Preliminary Investigation of the `Learnable Evolution Model' for Faster/Better Multiobjective Water Systems Design

The design of large scale water distribution systems is a very difficult optimisation problem which invariably requires the use of time-expensive simulations within the fitness function. The need to accelerate optimisation for such problems has not so far been seriously tackled. However, this is a very important issue, since as MOEAs become more and more recognised as the lsquoindustry standardrsquo technique for water system design, the demands placed on such systems (larger and larger water networks) will quickly meet with problems of scaleup. Meanwhile, LEM (Learnable Evolution Modelrsquo) has appeared in the Machine Learning literature, and provides a general approach to integrating machine learning into evolutionary search. Published results using LEM show very great promise in terms of finding near-optimal solutions with significantly reduced numbers of evaluations. Here we introduce LEMMO (Learnable Evolution Model for Multi-Objective optimization), which is a multi-objective adaptation of LEM, and we apply it to certain problems commonly used as benchmarks in the water systems community. Compared with NSGA-II, we find that LEMMO both significantly improves performance, and significantly reduces the number of evaluations needed to reach a given target. We conclude that the general approach used in LEMMO is a promising direction for meeting the scale-up challenges in multiobjective water system design

Artificial intelligence techniques for flood risk management in urban environments

Open Access journalCopyright © 2013 The Authors. Published by Elsevier Ltd.12th International Conference on Computing and Control for the Water Industry, CCWI2013Urban flooding is estimated to cause £270 million pounds worth of damage each year in England and Wales alone. There has, therefore, been a clear need to develop improved methods of identifying intervention strategies to reduce flood risk in urban environments. This paper describes ground-work performed towards evaluating the relative suitability of several algorithms applied to multi-objective optimisation of flood risk intervention strategies in an urban drainage network. An effective methodology is described for reducing an array of return period/duration rainfall files to a minimum, and it is described how this methodology makes possible comparisons of optimisation algorithms. This work has been undertaken as part of a STREAM-IDC EngD project which is a collaborative effort between the University of Exeter, and HR Wallingford

A hybrid, auto-adaptive, and rule-based multi-agent approach using evolutionary algorithms for improved searching

