin R. Reeves,et al.  Epistasis in Genetic Algorithms: An Experimental Design Perspective , 1995, ICGA.

[84]  Z. Rao,et al.  The Use of Neural Networks and Genetic Algorithms for Design of Groundwater Remediation Schemes , 1997 .

[85]  Bruce A. Robinson,et al.  Self-Adaptive Multimethod Search for Global Optimization in Real-Parameter Spaces , 2009, IEEE Transactions on Evolutionary Computation.

[86]  Angus R. Simpson,et al.  Genetic Algorithms for Reliability-Based Optimization of Water Distribution Systems , 2004 .

[87]  Peter J. Fleming,et al.  On the Evolutionary Optimization of Many Conflicting Objectives , 2007, IEEE Transactions on Evolutionary Computation.

[88]  Kenneth A. De Jong,et al.  Using Markov Chains to Analyze GAFOs , 1994, FOGA.

[89]  Holger R. Maier,et al.  Distance-based and stochastic uncertainty analysis for multi-criteria decision analysis in Excel using Visual Basic for Applications , 2006, Environ. Model. Softw..

[90]  Jeffrey Horn,et al.  Handbook of evolutionary computation , 1997 .

[91]  Yan Zhang,et al.  Reducing Long‐Term Remedial Costs by Transport Modeling Optimization , 2006, Ground water.

[92]  Keith Beven,et al.  A manifesto for the equifinality thesis , 2006 .

[93]  Manuel López-Ibáñez,et al.  Ant colony optimization , 2010, GECCO '10.

[94]  Adam J. Siade,et al.  Reduced order parameter estimation using quasilinearization and quadratic programming , 2012 .

[95]  Olivier Teytaud,et al.  On the Hardness of Offline Multi-objective Optimization , 2007, Evolutionary Computation.

[96]  Riccardo Poli,et al.  Particle swarm optimization , 1995, Swarm Intelligence.

[97]  Holger R. Maier,et al.  A framework for using ant colony optimization to schedule environmental flow management alternatives for rivers, wetlands, and floodplains , 2012 .

[98]  David E. Goldberg,et al.  Optimal sampling in a noisy genetic algorithm for risk-based remediation design , 2001 .

[99]  Avi Ostfeld,et al.  State of the Art for Genetic Algorithms and Beyond in Water Resources Planning and Management , 2010 .

[100]  S. Yakowitz Dynamic programming applications in water resources , 1982 .

[101]  Zoran Kapelan,et al.  Reducing the Complexity of Multiobjective Water Distribution System Optimization through Global Sensitivity Analysis , 2012 .

[102]  G. Kourakos,et al.  Remediation of heterogeneous aquifers based on multiobjective optimization and adaptive determination of critical realizations , 2008 .

[103]  Andrea Castelletti,et al.  Planning the Optimal Operation of a Multioutlet Water Reservoir with Water Quality and Quantity Targets , 2014 .

[104]  Hyde K.m.,et al.  Visual Basic for Applicationsを用いたExcelにおける多基準意思決定解析のための距離ベースの及び確率論的な不確実性解析 , 2006 .

[105]  H. Rittel,et al.  Dilemmas in a general theory of planning , 1973 .

[106]  Patrick M. Reed,et al.  Using interactive archives in evolutionary multiobjective optimization: A case study for long-term groundwater monitoring design , 2007, Environ. Model. Softw..

[107]  Xinan Yin,et al.  OPTIMIZING ENVIRONMENTAL FLOWS BELOW DAMS , 2012 .

[108]  Abhishek Singh,et al.  An interactive multi-objective optimization framework for groundwater inverse modeling , 2008 .

[109]  Piet Demeester,et al.  A Surrogate Modeling and Adaptive Sampling Toolbox for Computer Based Design , 2010, J. Mach. Learn. Res..

[110]  Joshua D. Knowles,et al.  On metrics for comparing nondominated sets , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[111]  Eckart Zitzler,et al.  Evolutionary Multi-Criterion Optimization, Third International Conference, EMO 2005, Guanajuato, Mexico, March 9-11, 2005, Proceedings , 2005, EMO.

[112]  Patrick M. Reed,et al.  Save now, pay later? Multi-period many-objective groundwater monitoring design given systematic model errors and uncertainty , 2011 .

[113]  Peter Rogers,et al.  Use of systems analysis in water management , 1986 .

