Singular Continuation: Generating Piece-wise Linear Approximations to Pareto Sets via Global Analysis

We propose a strategy for approximating Pareto optimal sets based on the global analysis framework proposed by Smale (Dynamical systems, New York, 1973, pp. 531-544). The method highlights and exploits the underlying manifold structure of the Pareto sets, approximating Pareto optima by means of simplicial complexes. The method distinguishes the hierarchy between singular set, Pareto critical set and stable Pareto critical set, and can handle the problem of superposition of local Pareto fronts, occurring in the general nonconvex case. Furthermore, a quadratic convergence result in a suitable set-wise sense is proven and tested in a number of numerical examples.Comment: 29 pages, 12 figure

Efficiently Constructing Convex Approximation Sets in Multiobjective Optimization Problems

Convex approximation sets for multiobjective optimization problems are a well-studied relaxation of the common notion of approximation sets. Instead of approximating each image of a feasible solution by the image of some solution in the approximation set up to a multiplicative factor in each component, a convex approximation set only requires this multiplicative approximation to be achieved by some convex combination of finitely many images of solutions in the set. This makes convex approximation sets efficiently computable for a wide range of multiobjective problems - even for many problems for which (classic) approximations sets are hard to compute. In this article, we propose a polynomial-time algorithm to compute convex approximation sets that builds upon an exact or approximate algorithm for the weighted sum scalarization and is, therefore, applicable to a large variety of multiobjective optimization problems. The provided convex approximation quality is arbitrarily close to the approximation quality of the underlying algorithm for the weighted sum scalarization. In essence, our algorithm can be interpreted as an approximate variant of the dual variant of Benson's Outer Approximation Algorithm. Thus, in contrast to existing convex approximation algorithms from the literature, information on solutions obtained during the approximation process is utilized to significantly reduce both the practical running time and the cardinality of the returned solution sets while still guaranteeing the same worst-case approximation quality. We underpin these advantages by the first comparison of all existing convex approximation algorithms on several instances of the triobjective knapsack problem and the triobjective symmetric metric traveling salesman problem

Computational intelligence approaches to robotics, automation, and control [Volume guest editors]

No abstract available

A Framework for Controllable Pareto Front Learning with Completed Scalarization Functions and its Applications

Pareto Front Learning (PFL) was recently introduced as an efficient method for approximating the entire Pareto front, the set of all optimal solutions to a Multi-Objective Optimization (MOO) problem. In the previous work, the mapping between a preference vector and a Pareto optimal solution is still ambiguous, rendering its results. This study demonstrates the convergence and completion aspects of solving MOO with pseudoconvex scalarization functions and combines them into Hypernetwork in order to offer a comprehensive framework for PFL, called Controllable Pareto Front Learning. Extensive experiments demonstrate that our approach is highly accurate and significantly less computationally expensive than prior methods in term of inference time.Comment: Under Review at Neural Networks Journa

Evolutionary Algorithms in Engineering Design Optimization

Evolutionary algorithms (EAs) are population-based global optimizers, which, due to their characteristics, have allowed us to solve, in a straightforward way, many real world optimization problems in the last three decades, particularly in engineering fields. Their main advantages are the following: they do not require any requisite to the objective/fitness evaluation function (continuity, derivability, convexity, etc.); they are not limited by the appearance of discrete and/or mixed variables or by the requirement of uncertainty quantification in the search. Moreover, they can deal with more than one objective function simultaneously through the use of evolutionary multi-objective optimization algorithms. This set of advantages, and the continuously increased computing capability of modern computers, has enhanced their application in research and industry. From the application point of view, in this Special Issue, all engineering fields are welcomed, such as aerospace and aeronautical, biomedical, civil, chemical and materials science, electronic and telecommunications, energy and electrical, manufacturing, logistics and transportation, mechanical, naval architecture, reliability, robotics, structural, etc. Within the EA field, the integration of innovative and improvement aspects in the algorithms for solving real world engineering design problems, in the abovementioned application fields, are welcomed and encouraged, such as the following: parallel EAs, surrogate modelling, hybridization with other optimization techniques, multi-objective and many-objective optimization, etc