Selecting the most appropriate heuristic for solving a specific problem is not easy, for many reasons. This article focuses on one of these reasons: traditionally, the solution search process has operated in a given manner regardless of the specific problem being solved, and the process has been the same regardless of the size, complexity and domain of the problem. To cope with this situation, search processes should mould the search into areas of the search space that are meaningful for the problem. This article builds on previous work in the development of a multi-agent paradigm using techniques derived from knowledge discovery (data-mining techniques) on databases of so-far visited solutions. The aim is to improve the search mechanisms, increase computational efficiency and use rules to enrich the formulation of optimization problems, while reducing the search space and catering to realistic problems.Izquierdo Sebastián, J.; Montalvo Arango, I.; Campbell, E.; Pérez García, R. (2015). A hybrid, auto-adaptive, and rule-based multi-agent approach using evolutionary algorithms for improved searching. Engineering Optimization. 1-13. doi:10.1080/0305215X.2015.1107434S113Becker, U., & Fahrmeir, L. (2001). Bump Hunting for Risk: a New Data Mining Tool and its Applications. Computational Statistics, 16(3), 373-386. doi:10.1007/s001800100073Bouguessa, M., & Shengrui Wang. (2009). Mining Projected Clusters in High-Dimensional Spaces. IEEE Transactions on Knowledge and Data Engineering, 21(4), 507-522. doi:10.1109/tkde.2008.162Chong, I.-G., & Jun, C.-H. (2005). Performance of some variable selection methods when multicollinearity is present. Chemometrics and Intelligent Laboratory Systems, 78(1-2), 103-112. doi:10.1016/j.chemolab.2004.12.011CHONG, I., & JUN, C. (2008). Flexible patient rule induction method for optimizing process variables in discrete type. Expert Systems with Applications, 34(4), 3014-3020. doi:10.1016/j.eswa.2007.05.047Cole, S. W., Galic, Z., & Zack, J. A. (2003). Controlling false-negative errors in microarray differential expression analysis: a PRIM approach. Bioinformatics, 19(14), 1808-1816. doi:10.1093/bioinformatics/btg242FRIEDMAN, J. H., & FISHER, N. I. (1999). Statistics and Computing, 9(2), 123-143. doi:10.1023/a:1008894516817Geem, Z. W. (2006). Optimal cost design of water distribution networks using harmony search. Engineering Optimization, 38(3), 259-277. doi:10.1080/03052150500467430Goncalves, L. B., Vellasco, M. M. B. R., Pacheco, M. A. C., & Flavio Joaquim de Souza. (2006). Inverted hierarchical neuro-fuzzy BSP system: a novel neuro-fuzzy model for pattern classification and rule extraction in databases. IEEE Transactions on Systems, Man and Cybernetics, Part C (Applications and Reviews), 36(2), 236-248. doi:10.1109/tsmcc.2004.843220Hastie, T., Friedman, J., & Tibshirani, R. (2001). The Elements of Statistical Learning. Springer Series in Statistics. doi:10.1007/978-0-387-21606-5Chih-Ming Hsu, & Ming-Syan Chen. (2009). On the Design and Applicability of Distance Functions in High-Dimensional Data Space. IEEE Transactions on Knowledge and Data Engineering, 21(4), 523-536. doi:10.1109/tkde.2008.178Hwang, S.-F., & He, R.-S. (2006). A hybrid real-parameter genetic algorithm for function optimization. Advanced Engineering Informatics, 20(1), 7-21. doi:10.1016/j.aei.2005.09.001Izquierdo, J., Montalvo, I., Pérez, R., & Fuertes, V. S. (2008). Design optimization of wastewater collection networks by PSO. Computers & Mathematics with Applications, 56(3), 777-784. doi:10.1016/j.camwa.2008.02.007Javadi, A. A., Farmani, R., & Tan, T. P. (2005). A hybrid intelligent genetic algorithm. Advanced Engineering Informatics, 19(4), 255-262. doi:10.1016/j.aei.2005.07.003Jin, X., Zhang, J., Gao, J., & Wu, W. (2008). Multi-objective optimization of water supply network rehabilitation with non-dominated sorting Genetic Algorithm-II. Journal of Zhejiang University-SCIENCE A, 9(3), 391-400. doi:10.1631/jzus.a071448Johns, M. B., Keedwell, E., & Savic, D. (2014). Adaptive locally constrained genetic algorithm for least-cost water distribution network design. Journal of Hydroinformatics, 16(2), 288-301. doi:10.2166/hydro.2013.218Jourdan, L., Corne, D., Savic, D., & Walters, G. (2005). Preliminary Investigation of the ‘Learnable Evolution Model’ for Faster/Better Multiobjective Water Systems Design. Evolutionary Multi-Criterion Optimization, 841-855. doi:10.1007/978-3-540-31880-4_58Kamwa, I., Samantaray, S. R., & Joos, G. (2009). Development of Rule-Based Classifiers for Rapid Stability Assessment of Wide-Area Post-Disturbance Records. IEEE Transactions on Power Systems, 24(1), 258-270. doi:10.1109/tpwrs.2008.2009430Kang, D., & Lansey, K. (2012). Revisiting Optimal Water-Distribution System Design: Issues and a Heuristic Hierarchical Approach. Journal of Water Resources Planning and Management, 138(3), 208-217. doi:10.1061/(asce)wr.1943-5452.0000165Keedwell, E., & Khu, S.