[114]  Lingguang Song,et al.  An eco-environmental water demand based model for optimising water resources using hybrid genetic simulated annealing algorithms. Part II. Model application and results. , 2009, Journal of environmental management.

[115]  Giovanni Righini,et al.  Heuristics from Nature for Hard Combinatorial Optimization Problems , 1996 .

[116]  James E. Smith,et al.  Self-Adaptation of Mutation Operator and Probability for Permutation Representations in Genetic Algorithms , 2010, Evolutionary Computation.

[117]  L. Shawn Matott,et al.  Application of MATLAB and Python optimizers to two case studies involving groundwater flow and contaminant transport modeling , 2011, Comput. Geosci..

[118]  Kalyanmoy Deb,et al.  Reference point based multi-objective optimization using evolutionary algorithms , 2006, GECCO.

[119]  Olaf David,et al.  A software engineering perspective on environmental modeling framework design: The Object Modeling System , 2013, Environ. Model. Softw..

[120]  Thomas Stützle,et al.  Exploratory Analysis of Stochastic Local Search Algorithms in Biobjective Optimization , 2010, Experimental Methods for the Analysis of Optimization Algorithms.

[121]  Holger R. Maier,et al.  Input determination for neural network models in water resources applications. Part 1—background and methodology , 2005 .

[122]  Barbara S. Minsker,et al.  Incorporating subjective and stochastic uncertainty in an interactive multi-objective groundwater calibration framework , 2010 .

[123]  P. Siarry,et al.  Multiobjective Optimization: Principles and Case Studies , 2004 .

[124]  Eckart Zitzler,et al.  Objective Reduction in Evolutionary Multiobjective Optimization: Theory and Applications , 2009, Evolutionary Computation.

[125]  E. Weinberger,et al.  Correlated and uncorrelated fitness landscapes and how to tell the difference , 1990, Biological Cybernetics.

[126]  George Kuczera,et al.  Bayesian analysis of input uncertainty in hydrological modeling: 1. Theory , 2006 .

[127]  Franz Rothlauf,et al.  Design of Modern Heuristics: Principles and Application , 2011 .

[128]  Barbara S. Minsker,et al.  Optimal groundwater remediation design using an Adaptive Neural Network Genetic Algorithm , 2006 .

[129]  George I. N. Rozvany,et al.  Structural and Multidisciplinary Optimization , 1995 .

[130]  S. Sorooshian,et al.  A Shuffled Complex Evolution Metropolis algorithm for optimization and uncertainty assessment of hydrologic model parameters , 2002 .

[131]  P. Reed,et al.  Managing population and drought risks using many‐objective water portfolio planning under uncertainty , 2009 .

[132]  Yacov Y. Haimes,et al.  Sensitivity, responsivity, stability and irreversibility as multiple objectives in civil systems , 1977 .

[133]  Lothar Thiele,et al.  Comparison of Multiobjective Evolutionary Algorithms: Empirical Results , 2000, Evolutionary Computation.

[134]  Nien-Sheng Hsu,et al.  Network Flow Optimization Model for Basin-Scale Water Supply Planning , 2002 .

[135]  Robert J Lempert,et al.  A new decision sciences for complex systems , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[136]  Rainer Laur,et al.  Stopping Criteria for a Constrained Single-Objective Particle Swarm Optimization Algorithm , 2007, Informatica.

[137]  Abhishek Singh,et al.  Uncertainty‐based multiobjective optimization of groundwater remediation design , 2003 .

[138]  Bart Naudts,et al.  A comparison of predictive measures of problem difficulty in evolutionary algorithms , 2000, IEEE Trans. Evol. Comput..

[139]  Thomas M. Walski,et al.  Water distribution system optimization , 1985 .

[140]  G RegisRommel,et al.  Constrained Global Optimization of Expensive Black Box Functions Using Radial Basis Functions , 2005 .

[141]  Leila Kallel,et al.  Inside GA Dynamics: Ground Basis for Comparison , 1998, PPSN.

[142]  Rodolfo Soncini-Sessa,et al.  A dimensionality reduction approach for many-objective Markov Decision Processes: Application to a water reservoir operation problem , 2014, Environ. Model. Softw..

[143]  William H. Hsu,et al.  GA-Hardness Revisited , 2003, GECCO.

[144]  Patrick M. Reed,et al.  Comparing state-of-the-art evolutionary multi-objective algorithms for long-term groundwater monitoring design , 2005 .

