On the estimation of Pareto fronts from the point of view of copula theory

International audienceGiven a first set of observations from a design of experiments sampled randomly in the design space, the corresponding set of non-dominated points usually does not give a good approximation of the Pareto front. We propose here to study this problem from the point of view of multivariate analysis, introducing a probabilistic framework with the use of copulas. This approach enables the expression of level lines in the objective space, giving an estimation of the position of the Pareto front when the level tends to zero. In particular, when it is possible to use Archimedean copulas, analytical expressions for Pareto front estimators are available. Several case studies illustrate the interest of the approach, which can be used at the beginning of the optimization when sampling randomly in the design space

Optimisation of Product Recovery Options in End-of-Life Product Disassembly by Robots

In a circular economy, strategies for product recovery, such as reuse, recycling, and remanufacturing, play an important role at the end of a product’s life. A sustainability model was developed to solve the problem of sequence-dependent robotic disassembly line balancing. This research aimed to assess the viability of the model, which was optimised using the Multi-Objective Bees Algorithm in a robotic disassembly setting. Two industrial gear pumps were used as case studies. Four objectives (maximising profit, energy savings, emissions reductions and minimising line imbalance) were set. Several product recovery scenarios were developed to find the best recovery plans for each component. An efficient metaheuristic, the Bees Algorithm, was used to find the best solution. The robotic disassembly plans were generated and assigned to robotic workstations simultaneously. Using the proposed sustainability model on end-of-life industrial gear pumps shows the applicability of the model to real-world problems. The Multi-Objective Bees Algorithm was able to find the best scenario for product recovery by assigning each component to recycling, reuse, remanufacturing, or disposal. The performance of the algorithm is consistent, producing a similar performance for all sustainable strategies. This study addresses issues that arise with product recovery options for end-of-life products and provides optimal solutions through case studies

Fractional Order Load-Frequency Control of Interconnected Power Systems Using Chaotic Multi-objective Optimization

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.Fractional order proportional-integral-derivative (FOPID) controllers are designed for load frequency control (LFC) of two interconnected power systems. Conflicting time domain design objectives are considered in a multi objective optimization (MOO) based design framework to design the gains and the fractional differ-integral orders of the FOPID controllers in the two areas. Here, we explore the effect of augmenting two different chaotic maps along with the uniform random number generator (RNG) in the popular MOO algorithm - the Non-dominated Sorting Genetic Algorithm-II (NSGA-II). Different measures of quality for MOO e.g. hypervolume indicator, moment of inertia based diversity metric, total Pareto spread, spacing metric are adopted to select the best set of controller parameters from multiple runs of all the NSGA-II variants (i.e. nominal and chaotic versions). The chaotic versions of the NSGA-II algorithm are compared with the standard NSGA-II in terms of solution quality and computational time. In addition, the Pareto optimal fronts showing the trade-off between the two conflicting time domain design objectives are compared to show the advantage of using the FOPID controller over that with simple PID controller. The nature of fast/slow and high/low noise amplification effects of the FOPID structure or the four quadrant operation in the two inter-connected areas of the power system is also explored. A fuzzy logic based method has been adopted next to select the best compromise solution from the best Pareto fronts corresponding to each MOO comparison criteria. The time domain system responses are shown for the fuzzy best compromise solutions under nominal operating conditions. Comparative analysis on the merits and de-merits of each controller structure is reported then. A robustness analysis is also done for the PID and the FOPID controllers

jHawanet: an open-source project for the implementation and assessment of multi-objective evolutionary algorithms on water distribution networks