-T. (2005). A hybrid genetic algorithm for the design of water distribution networks. Engineering Applications of Artificial Intelligence, 18(4), 461-472. doi:10.1016/j.engappai.2004.10.001Kehl, V., & Ulm, K. (2006). Responder identification in clinical trials with censored data. Computational Statistics & Data Analysis, 50(5), 1338-1355. doi:10.1016/j.csda.2004.11.015Liu, X., Minin, V., Huang, Y., Seligson, D. B., & Horvath, S. (2004). Statistical Methods for Analyzing Tissue Microarray Data. Journal of Biopharmaceutical Statistics, 14(3), 671-685. doi:10.1081/bip-200025657Marchi, A., Dandy, G., Wilkins, A., & Rohrlach, H. (2014). Methodology for Comparing Evolutionary Algorithms for Optimization of Water Distribution Systems. Journal of Water Resources Planning and Management, 140(1), 22-31. doi:10.1061/(asce)wr.1943-5452.0000321Martínez-Rodríguez, J. B., Montalvo, I., Izquierdo, J., & Pérez-García, R. (2011). Reliability and Tolerance Comparison in Water Supply Networks. Water Resources Management, 25(5), 1437-1448. doi:10.1007/s11269-010-9753-2McClymont, K., Keedwell, E., Savić, D., & Randall-Smith, M. (2013). A general multi-objective hyper-heuristic for water distribution network design with discolouration risk. Journal of Hydroinformatics, 15(3), 700-716. doi:10.2166/hydro.2012.022McClymont, K., Keedwell, E. C., Savić, D., & Randall-Smith, M. (2014). Automated construction of evolutionary algorithm operators for the bi-objective water distribution network design problem using a genetic programming based hyper-heuristic approach. Journal of Hydroinformatics, 16(2), 302-318. doi:10.2166/hydro.2013.226Michalski, R. S. (2000). Machine Learning, 38(1/2), 9-40. doi:10.1023/a:1007677805582Montalvo, I., Izquierdo, J., Pérez-García, R., & Herrera, M. (2014). Water Distribution System Computer-Aided Design by Agent Swarm Optimization. Computer-Aided Civil and Infrastructure Engineering, 29(6), 433-448. doi:10.1111/mice.12062Montalvo, I., Izquierdo, J., Schwarze, S., & Pérez-García, R. (2010). Multi-objective particle swarm optimization applied to water distribution systems design: An approach with human interaction. Mathematical and Computer Modelling, 52(7-8), 1219-1227. doi:10.1016/j.mcm.2010.02.017Nguyen, V. V., Hartmann, D., & König, M. (2012). A distributed agent-based approach for simulation-based optimization. Advanced Engineering Informatics, 26(4), 814-832. doi:10.1016/j.aei.2012.06.001Nicklow, J., Reed, P., Savic, D., Dessalegne, T., Harrell, L., … Chan-Hilton, A. (2010). State of the Art for Genetic Algorithms and Beyond in Water Resources Planning and Management. Journal of Water Resources Planning and Management, 136(4), 412-432. doi:10.1061/(asce)wr.1943-5452.0000053Onwubolu, G. C., & Babu, B. V. (2004). New Optimization Techniques in Engineering. Studies in Fuzziness and Soft Computing. doi:10.1007/978-3-540-39930-8Pelikan, M., Goldberg, D. E., & Lobo, F. G. (2002). Computational Optimization and Applications, 21(1), 5-20. doi:10.1023/a:1013500812258Reed, P. M., Hadka, D., Herman, J. D., Kasprzyk, J. R., & Kollat, J. B. (2013). Evolutionary multiobjective optimization in water resources: The past, present, and future. Advances in Water Resources, 51, 438-456. doi:10.1016/j.advwatres.2012.01.005Shang, W., Zhao, S., & Shen, Y. (2009). A flexible tolerance genetic algorithm for optimal problems with nonlinear equality constraints. Advanced Engineering Informatics, 23(3), 253-264. doi:10.1016/j.aei.2008.09.001Vrugt, J. A., & Robinson, B. A. (2007). Improved evolutionary optimization from genetically adaptive multimethod search. Proceedings of the National Academy of Sciences, 104(3), 708-711. doi:10.1073/pnas.0610471104Vrugt, J. A., Robinson, B. A., & Hyman, J. M. (2009). Self-Adaptive Multimethod Search for Global Optimization in Real-Parameter Spaces. IEEE Transactions on Evolutionary Computation, 13(2), 243-259. doi:10.1109/tevc.2008.924428Xie, X.-F., & Liu, J. (2008). Graph coloring by multiagent fusion search. Journal of Combinatorial Optimization, 18(2), 99-123. doi:10.1007/s10878-008-9140-6Xiao-Feng Xie, & Jiming Liu. (2009). Multiagent Optimization System for Solving the Traveling Salesman Problem (TSP). IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 39(2), 489-502. doi:10.1109/tsmcb.2008.2006910Zheng, F., Simpson, A. R., & Zecchin, A. C. (2013). A decomposition and multistage optimization approach applied to the optimization of water distribution systems with multiple supply sources. Water Resources Research, 49(1), 380-399. doi:10.1029/2012wr013160Zheng, F., Simpson, A. R., & Zecchin, A. C. (2014). Coupled Binary Linear Programming–Differential Evolution Algorithm Approach for Water Distribution System Optimization. Journal of Water Resources Planning and Management, 140(5), 585-597. doi:10.1061/(asce)wr.1943-5452.000036