On the Complexities of the Design of Water Distribution Networks

Water supply is one of the most recognizable and important public services contributing to quality of life. Water distribution networks WDNs are extremely complex assets. A number of complex tasks, such as design, planning, operation, maintenance, and management, are inherently associated with such networks. In this paper, we focus on the design of a WDN, which is a wide and open problem in hydraulic engineering. This problem is a large-scale combinatorial, nonlinear, nonconvex, multiobjective optimization problem, involving various types of decision variables and many complex implicit constraints. To handle this problem, we provide a synergetic association between swarm intelligence and multiagent systems where human interaction is also enabled. This results in a powerful collaborative system for finding solutions to such a complex hydraulic engineering problem. All the ingredients have been integrated into a software tool that has also been shown to efficiently solve problems from other engineering fields.This work has been developed with the support of the project IDAWAS, DPI2009-11591, of the Direccion General de Investigacion of the Ministerio de Educacion y Ciencia, and ACOMP/2010/146 of the Conselleria d'Educacio of the Generalitat Valenciana. The first author is also indebted to the Universitat Politecnica de Valencia for the sabbatical leave granted during the first semester of 2011. The use of English in this paper was revised by John Rawlins.Izquierdo Sebastián, J.; Montalvo Arango, I.; Pérez García, R.; Matías, A. (2012). On the Complexities of the Design of Water Distribution Networks. Mathematical Problems in Engineering. 2012:1-25. https://doi.org/10.1155/2012/9479611252012Goulter, I. C., & Coals, A. V. (1986). Quantitative Approaches to Reliability Assessment in Pipe Networks. Journal of Transportation Engineering, 112(3), 287-301. doi:10.1061/(asce)0733-947x(1986)112:3(287)Goulter, I. C., & Bouchart, F. (1990). Reliability‐Constrained Pipe Network Model. Journal of Hydraulic Engineering, 116(2), 211-229. doi:10.1061/(asce)0733-9429(1990)116:2(211)Kleiner, Y., Adams, B. J., & Rogers, J. S. (2001). Water Distribution Network Renewal Planning. Journal of Computing in Civil Engineering, 15(1), 15-26. doi:10.1061/(asce)0887-3801(2001)15:1(15)Dandy, G. C., & Engelhardt, M. O. (2006). Multi-Objective Trade-Offs between Cost and Reliability in the Replacement of Water Mains. Journal of Water Resources Planning and Management, 132(2), 79-88. doi:10.1061/(asce)0733-9496(2006)132:2(79)Izquierdo, J., Pérez, R., & Iglesias, P. L. (2004). Mathematical models and methods in the water industry. Mathematical and Computer Modelling, 39(11-12), 1353-1374. doi:10.1016/j.mcm.2004.06.012Giustolisi, O., Savic, D., & Kapelan, Z. (2008). Pressure-Driven Demand and Leakage Simulation for Water Distribution Networks. Journal of Hydraulic Engineering, 134(5), 626-635. doi:10.1061/(asce)0733-9429(2008)134:5(626)Montalvo, I., Izquierdo, J., Pérez, R., & Tung, M. M. (2008). Particle Swarm Optimization applied to the design of water supply systems. Computers & Mathematics with Applications, 56(3), 769-776. doi:10.1016/j.camwa.2008.02.006Montalvo, I., Izquierdo, J., Pérez, R., & Iglesias, P. L. (2008). A diversity-enriched variant of discrete PSO applied to the design of water distribution networks. Engineering Optimization, 