[145]  Kourosh Behzadian,et al.  Stochastic sampling design using a multi-objective genetic algorithm and adaptive neural networks , 2009, Environ. Model. Softw..

[146]  O. Larichev Cognitive validity in design of decision‐aiding techniques , 1992 .

[147]  K. Kinnear Fitness landscapes and difficulty in genetic programming , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[148]  Patrick Siarry,et al.  Three new metrics to measure the convergence of metaheuristics towards the Pareto frontier and the aesthetic of a set of solutions in biobjective optimization , 2005, Comput. Oper. Res..

[149]  C. A. Murthy,et al.  Variance as a Stopping Criterion for Genetic Algorithms with Elitist Model , 2012, Fundam. Informaticae.

[150]  Carlos A. Coello Coello,et al.  A Review of Techniques for Handling Expensive Functions in Evolutionary Multi-Objective Optimization , 2010 .

[151]  Dragan Savic,et al.  Improved design of “Anytown” distribution network using structured messy genetic algorithms , 1999 .

[152]  Joseph R. Kasprzyk,et al.  Many-objective de Novo water supply portfolio planning under deep uncertainty , 2012, Environ. Model. Softw..

[153]  Andrea Castelletti,et al.  A procedural approach to strengthening integration and participation in water resource planning , 2006, Environ. Model. Softw..

[154]  Abhishek Singh,et al.  Image-Based Machine Learning for Reduction of User Fatigue in an Interactive Model Calibration System , 2010, J. Comput. Civ. Eng..

[155]  Peter J. Fleming,et al.  Many-Objective Optimization: An Engineering Design Perspective , 2005, EMO.

[156]  Thomas Bäck,et al.  Parallel Problem Solving from Nature — PPSN V , 1998, Lecture Notes in Computer Science.

[157]  Patrick M. Reed,et al.  Visual Analytics Clarify The Scalability And Effectiveness Of Massively Parallel Many-Objective Optimization: A Groundwater Monitoring Design Example , 2013 .

[158]  Holger R. Maier,et al.  Multiobjective optimization of cluster‐scale urban water systems investigating alternative water sources and level of decentralization , 2014 .

[159]  Patrick M. Reed,et al.  Many‐objective groundwater monitoring network design using bias‐aware ensemble Kalman filtering, evolutionary optimization, and visual analytics , 2011 .

[160]  Kalyanmoy Deb,et al.  Sufficient conditions for deceptive and easy binary functions , 1994, Annals of Mathematics and Artificial Intelligence.

[161]  John W. Labadie,et al.  Optimal Operation of Multireservoir Systems: State-of-the-Art Review , 2004 .

[162]  C. Hwang Multiple Objective Decision Making - Methods and Applications: A State-of-the-Art Survey , 1979 .

[163]  Holger R. Maier,et al.  Application of partial mutual information variable selection to ANN forecasting of water quality in water distribution systems , 2008, Environ. Model. Softw..

[164]  Mehrdad Tamiz,et al.  Multi-objective meta-heuristics: An overview of the current state-of-the-art , 2002, Eur. J. Oper. Res..

[165]  Ed Keedwell,et al.  A hybrid genetic algorithm for the design of water distribution networks , 2005, Eng. Appl. Artif. Intell..

[166]  Kazuhiro Ohkura,et al.  Estimating the Degree of Neutrality in Fitness Landscapes by the Nei's Standard Genetic Distance-An Application to Evolutionary Robotics , 2005 .

[167]  Graeme C. Dandy,et al.  Optimization of Water Distribution Systems Using Online Retrained Metamodels , 2014 .

[168]  Stefan M. Wild,et al.  BENEFITS OF DEEPER ANALYSIS IN SIMULATION- BASED GROUNDWATER OPTIMIZATION PROBLEMS , 2012 .

[169]  George H. Leavesley,et al.  A modular approach to addressing model design, scale, and parameter estimation issues in distributed hydrological modelling , 2002 .

[170]  Michael E. Wall,et al.  Galib: a c++ library of genetic algorithm components , 1996 .

[171]  Julien J. Harou,et al.  Robust Decision Making and Info-Gap Decision Theory for water resource system planning , 2013 .

[172]  C. Diks,et al.  Improved treatment of uncertainty in hydrologic modeling: Combining the strengths of global optimization and data assimilation , 2005 .

[173]  S. Sorooshian,et al.  Shuffled complex evolution approach for effective and efficient global minimization , 1993 .