Preliminary investigation of the ‘learnable evolution model’ for faster/better multiobjective water systems design

Abstract. The design of large scale water distribution systems is a very difficult optimisation problem which invariably requires the use of timeexpensive simulations within the fitness function. The need to accelerate optimisation for such problems has not so far been seriously tackled. However, this is a very important issue, since as MOEAs become more and more recognised as the ‘industry standard ’ technique for water system design, the demands placed on such systems (larger and larger water networks) will quickly meet with problems of scaleup. Meanwhile, LEM (Learnable Evolution Model’) has appeared in the Machine Learning literature, and provides a general approach to integrating machine learning into evolutionary search. Published results using LEM show very great promise in terms of finding near-optimal solutions with significantly reduced numbers of evaluations. Here we introduce LEMMO (Learnable Evolution Model for Multi-Objective optimization), which is a multiobjective adaptation of LEM, and we apply it to certain problems commonly used as benchmarks in the water systems community. Compared with NSGA-II, we find that LEMMO both significantly improves performance, and significantly reduces the number of evaluations needed to reach a given target. We conclude that the general approach used in LEMMO is a promising direction for meeting the scale-up challenges in multiobjective water system design.

Developing Parsimonious and Efficient Algorithms for Water Resources Optimization Problems

In the current water resources scientific literature, a wide variety of engineering design problems are solved in a simulation-optimization framework. These problems can have single or multiple objective functions and their decision variables can have discrete or continuous values. The majority of current literature in the field of water resources systems optimization report using heuristic global optimization algorithms, including evolutionary algorithms, with great success. These algorithms have multiple parameters that control their behavior both in terms of computational efficiency and the ability to find near globally optimal solutions. Values of these parameters are generally obtained by trial and error and are case study dependent. On the other hand, water resources simulation-optimization problems often have computationally intensive simulation models that can require seconds to hours for a single simulation. Furthermore, analysts may have limited computational budget to solve these problems, as such, the analyst may not be able to spend some of the computational budget to fine-tune the algorithm settings and parameter values. So, in general, algorithm parsimony in the number of parameters is an important factor in the applicability and performance of optimization algorithms for solving computationally intensive problems. A major contribution of this thesis is the development of a highly efficient, single objective, parsimonious optimization algorithm for solving problems with discrete decision variables. The algorithm is called Hybrid Discrete Dynamically Dimensioned Search, HD-DDS, and is designed based on Dynamically Dimensioned Search (DDS) that was developed by Tolson and Shoemaker (2007) for solving single objective hydrologic model calibration problems with continuous decision variables. The motivation for developing HD-DDS comes from the parsimony and high performance of original version of DDS. Similar to DDS, HD-DDS has a single parameter with a robust default value. HD-DDS is successfully applied to several benchmark water distribution system design problems where decision variables are pipe sizes among the available pipe size options. Results show that HD-DDS exhibits superior performance in specific comparisons to state-of-the-art optimization algorithms. The parsimony and efficiency of the original and discrete versions of DDS and their successful application to single objective water resources optimization problems with discrete and continuous decision variables motivated the development of a multi-objective optimization algorithm based on DDS. This algorithm is called Pareto Archived Dynamically Dimensioned Search (PA-DDS). The algorithm parsimony is a major factor in the design of PA-DDS. PA-DDS has a single parameter from its search engine DDS. In each iteration, PA-DDS selects one archived non-dominated solution and perturbs it to search for new solutions. The solution perturbation scheme of PA-DDS is similar to the original and discrete versions of DDS depending on whether the decision variable is discrete or continuous. So, PA-DDS can handle both types of decision variables. PA-DDS is applied to several benchmark mathematical problems, water distribution system design problems, and water resources model calibration problems with great success. It is shown that hypervolume contribution, HVC1, as defined in Knowles et al. (2003) is the superior selection metric for PA-DDS when solving multi-objective optimization problems with Pareto fronts that have a general (unknown) shape. However, one of the main contributions of this thesis is the development of a selection metric specifically designed for solving multi-objective optimization problems with a known or expected convex Pareto front such as water resources model calibration problems. The selection metric is called convex hull contribution (CHC) and makes the optimization algorithm sample solely from a subset of archived solutions that form the convex approximation of the Pareto front. Although CHC is generally applicable to any stochastic search optimization algorithm, it is applied to PA-DDS for solving six water resources calibration case studies with two or three objective functions. These case studies are solved by PA-DDS with CHC and HVC1 selections using 1,000 solution evaluations and by PA-DDS with CHC selection and two popular multi-objective optimization algorithms, AMALGAM and ε-NSGAII, using 10,000 solution evaluations. Results are compared based on the best case and worst case performances (out of multiple optimization trials) from each algorithm to measure the expected performance range for each algorithm. Comparing the best case performance of these algorithms shows that, PA-DDS with CHC selection using 1,000 solution evaluations perform very well in five out of six case studies. Comparing the worst case performance of the algorithms shows that with 1,000 solution evaluations, PA-DDS with CHC selection perform well in four out of six case studies. Furthermore, PA-DDS with CHC selection using 10,000 solution evaluations perform comparable to AMALGAM and ε-NSGAII. Therefore, it is concluded that PA-DDS with CHC selection is a powerful optimization algorithm for finding high quality solutions of multi-objective water resources model calibration problems with convex Pareto front especially when the computational budget is limited

