Multi-Objective Reservoir Optimization

SYNTHETIC HYDROLOGY

MULTI-OBJECTIVE TRADEOFFS

ALGORITHM FRONTS

X-Axis:

Y-Axis:

NSGA-II

MO-Adam

MOEA/D

MGDA

SELECTED POLICY PARAMETERS

STORAGE TRAJECTORIES

Best Yield: -

Best Avg Storage: -

Min Stage 2 Days: -

Global Pareto Count: -

Optimization Mode

Single Algorithm Compare 4 Algorithms

Algorithm:

Reservoir Parameters

Capacity (ac-ft): 100

Simulation Length (years): 30

Flow Skewness: 0.5

Demand (% of capacity/year)

Municipal: 40%

Irrigation: 50%

4th Objective (Optional)

Select 4th Objective:

Algorithm Settings

Population Size: 60

Generations: 150

Crossover Rate: 0.9

Mutation Rate: 0.2

Learning Rate (Adam): 0.3

Key Concepts (3 Objectives)

Pareto Front: The set of all non-dominated solutions where you can't improve one objective without making another worse. With 3 objectives, forms a surface in 3D space.

Yield: Percentage of water demand that can be reliably met over the simulation period. Higher is better.

Average Storage: Mean reservoir level as percentage of capacity over simulation. Higher storage provides buffer against droughts. Higher is better.

Stage 2 Restrictions: Days when reservoir storage drops below a threshold, triggering demand cutbacks. Lower is better.

Operating Policy: Rules defining when to implement water restrictions based on reservoir levels. Optimized to balance reliability, shortage severity, and storage levels.

Algorithms

NSGA-II: Non-dominated Sorting Genetic Algorithm. Uses tournament selection, crossover, and mutation to evolve solutions. Proven baseline for multi-objective optimization.

MO-Adam: Multi-Objective Adam optimizer. Uses gradient descent with adaptive learning rates to search for Pareto-optimal solutions. Includes random exploration to escape local optima.

MOEA/D: Multi-Objective Evolutionary Algorithm based on Decomposition. Divides the problem into subproblems using weight vectors, optimizing each with gradient descent and crossover.

MGDA: Multiple Gradient Descent Algorithm. Finds compromise gradients that improve multiple objectives simultaneously by averaging normalized objective gradients.

Pareto-Adam: Hybrid approach combining gradient descent when far from Pareto front and genetic operators when near it for fine-tuning.

Parameters

Population Size: Number of candidate solutions maintained each generation. Larger populations explore more diverse solutions but take longer.

Generations: Number of evolution cycles. More generations allow convergence to better solutions but increase computation time.

Crossover Rate: Probability of combining two parent solutions. Higher rates increase exploration but may disrupt good solutions.

Mutation Rate: Probability of random changes to solutions. Helps escape local optima and maintain diversity.

Learning Rate: Step size for gradient-based methods (Adam). Higher rates converge faster but may overshoot optimal solutions.