40(7), 655-668. doi:10.1080/03052150802010607Montalvo, I., Izquierdo, J., Pérez-García, R., & Herrera, M. (2010). Improved performance of PSO with self-adaptive parameters for computing the optimal design of Water Supply Systems. Engineering Applications of Artificial Intelligence, 23(5), 727-735. doi:10.1016/j.engappai.2010.01.015Martínez, J. B. (2010). Cost and reliability comparison between branched and looped water supply networks. Journal of Hydroinformatics, 12(2), 150-160. doi:10.2166/hydro.2009.080Goulter, I. C. (1992). Systems Analysis in Water‐Distribution Network Design: From Theory to Practice. Journal of Water Resources Planning and Management, 118(3), 238-248. doi:10.1061/(asce)0733-9496(1992)118:3(238)Park, H., & Liebman, J. C. (1993). Redundancy‐Constrained Minimum‐Cost Design of Water‐Distribution Nets. Journal of Water Resources Planning and Management, 119(1), 83-98. doi:10.1061/(asce)0733-9496(1993)119:1(83)Khomsi, D., Walters, G. A., Thorley, A. R. D., & Ouazar, D. (1996). Reliability Tester for Water-Distribution Networks. Journal of Computing in Civil Engineering, 10(1), 10-19. doi:10.1061/(asce)0887-3801(1996)10:1(10)Tanyimboh, T. T., Tabesh, M., & Burrows, R. (2001). Appraisal of Source Head Methods for Calculating Reliability of Water Distribution Networks. Journal of Water Resources Planning and Management, 127(4), 206-213. doi:10.1061/(asce)0733-9496(2001)127:4(206)Kalungi, P., & Tanyimboh, T. T. (2003). Redundancy model for water distribution systems. Reliability Engineering & System Safety, 82(3), 275-286. doi:10.1016/s0951-8320(03)00168-6Morgan, D. R., & Goulter, I. C. (1985). Optimal urban water distribution design. Water Resources Research, 21(5), 642-652. doi:10.1029/wr021i005p00642Walters, G. A., & Knezevic, J. (1989). Discussion of « Reliability‐Based Optimization Model for Water Distribution Systems » by Yu‐Chun Su, Larry W. Mays, Ning Duan, and Kevin E. Lansey (December, 1987, Vol. 113, No. 12). Journal of Hydraulic Engineering, 115(8), 1157-1158. doi:10.1061/(asce)0733-9429(1989)115:8(1157)LOGANATHAN, G. V., SHERALI, H. D., & SHAH, M. P. (1990). A TWO-PHASE NETWORK DESIGN HEURISTIC FOR MINIMUM COST WATER DISTRIBUTION SYSTEMS UNDER A RELIABILITY CONSTRAINT. Engineering Optimization, 15(4), 311-336. doi:10.1080/03052159008941160Bouchart, F., & Goulter, I. (1991). Reliability Improvements in Design of Water Distribution Networks Recognizing Valve Location. Water Resources Research, 27(12), 3029-3040. doi:10.1029/91wr00590Gupta, R., & Bhave, P. R. (1994). Reliability Analysis of Water‐Distribution Systems. Journal of Environmental Engineering, 120(2), 447-461. doi:10.1061/(asce)0733-9372(1994)120:2(447)Xu, C., & Goulter, I. C. (1999). Reliability-Based Optimal Design of Water Distribution Networks. Journal of Water Resources Planning and Management, 125(6), 352-362. doi:10.1061/(asce)0733-9496(1999)125:6(352)Su, Y., Mays, L. W., Duan, N., & Lansey, K. E. (1987). Reliability‐Based Optimization Model for Water Distribution Systems. Journal of Hydraulic Engineering, 113(12), 1539-1556. doi:10.1061/(asce)0733-9429(1987)113:12(1539)Cullinane, M. J., Lansey, K. E., & Mays, L. W. (1992). Optimization‐Availability‐Based Design of Water‐Distribution Networks. Journal of Hydraulic Engineering, 118(3), 420-441. doi:10.1061/(asce)0733-9429(1992)118:3(420)Vamvakeridou-Lyroudia, L. S., Walters, G. A., & Savic, D. A. (2005). Fuzzy Multiobjective Optimization of Water Distribution Networks. Journal of Water Resources Planning and Management, 131(6), 467-476. doi:10.1061/(asce)0733-9496(2005)131:6(467)Montalvo, 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.2010.02.017Izquierdo, 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.2008.02.007Dong, Y., Tang, J., Xu, B., & Wang, D. (2005). An application of swarm optimization to nonlinear programming. Computers & Mathematics with Applications, 49(11-12), 1655-1668. doi:10.1016/j.camwa.2005.02.006Jin, Y.