[174]  H. Madsen,et al.  A fast Evolutionary-based Meta-Modelling Approach for the Calibration of a Rainfall-Runoff Model , 2004 .

[175]  W. Grayman,et al.  Toward a Sustainable Water Future: Visions for 2050 , 2012 .

[176]  David E. Goldberg,et al.  Risk‐based in situ bioremediation design using a noisy genetic algorithm , 2000 .

[177]  Thomas Stützle,et al.  Ant Colony Optimization , 2009, EMO.

[178]  Ximing Cai,et al.  Reservoir Reoperation for Fish Ecosystem Restoration Using Daily Inflows—Case Study of Lake Shelbyville , 2011 .

[179]  Dimitri Solomatine,et al.  Groundwater Model Approximation with Artificial Neural Network for Selecting Optimum Pumping Strategy for Plume Removal , 2001 .

[180]  W. Yeh,et al.  Experimental design for estimating unknown groundwater pumping using genetic algorithm and reduced order model , 2013 .

[181]  Kevin E Lansey,et al.  Revisiting Optimal Water-Distribution System Design: Issues and a Heuristic Hierarchical Approach , 2012 .

[182]  Milan Zeleny,et al.  The Evolution of Optimality: De Novo Programming , 2005, EMO.

[183]  Michael de Paly,et al.  Optimization of high‐reliability‐based hydrological design problems by robust automatic sampling of critical model realizations , 2010 .

[184]  George Kuczera,et al.  Optimizing water supply headworks operating rules under stochastic inputs: Assessment of genetic algorithm performance , 2005 .

[185]  Michel Gendreau,et al.  Metaheuristics in Combinatorial Optimization , 2022 .

[186]  Patrick M. Reed,et al.  Computational Scaling Analysis of Multiobjective Evolutionary Algorithms in Long-Term Groundwater Monitoring Applications , 2006 .

[187]  Peter M. A. Sloot,et al.  Application of parallel computing to stochastic parameter estimation in environmental models , 2006, Comput. Geosci..

[188]  Boris Kompare,et al.  Environmental Modelling & Software , 2014 .

[189]  Angus R. Simpson,et al.  Dynamically Expanding Choice-Table Approach to Genetic Algorithm Optimization of Water Distribution Systems , 2011 .

[190]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems (Genetic and Evolutionary Computation) , 2006 .

[191]  Yong Tang,et al.  Parallelization strategies for rapid and robust evolutionary multiobjective optimization in water resources applications , 2007 .

[192]  Bernard Roy,et al.  Problems and methods with multiple objective functions , 1971, Math. Program..

[193]  Michael S. Eldred,et al.  DAKOTA : a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis. Version 5.0, user's reference manual. , 2010 .

[194]  Holger R. Maier,et al.  An adaptive ant colony optimization framework for scheduling environmental flow management alternatives under varied environmental water availability conditions , 2014 .

[195]  A. V. Lotova,et al.  Experience of model integration and Pareto frontier visualization in the search for preferable water quality strategies , 2004 .

[196]  Ed Keedwell,et al.  Hybridizing Cellular Automata Principles and NSGAII for Multi-objective Design of Urban Water Networks , 2006, EMO.

[197]  Tor Arne Johansen,et al.  Real-Time Production Optimization of Oil and Gas Production Systems: A Technology Survey , 2007 .

[198]  William W.-G. Yeh,et al.  Groundwater Management Using Model Reduction via Empirical Orthogonal Functions , 2008 .

[199]  S. Ranjithan,et al.  Using genetic algorithms to solve a multiple objective groundwater pollution containment problem , 1994 .

[200]  Yaochu Jin,et al.  A comprehensive survey of fitness approximation in evolutionary computation , 2005, Soft Comput..

[201]  J. A. Bagley,et al.  Progress in Aerospace Sciences , 2019 .

[202]  John M. Flach,et al.  MGA: a decision support system for complex, incompletely defined problems , 1990, IEEE Trans. Syst. Man Cybern..

[203]  M. Schoenauer,et al.  On functions with a given fitness-distance relation , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[204]  Leo Dobes,et al.  Getting Real about Adapting to Climate Change: Using 'Real Options' to Address the Uncertainties , 2008 .

[205]  Holger R. Maier,et al.  Power plant maintenance scheduling using ant colony optimization: an improved formulation , 2008 .

[206]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems , 2002, Genetic Algorithms and Evolutionary Computation.

