Efficient optimization of pumping systems is crucial for managing salinity intrusion and ensuring groundwater sustainability in coastal aquifers. Surrogate models (SMs) are widely used in aquifer management as efficient alternatives to complex groundwater simulations. This study develops and compares six deep learning (DL)-based SMs for an optimal groundwater pumping problem. These include Simple and Deep Feed Forward Neural Networks, and four Recurrent Neural Networks (Long Short-Term Memory (LSTM), Bi-directional LSTM (Bi-LSTM), Projected Layer LSTM (pro-LSTM), and Gated Recurrent Unit Neural Network). The best DL-based SM at different monitoring locations (MLs) provided accurate predictions with high accuracy and low error metrics. To solve the coupled simulation-optimization (S-O) problem, the Multi-Objective Genetic Algorithm with Controlled Elitism (CEMOGA) and Multiple Objective Feasibility Enhanced Particle Swarm Optimization (MOFEPSO) were employed to derive Pareto-optimal groundwater abstractions. The precision of optimal pumping schedules derived from the best DL-based S-O approach was validated through the numerical model. Validation showed that MOFEPSO outperformed CEMOGA, with percentage relative error values ranging from 0 to 0.030% for CEMOGA and 0-0.025% for MOFEPSO. The best feasible bargaining solution from the Pareto front was selected using the Simple Additive Weighting (SAW) and Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) methods, considering trade-offs between two competing objectives. The Pareto-optimal solutions and the selected best compromise provide guidance for water resource managers in planning groundwater use. These findings offer valuable insights for sustainable water resource planning and are adaptable to various groundwater management challenges.