-X., Cheng, H.-Z., Yan, J., & Zhang, L. (2007). New discrete method for particle swarm optimization and its application in transmission network expansion planning. Electric Power Systems Research, 77(3-4), 227-233. doi:10.1016/j.epsr.2006.02.016Arumugam, M. S., & Rao, M. V. C. (2008). On the improved performances of the particle swarm optimization algorithms with adaptive parameters, cross-over operators and root mean square (RMS) variants for computing optimal control of a class of hybrid systems. Applied Soft Computing, 8(1), 324-336. doi:10.1016/j.asoc.2007.01.010Izquierdo, J., Montalvo, I., Pérez, R., & Fuertes, V. S. (2009). Forecasting pedestrian evacuation times by using swarm intelligence. Physica A: Statistical Mechanics and its Applications, 388(7), 1213-1220. doi:10.1016/j.physa.2008.12.008Herrera, M., Izquierdo, J., Montalvo, I., García-Armengol, J., & Roig, J. V. (2009). Identification of surgical practice patterns using evolutionary cluster analysis. Mathematical and Computer Modelling, 50(5-6), 705-712. doi:10.1016/j.mcm.2008.12.026Molina, J., Santana, L. V., Hernández-Díaz, A. G., Coello Coello, C. A., & Caballero, R. (2009). g-dominance: Reference point based dominance for multiobjective metaheuristics. European Journal of Operational Research, 197(2), 685-692. doi:10.1016/j.ejor.2008.07.01510.1029/89WR02879. (2010). Water Resources Research. doi:10.1029/89wr02879Savic, D. A., & Walters, G. A. (1997). Genetic Algorithms for Least-Cost Design of Water Distribution Networks. Journal of Water Resources Planning and Management, 123(2), 67-77. doi:10.1061/(asce)0733-9496(1997)123:2(67)Zecchin, A. C., Simpson, A. R., Maier, H. R., & Nixon, J. B. (2005). Parametric Study for an Ant Algorithm Applied to Water Distribution System Optimization. IEEE Transactions on Evolutionary Computation, 9(2), 175-191. doi:10.1109/tevc.2005.844168Yurong Liu, Zidong Wang, Jinling Liang, & Xiaohui Liu. (2009). Stability and Synchronization of Discrete-Time Markovian Jumping Neural Networks With Mixed Mode-Dependent Time Delays. IEEE Transactions on Neural Networks, 20(7), 1102-1116. doi:10.1109/tnn.2009.2016210Jinling Liang, Zidong Wang, & Xiaohui Liu. (2009). State Estimation for Coupled Uncertain Stochastic Networks With Missing Measurements and Time-Varying Delays: The Discrete-Time Case. IEEE Transactions on Neural Networks, 20(5), 781-793. doi:10.1109/tnn.2009.2013240Zidong Wang, Yao Wang, & Yurong Liu. (2010). Global Synchronization for Discrete-Time Stochastic Complex Networks With Randomly Occurred Nonlinearities and Mixed Time Delays. IEEE Transactions on Neural Networks, 21(1), 11-25. doi:10.1109/tnn.2009.2033599Bo Shen, Zidong Wang, & Xiaohui Liu. (2011). Bounded $H_{\infty}$ Synchronization and State Estimation for Discrete Time-Varying Stochastic Complex Networks Over a Finite Horizon. IEEE Transactions on Neural Networks, 22(1), 145-157. doi:10.1109/tnn.2010.209066