[207]  Alfred Inselberg,et al.  Multidimensional detective , 1997, Proceedings of VIZ '97: Visualization Conference, Information Visualization Symposium and Parallel Rendering Symposium.

[208]  David A. Van Veldhuizen,et al.  Evolutionary Computation and Convergence to a Pareto Front , 1998 .

[209]  Andrew B. Kahng,et al.  A new adaptive multi-start technique for combinatorial global optimizations , 1994, Oper. Res. Lett..

[210]  Angus R. Simpson,et al.  Competent Genetic-Evolutionary Optimization of Water Distribution Systems , 2001 .

[211]  Carl Tim Kelley,et al.  Numerical simulation of water resources problems: Models, methods, and trends , 2013 .

[212]  Heng Tao Shen,et al.  Dimensionality Reduction , 2009, Encyclopedia of Database Systems.

[213]  Quentin W. Martin Optimal Operation of Multiple Reservoir Systems , 1983 .

[214]  Eileen Poeter,et al.  Building model analysis applications with the Joint Universal Parameter IdenTification and Evaluation of Reliability (JUPITER) API , 2008, Comput. Geosci..

[215]  Michael Affenzeller,et al.  A Comprehensive Survey on Fitness Landscape Analysis , 2012, Recent Advances in Intelligent Engineering Systems.

[216]  Kalyanmoy Deb,et al.  Messy Genetic Algorithms: Motivation, Analysis, and First Results , 1989, Complex Syst..

[217]  David R. White Software review: the ECJ toolkit , 2011, Genetic Programming and Evolvable Machines.

[218]  Patrick M. Reed,et al.  Diagnostic Assessment of Search Controls and Failure Modes in Many-Objective Evolutionary Optimization , 2012, Evolutionary Computation.

[219]  K. M. Hyde,et al.  A distance-based uncertainty analysis approach to multi-criteria decision analysis for water resource decision making. , 2005, Journal of environmental management.

[220]  Bryan A. Tolson,et al.  Dynamically dimensioned search algorithm for computationally efficient watershed model calibration , 2007 .

[221]  Chi-Keong Goh,et al.  Computational Intelligence in Expensive Optimization Problems , 2010 .

[222]  Holger R. Maier,et al.  Selection of input variables for data driven models: An average shifted histogram partial mutual information estimator approach , 2009 .

[223]  Khaled Rasheed,et al.  A Survey of Fitness Approximation Methods Applied in Evolutionary Algorithms , 2010 .

[224]  Jack P. C. Kleijnen,et al.  Kriging Metamodeling in Simulation: A Review , 2007, Eur. J. Oper. Res..

[225]  Waldo Gonzalo Cancino Ticona,et al.  Multiobjective Evolutionary Algorithms Applied to the Rehabilitation of a Water Distribution System: A Comparative Study , 2003, EMO.

[226]  David W. Watkins,et al.  Finding Robust Solutions to Water Resources Problems , 1997 .

[227]  Jennifer Creek,et al.  Towards a Theory of Practice , 2006 .

[228]  George Kuczera,et al.  How flexibility in urban water resource decisions helps to manage uncertainty , 2013 .

[229]  Anthony J. Jakeman,et al.  Integrated assessment and modelling: features, principles and examples for catchment management , 2003, Environ. Model. Softw..

[230]  Mary C. Hill,et al.  Integrated environmental modeling: A vision and roadmap for the future , 2013, Environ. Model. Softw..

[231]  Kent McClymont,et al.  A general multi-objective hyper-heuristic for water distribution network design with discolouration risk , 2013 .

[232]  M. F K Pasha,et al.  STRATEGIES FOR REAL TIME PUMP OPERATION FOR WATER DISTRIBUTION SYSTEMS , 2011 .

[233]  H. Maier,et al.  Including adaptation and mitigation responses to climate change in a multiobjective evolutionary algorithm framework for urban water supply systems incorporating GHG emissions , 2014 .

[234]  António Gaspar-Cunha,et al.  A Multi-Objective Evolutionary Algorithm Using Neural Networks to Approximate Fitness Evaluations , 2005, Int. J. Comput. Syst. Signals.

[235]  Konstantin Staschus,et al.  Optimization of Value of CVP’s Hydropower Production , 1990 .

[236]  Yuqiong Liu,et al.  Reconciling theory with observations: elements of a diagnostic approach to model evaluation , 2008 .

