Comparative study of multi-objective evolutionary algorithms for hydraulic rehabilitation of urban drainage networks

Abstract Multi-Objective Evolutionary Algorithms (MOEAs) are flexible and powerful tools for solving a wide variety of non-linear and non-convex problems in water resources engineering contexts. In this work, two well-known MOEAs, the Strength Pareto Evolutionary Algorithm (SPEA2) and Non-dominated Sorting Genetic Algorithm (NSGA2), and two additional MOEAs that are extended versions of harmony search (HS) and differential evolution (DE), are linked to the Environmental Protection Agency’s Storm Water Management Model (SWMM-EPA), which is a hydraulic model used to determine the best pipe replacements in a set of sewer pipe networks to decrease urban flooding overflows. The performance of the algorithms is compared for several comparative metrics. The results show that the algorithms exhibit different behaviours in solving the hydraulic rehabilitation problem. In particular, the multi-objective version of the HS algorithm provides better optimal solutions and clearly outperforms the other algorithms for this type of nondeterministic polynomial-time hard (NP-hard) problem.

[1]  Guangtao Fu,et al.  A global analysis approach for investigating structural resilience in urban drainage systems. , 2015, Water research.

[2]  Kalyanmoy Deb,et al.  A Fast Elitist Non-dominated Sorting Genetic Algorithm for Multi-objective Optimisation: NSGA-II , 2000, PPSN.

[3]  Avi Ostfeld,et al.  Evolutionary algorithms and other metaheuristics in water resources: Current status, research challenges and future directions , 2014, Environ. Model. Softw..

[4]  Roland K. Price,et al.  Multiobjective Evolutionary Approach to Rehabilitation of Urban Drainage Systems , 2010 .

[5]  Marco Laumanns,et al.  SPEA2: Improving the Strength Pareto Evolutionary Algorithm For Multiobjective Optimization , 2002 .

[6]  Do Guen Yoo,et al.  Application of multi‐objective evolutionary algorithms for the rehabilitation of storm sewer pipe networks , 2017 .

[7]  Marc Schoenauer,et al.  A Steady Performance Stopping Criterion for Pareto-based Evolutionary Algorithms , 2004 .

[8]  R. Farmani,et al.  Evolutionary multi-objective optimization in water distribution network design , 2005 .

[9]  Andrew B. Templeman,et al.  THE COMPUTATIONAL COMPLEXITY OF THE PROBLEM OF DETERMINING LEAST CAPITAL COST DESIGNS FOR WATER SUPPLY NETWORKS , 1984 .

[10]  Floyd A. Huff.  Time distributions of heavy rainstorms in Illinois , 1990 .

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

[12]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

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

[14]  Anupam Yadav,et al.  A Study of Harmony Search Algorithms: Exploration and Convergence Ability , 2015, ICHSA.

[15]  Qi Wang,et al.  Two-Objective Design of Benchmark Problems of a Water Distribution System via MOEAs: Towards the Best-Known Approximation of the True Pareto Front , 2015 .

[16]  Soon-Thiam Khu,et al.  A general framework for flood risk-based storm sewer network design , 2011 .

[17]  Carlos A. Coello Coello,et al.  An Introduction to Multi-Objective Particle Swarm Optimizers , 2011 .

[18]  Joong Hoon Kim,et al.  Stochastic Multiobjective Optimization Model for Urban Drainage Network Rehabilitation , 2015 .

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