[EN] Efficient design and management of water distribution networks is critical for conservation of water resources and minimization of both energy requirements and maintenance costs. Several computational routines have been proposed for the optimization of operational parameters that govern such networks. In particular, multi-objective evolutionary algorithms have proven to be useful both properly describing a network and optimizing its performance. Despite these computational advances, practical implementation of multi-objective optimization algorithms for water networks is an abstruse subject for researchers and engineers, particularly since efficient coupling between multi-objective algorithms and the hydraulic network model is required. Further, even if the coupling is successfully implemented, selecting the proper set of multi-objective algorithms for a given network, and addressing the quality of the obtained results (i.e., the approximate Pareto frontier) introduces additional complexities that further hinder the practical application of these algorithms. Here, we present an open-source project that couples the EPANET hydraulic network model with the jMetal framework for multi-objective optimization, allowing flexible implementation and comparison of different metaheuristic optimization algorithms through statistical quality assessment. Advantages of this project are discussed by comparing the performance of different multi-objective algorithms (i.e., NSGA-II, SPEA2, SMPSO) on case study water pump networks available in the literatureThis research and the APC were funded by the Comision Nacional de Investigacion Cientifica y Tecnologica (Conicyt), grant number 1180660Gutierrez-Bahamondes, JH.; Salgueiro, Y.; Silva-Rubio, SA.; Alsina, MA.; Mora-Melia, D.; Fuertes-Miquel, VS. (2019). jHawanet: an open-source project for the implementation and assessment of multi-objective evolutionary algorithms on water distribution networks. Water. 11(10):1-17. https://doi.org/10.3390/w111020181171110Wang, Y., Hua, Z., & Wang, L. (2018). Parameter Estimation of Water Quality Models Using an Improved Multi-Objective Particle Swarm Optimization. Water, 10(1), 32. doi:10.3390/w10010032Letting, L., Hamam, Y., & Abu-Mahfouz, A. (2017). Estimation of Water Demand in Water Distribution Systems Using Particle Swarm Optimization. Water, 9(8), 593. doi:10.3390/w9080593Ngamalieu-Nengoue, U. A., Martínez-Solano, F. J., Iglesias-Rey, P. L., & Mora-Meliá, D. (2019). Multi-Objective Optimization for Urban Drainage or Sewer Networks Rehabilitation through Pipes Substitution and Storage Tanks Installation. Water, 11(5), 935. doi:10.3390/w11050935Morley, M. ., Atkinson, R. ., Savić, D. ., & Walters, G. . (2001). GAnet: genetic algorithm platform for pipe network optimisation. Advances in Engineering Software, 32(6), 467-475. doi:10.1016/s0965-9978(00)00107-1Van Thienen, P., & Vertommen, I. (2015). Gondwana: A Generic Optimization Tool for Drinking Water Distribution Systems Design and Operation. Procedia Engineering, 119, 1212-1220. doi:10.1016/j.proeng.2015.08.978Mala-Jetmarova, H., Sultanova, N., & Savic, D. (2017). Lost in optimisation of water distribution systems? A literature review of system operation. Environmental Modelling & Software, 93, 209-254. doi:10.1016/j.envsoft.2017.02.009Durillo, J. J., & Nebro, A. J. (2011). jMetal: A Java framework for multi-objective optimization. Advances in Engineering Software, 42(10), 760-771. doi:10.1016/j.advengsoft.2011.05.014Ravber, M., Mernik, M., & Črepinšek, M. (2017). The impact of Quality Indicators on the rating of Multi-objective Evolutionary Algorithms. Applied Soft Computing, 55, 265-275. doi:10.1016/j.asoc.2017.01.03

Metaheuristics for Transmission Network Expansion Planning

This chapter presents the characteristics of the metaheuristic algorithms used to solve the transmission network expansion planning (TNEP) problem. The algorithms used to handle single or multiple objectives are discussed on the basis of selected literature contributions. Besides the main objective given by the costs of the transmission system infrastructure, various other objectives are taken into account, representing generation, demand, reliability and environmental aspects. In the single-objective case, many metaheuristics have been proposed, in general without making strong comparisons with other solution methods and without providing superior results with respect to classical mathematical programming. In the multi-objective case, there is a better convenience of using metaheuristics able to handle conflicting objectives, in particular with a Pareto front-based approach. In all cases, improvements are still expected in the definition of benchmark functions, benchmark networks and robust comparison criteria

Piecewise Linear Representation Segmentation in Noisy Domains with a Large Number of Measurements: The Air Traffic Control Domain

The importance of time series segmentation techniques is rapidly expanding, due to the growth in collection and storage technologies. Among them, one of the most used ones is Piecewise Linear Representation, probably due to its ease of use. This work tries to determine the difficulties faced by this technique when the analyzed time series shows noisy data and a large number of measurements and how to introduce the information about the present noise in the segmentation process. Both difficulties are met in the Air Traffic Control domain, which exhibits position measurements of aircraft's trajectories coming from sensor devices (basically surveillance radar and aircraft-derived data), being used as the motivating domain. Results from the three main traditional techniques are presented (sliding window, top down and bottom up approaches) and compared with a new introduced approach, the Hybrid Local Residue Analysis technique.This work was supported in part by Projects CICYT TIN2008-06742-C02-02/TSI, CICYT TEC2008-06732-C02-02/TEC, CAM CONTEXTS (S2009/TIC-1485) and DPS2008-07029-C02-02Publicad