[237]  E. A. Silver,et al.  An overview of heuristic solution methods , 2004, J. Oper. Res. Soc..

[238]  Kaisa Miettinen,et al.  Visualizing the Pareto Frontier , 2008, Multiobjective Optimization.

[239]  Andrea Castelletti,et al.  Many‐objective reservoir policy identification and refinement to reduce policy inertia and myopia in water management , 2014 .

[240]  Carlos M. Fonseca,et al.  Inferential Performance Assessment of Stochastic Optimisers and the Attainment Function , 2001, EMO.

[241]  Phil Husbands,et al.  Fitness Landscapes and Evolvability , 2002, Evolutionary Computation.

[242]  Lothar Thiele,et al.  Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach , 1999, IEEE Trans. Evol. Comput..

[243]  Kazuhiro Ohkura,et al.  Estimating the Degree of Neutrality in Fitness Landscapes by the Nei’s Standard Genetic Distance – An Application to Evolutionary Robotics – , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[244]  Bryan A. Tolson,et al.  Review of surrogate modeling in water resources , 2012 .

[245]  Angus R. Simpson,et al.  Ant colony optimization for power plant maintenance scheduling optimization—a five-station hydropower system , 2008, Ann. Oper. Res..

[246]  D. Mallants,et al.  Efficient posterior exploration of a high‐dimensional groundwater model from two‐stage Markov chain Monte Carlo simulation and polynomial chaos expansion , 2013 .

[247]  Maria da Conceição Cunha,et al.  Tabu search algorithms for water network optimization , 2004, Eur. J. Oper. Res..

[248]  Hirotaka Nakayama,et al.  Meta-Modeling in Multiobjective Optimization , 2008, Multiobjective Optimization.

[249]  Mohamed Slimane,et al.  A Critical and Empirical Study of Epistasis Measures for Predicting GA Performances: A Summary , 1997, Artificial Evolution.

[250]  Andrea Castelletti,et al.  Interactive response surface approaches using computationally intensive models for multiobjective planning of lake water quality remediation , 2011 .

[251]  J. Antenucci,et al.  A multiobjective response surface approach for improved water quality planning in lakes and reservoirs , 2010 .

[252]  Dan Boneh,et al.  On genetic algorithms , 1995, COLT '95.

[253]  Holger R. Maier,et al.  Optimal operation of complex water distribution systems using metamodels. , 2010 .

[254]  H. Raiffa,et al.  Decisions with Multiple Objectives , 1993 .

[255]  Kalyanmoy Deb,et al.  A Multi-Objective Optimization Procedure with Successive Approximate Models , .

[256]  Holger R. Maier,et al.  Input determination for neural network models in water resources applications. Part 2. Case study: forecasting salinity in a river , 2005 .

[257]  Jesús García,et al.  An approach to stopping criteria for multi-objective optimization evolutionary algorithms: The MGBM criterion , 2009, 2009 IEEE Congress on Evolutionary Computation.

[258]  Godfrey A. Walters,et al.  EVOLUTIONARY DESIGN ALGORITHM FOR OPTIMAL LAYOUT OF TREE NETWORKS , 1995 .

[259]  Patrick M. Reed,et al.  Many objective visual analytics: rethinking the design of complex engineered systems , 2013, Structural and Multidisciplinary Optimization.

[260]  L. Darrell Whitley,et al.  Delta Coding: An Iterative Search Strategy for Genetic Algorithms , 1991, ICGA.

[261]  Meghna Babbar-Sebens,et al.  Optimizing conservation practices in watersheds: Do community preferences matter? , 2013 .

[262]  Enrique Alba,et al.  Algorithm::Evolutionary, a flexible Perl module for evolutionary computation , 2010, Soft Comput..

[263]  Helder Coelho,et al.  The Design of Innovation: Lessons from and for Competent Genetic Algorithms by David E. Goldberg , 2005, J. Artif. Soc. Soc. Simul..

[264]  Joseph R. Kasprzyk,et al.  A new epsilon-dominance hierarchical Bayesian optimization algorithm for large multiobjective monitoring network design problems , 2008 .

[265]  Q. Kang,et al.  Optimization and uncertainty assessment of strongly nonlinear groundwater models with high parameter dimensionality , 2010 .

[266]  Tingting Zhao,et al.  Enabling Real-time Water Decision Support Services Using Model as a Service , 2014 .