Artificial Intelligence Techniques for Flood Risk Management in Urban Environments

Flooding is an important concern for the UK, as evidenced by the many extreme flooding events in the last decade. Improved flood risk intervention strategies are therefore highly desirable. The application of hydroinformatics tools, and optimisation algorithms in particular, which could provide guidance towards improved intervention strategies, is hindered by the necessity of performing flood modelling in the process of evaluating solutions. Flood modelling is a computationally demanding task; reducing its impact upon the optimisation process would therefore be a significant achievement and of considerable benefit to this research area. In this thesis sophisticated multi-objective optimisation algorithms have been utilised in combination with cutting-edge flood-risk assessment models to identify least-cost and most-benefit flood risk interventions that can be made on a drainage network. Software analysis and optimisation has improved the flood risk model performance. Additionally, artificial neural networks used as feature detectors have been employed as part of a novel development of an optimisation algorithm. This has alleviated the computational time-demands caused by using extremely complex models. The results from testing indicate that the developed algorithm with feature detectors outperforms (given limited computational resources available) a base multi-objective genetic algorithm. It does so in terms of both dominated hypervolume and a modified convergence metric, at each iteration. This indicates both that a shorter run of the algorithm produces a more optimal result than a similar length run of a chosen base algorithm, and also that a full run to complete convergence takes fewer iterations (and therefore less time) with the new algorithm.EPSRCSTREAM-ID

Hybrid Optimisation Algorithms for Two-Objective Design of Water Distribution Systems

Multi-objective design or extended design of Water Distribution Systems (WDSs) has received more attention in recent years. It is of particular interest for obtaining the trade-offs between cost and hydraulic benefit to support the decision-making process. The design problem is usually formulated as a multi-objective optimisation problem, featuring a huge search space associated with a great number of constraints. Multi-objective evolutionary algorithms (MOEAs) are popular tools for addressing this kind of problem because they are capable of approximating the Pareto-optimal front effectively in a single run. However, these methods are often held by the “No Free Lunch” theorem (Wolpert and Macready 1997) that there is no guarantee that they can perform well on a wide range of cases. To overcome this drawback, many hybrid optimisation methods have been proposed to take advantage of multiple search mechanisms which can synergistically facilitate optimisation. In this thesis, a novel hybrid algorithm, called Genetically Adaptive Leaping Algorithm for approXimation and diversitY (GALAXY), is proposed. It is a dedicated optimiser for solving the discrete two-objective design or extended design of WDSs, minimising the total cost and maximising the network resilience, which is a surrogate indicator of hydraulic benefit. GALAXY is developed using the general framework of MOEAs with substantial improvements and modifications tailored for WDS design. It features a generational framework, a hybrid use of the traditional Pareto-dominance and the epsilon-dominance concepts, an integer coding scheme, and six search operators organised in a high-level teamwork hybrid paradigm. In addition, several important strategies are implemented within GALAXY, including the genetically adaptive strategy, the global information sharing strategy, the duplicates handling strategy and the hybrid replacement strategy. One great advantage of GALAXY over other state-of-the-art MOEAs lies in the fact that it eliminates all the individual parameters of search operators, thus providing an effective and efficient tool to researchers and practitioners alike for dealing with real-world cases. To verify the capability of GALAXY, an archive of benchmark problems of WDS design collected from the literature is first established, ranging from small to large cases. GALAXY has been applied to solve these benchmark design problems and its achievements in terms of both ultimate and dynamic performances are compared with those obtained by two state-of-the-art hybrid algorithms and two baseline MOEAs. GALAXY generally outperforms these MOEAs according to various numerical indicators and a graphical comparison tool. For the largest problem considered in this thesis, GALAXY does not perform as well as its competitors due to the limited computational budget in terms of number of function evaluations. All the algorithms have also been applied to solve the challenging Anytown rehabilitation problem, which considers both the design and operation of a system from the extended period simulation perspective. The performance of each algorithm is sensitive to the quality of the initial population and the random seed used. GALAXY and the Pareto-dominance based MOEAs are superior to the epsilon-dominance based methods; however, there is a tie between GALAXY and the Pareto-dominance based approaches. At the end, a summary of this thesis is provided and relevant conclusions are drawn. Recommendations for future research work are also made