Multi-objective Evolutionary Algorithms Based Simulationoptimization Models For Groundwater System

Groundwater resource,as the essential part of water supply worldwide,plays a crucial role in eco-environmental conservation and socioeconomic development.However,human activities with increasing population numbers and socioeconomic development have detrimental effects on groundwater system and result in a series of environmental problems.Therefore,the focus of groundwater management is how to ensure the security of groundwater quantity and quality while keep the sustainable development of economy.The simulationoptimization(S/O)method,which integrates the simulation model explaining the physical behaviors of groundwater flow and transport with evolutionary algorithms inspired by various mechanisms of heuristic search,can effectively solve groundwater management problem(GMP)associated with nonlinear,multimodal,non-convex and stochastic objectives and constraints.Meanwhile,groundwater management calls for decision-makers to consider the benefits of economy and environment,that's a typical multi-objective optimization problem.Therefore,the multi-objective evolutionary algorithms(MOEAs)with the S/O framework are the effective techniques to solve the multi-objective GMPs.Groundwater system involves complex physical and chemical processes leading to multifaceted challenges for solving GMP.For example,the large-scale simulation model is numerically complicated and computationally demanding,which results in unaffordable computational burden for solving optimization problems with S/O framework.Therefore,the difficulty of MOEA in solving CPU-intensive GMPs is how to save computational cost and achieve Pareto-optimal solutions simultaneously.The real-world groundwater management probably involves multi-stakeholders,which calls for decision-makers consider many-objective optimization that refers to the system design with four and more objectives.The one of key problems is to develop the advanced MOEA which is suitable for solving GMPs with the highdimensional objective vector.The predictive uncertainty of numerical model is inevitable due to limited observation data for hydrogeological conditions and conceptualized mathematical model.Therefore,it is essential for GMPs to consider model uncertainty derived from model parameters or structures,that's the key problem of achieving robust and effective groundwater management schemes.This study developed three multi-objective simulation-optimization frameworks corresponding to aforementioned challenges for solving coastal groundwater management,conjunctive management of surface water(SW)and groundwater(GW)and groundwater quality monitoring network design.(1)The study firstly developed an improved surrogate model assisted multi-objective memetic algorithm-kernel extreme learning machine(SMOAM-KELM)for solving coastal GMPs.The algorithm can obtain Pareto-optimal front while save unaffordable computational burden at the large-scale or complex sites.SMOMA-KELM selects new sample points based on hypervolume improvement and crowding distance metrics for achieving the promising Pareto solutions in the optimization.Then,the training dataset is constantly augmented to retrain KELM models.Therefore,the improved accuracy of surrogate model reduces the influence of predictive error on the search capacity of evolutionary algorithm.The large-scale real-world coastal groundwater management at Baldwin County in southwestern Alabama demonstrates that SMOMA-KELM can lead to 94% of CPU time saving while guaranteeing the accuracy of Pareto solutions to achieve the desired level.(2)The water resources management and planning in Yanqi Basin(YB),a typical arid inland basin in northwest China,needs to consider the capital and operation cost of groundwater abstraction and surface water diversion and water demands,while maintaining environmental flow for water recharge to the terminal lake and regional groundwater storage due to the fragile ecosystem in YB.Therefore,the conjunctive management of SW and GW in YB composed of high-dimensional objective vector is a typical many-objective optimization problem.This study developed an epsilon multi-objective memetic algorithm(?-MOMA),that effectively alleviates the difficulty of many-objective optimization.Then,the algorithm is applied to solve integrated SW-GW management problem.The study results indicate decision-makers should constrain water demands by surface water diversion and adjust spatial scheme of groundwater abstraction for satisfying multi-stakeholders' benefits.Additionally,this study implemented the manyobjective optimization with the different runoff scenarios in relation to climate change to investigate the influences of runoff depletion in Kaidu River on the regional water resources management.The results show the depletion of river runoff inflow to YB could lead to the degradation of Pareto solutions compared with those based on the current runoff scenario.(3)Optimal design of groundwater monitoring network that is capable of providing accurate and informative data is to achieve comprehensive understanding for the distribution and transport of groundwater contaminant.However,the heterogeneity of spatially distributed parameters in the aquifer system is not able to be fully characterized which results in the predictive uncertainty of groundwater transport.This study proposed a two-stage stochastic multi-objective optimization framework,which firstly used sparse polynomial chaos expansion to build surrogate model and implemented accurate uncertainty quantification.Then the typical scenario of groundwater plume can be generated using the centroid of plume.Finally,the study integrated ?-MOMA to the framework of noisy genetic algorithm(NGA)and proposed the epsilon multi-objective noisy memetic algorithm(?-MONMA)to solving the management model.The study results indicate that the novel stochastic optimization framework can achieve the largest improvement of robustness of groundwater monitoring design and provide diverse Pareto-optimal solutions in the high-order objective space.