[267]  Holger R. Maier,et al.  Development of a modelling framework for optimal sequencing of water supply options at the regional scale incorporating sustainability and uncertainty , 2011 .

[268]  Jonathan Rosenhead,et al.  What's the Problem? An Introduction to Problem Structuring Methods , 1996 .

[269]  George Kuczera,et al.  Robust optimisation of urban drought security for an uncertain climate , 2013 .

[270]  Angus R. Simpson,et al.  Power Plant Maintenance Scheduling Using Ant Colony Optimization , 2007 .

[271]  Peter Merz,et al.  Advanced Fitness Landscape Analysis and the Performance of Memetic Algorithms , 2004, Evolutionary Computation.

[272]  George Kuczera,et al.  Toward a reliable decomposition of predictive uncertainty in hydrological modeling: Characterizing rainfall errors using conditional simulation , 2011 .

[273]  J. Ndiritu,et al.  An improved genetic algorithm for rainfall-runoff model calibration and function optimization , 2001 .

[274]  Joseph R. Kasprzyk,et al.  Evolutionary multiobjective optimization in water resources: The past, present, and future , 2012 .

[275]  Daniel P. Loucks Water Resource Management Modeling in 2050 , 2012 .

[276]  Zoran Kapelan,et al.  Probabilistic building block identification for the optimal design and rehabilitation of water distribution systems , 2009 .

[277]  Ben Gouldby,et al.  Multiobjective optimisation for improved management of flood risk , 2014 .

[278]  Raphael T. Haftka,et al.  Surrogate-based Analysis and Optimization , 2005 .

[279]  António Pais Antunes,et al.  An Efficient Simulated Annealing Algorithm for Regional Wastewater System Planning , 2009, Comput. Aided Civ. Infrastructure Eng..

[280]  Ralph L. Keeney,et al.  Decisions with multiple objectives: preferences and value tradeoffs , 1976 .

[281]  Andrea Castelletti,et al.  A general framework for Dynamic Emulation Modelling in environmental problems , 2012, Environ. Model. Softw..

[282]  Nicolas Zufferey,et al.  Metaheuristics: Some Principles for an Efficient Design , 2012 .

[283]  Godfrey A. Walters,et al.  OPTIMAL LAYOUT OF TREE NETWORKS USING GENETIC ALGORITHMS , 1993 .

[284]  Georges R. Harik,et al.  Foundations of Genetic Algorithms , 1997 .

[285]  Ching-Lai Hwang,et al.  Fuzzy Multiple Attribute Decision Making - Methods and Applications , 1992, Lecture Notes in Economics and Mathematical Systems.

[286]  Andrea Castelletti,et al.  Data-driven dynamic emulation modelling for the optimal management of environmental systems , 2012, Environ. Model. Softw..

[287]  Peter Bayer,et al.  Optimization of concentration control by evolution strategies: Formulation, application, and assessment of remedial solutions , 2007 .

[288]  Patrick M. Reed,et al.  Many objective visual analytics: rethinking the design of complex engineered systems , 2013 .

[289]  Zoran Kapelan,et al.  Dealing with Uncertainty in Water Distribution System Models: A Framework for Real-Time Modeling and Data Assimilation , 2014 .

[290]  Yuval Davidor,et al.  Epistasis Variance: A Viewpoint on GA-Hardness , 1990, FOGA.

[291]  Andrea Castelletti,et al.  Visualization-based multi-objective improvement of environmental decision-making using linearization of response surfaces , 2010, Environ. Model. Softw..

[292]  R. K. Ursem Multi-objective Optimization using Evolutionary Algorithms , 2009 .

[293]  Colin R. Reeves,et al.  Genetic Algorithms , 1993, Encyclopedia of Database Systems.

[294]  Meghna Babbar-Sebens,et al.  Reinforcement learning for human-machine collaborative optimization: Application in ground water monitoring , 2009, 2009 IEEE International Conference on Systems, Man and Cybernetics.

[295]  Lawrence Buja,et al.  The computational future for climate and Earth system models: on the path to petaflop and beyond , 2009, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[296]  Andrea Castelletti,et al.  An evaluation framework for input variable selection algorithms for environmental data-driven models , 2014, Environ. Model. Softw..

[297]  Kalyanmoy Deb,et al.  Visualizing multi-dimensional pareto-optimal fronts with a 3D virtual reality system , 2008, 2008 International Multiconference on Computer Science and Information Technology.

[298]  Carl Tim Kelley,et al.  Iterative methods for optimization , 1999, Frontiers in applied mathematics.

[299]  Sharon A. Johnson,et al.  The Value of Hydrologic Information in Stochastic Dynamic Programming Models of a Multireservoir System , 1995 .

[300]  Kent McClymont Recent advances in problem understanding: changes in the landscape a year on , 2013, GECCO '13 Companion.

[301]  Alexis Tsoukiàs,et al.  From decision theory to decision aiding methodology , 2008, Eur. J. Oper. Res..

[302]  R. L. Keeney,et al.  Decisions with Multiple Objectives: Preferences and Value Trade-Offs , 1977, IEEE Transactions on Systems, Man, and Cybernetics.

[303]  Mohammad Hadi Afshar,et al.  Rebirthing genetic algorithm for storm sewer network design , 2012 .

[304]  P. Stadler Fitness Landscapes , 1993 .

[305]  P. Reed,et al.  A computational scaling analysis of multiobjective evolutionary algorithms in long-term groundwater monitoring applications , 2007 .

[306]  Hitoshi Iba,et al.  Genetic Programming 1998: Proceedings of the Third Annual Conference , 1999, IEEE Trans. Evol. Comput..

[307]  Craig A. Aumann,et al.  Constructing model credibility in the context of policy appraisal , 2011, Environ. Model. Softw..

[308]  Christine A. Shoemaker,et al.  Constrained Global Optimization of Expensive Black Box Functions Using Radial Basis Functions , 2005, J. Glob. Optim..

[309]  Erick Cantú-Paz,et al.  Efficient and Accurate Parallel Genetic Algorithms , 2000, Genetic Algorithms and Evolutionary Computation.

[310]  D. P. Solomatine Neural Network Approximation of a Hydrodynamic Model in Optimizing Reservoir Operation , 2006 .

[311]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[312]  Dragan Savic,et al.  AN EVOLUTION PROGRAM FOR OPTIMAL PRESSURE REGULATION IN WATER DISTRIBUTION NETWORKS , 1995 .

[313]  Joseph C. Culberson,et al.  On Searching \alpha-ary Hypercubes and Related Graphs , 1996, FOGA.

[314]  Anna Sikora,et al.  AutoTune: A Plugin-Driven Approach to the Automatic Tuning of Parallel Applications , 2012, PARA.

[315]  Cajo J. F. ter Braak,et al.  Treatment of input uncertainty in hydrologic modeling: Doing hydrology backward with Markov chain Monte Carlo simulation , 2008 .

[316]  Robert A. Marryott,et al.  Optimal Groundwater Management: 1. Simulated Annealing , 1991 .

[317]  P. Bayer,et al.  Evolutionary algorithms for the optimization of advective control of contaminated aquifer zones , 2004 .

[318]  Christian Blum,et al.  Metaheuristics in combinatorial optimization: Overview and conceptual comparison , 2003, CSUR.

[319]  Dragan Savic,et al.  WATER NETWORK REHABILITATION WITH STRUCTURED MESSY GENETIC ALGORITHM , 1997 .

[320]  David E. Goldberg,et al.  The Design of Innovation: Lessons from and for Competent Genetic Algorithms , 2002 .

[321]  J. Black,et al.  What is research in engineering design , 1989 .

[322]  Günter Rudolph,et al.  Convergence analysis of canonical genetic algorithms , 1994, IEEE Trans. Neural Networks.

[323]  Soroosh Sorooshian,et al.  Toward improved calibration of hydrologic models: Multiple and noncommensurable measures of information , 1998 .

[324]  Aaron C. Zecchin,et al.  Improved understanding of the searching behavior of ant colony optimization algorithms applied to the water distribution design problem , 2012 .

[325]  Jasper A Vrugt,et al.  Improved evolutionary optimization from genetically adaptive multimethod search , 2007, Proceedings of the National Academy of Sciences.

[326]  Thomas Jansen,et al.  Design and Management of Complex Technical Processes and Systems by Means of Computational Intelligence Methods Perhaps Not a Free Lunch but at Least a Free Appetizer Perhaps Not a Free Lunch but at Least a Free Appetizer , 2022 .

[327]  Bryan A. Tolson,et al.  Achieving Water Quality System Reliability Using Genetic Algorithms , 2000 .

[328]  Joseph R. Kasprzyk,et al.  Optimal Design of Water Distribution Systems Using Many-Objective Visual Analytics , 2013 .