You are a company commander planning next quarter's training. Your unit has a limited budget of training hours and five possible events to resource. You can run 3 events on your own, or 4 if you coordinate with a sister company (at a cost). Each event has diminishing returns, some combinations unlock hidden synergies, unselected events suffer atrophy, a 4th event costs 5-15 points of overhead, and every evaluation is noisy. Your goal: allocate hours to maximize total readiness.
Individual Payoff Curves
Your Simulation Results
Score Breakdown

                  

                  
                

              

            

            
            
            
          

          
          

            

              
◆ THE BLUEPRINT

              
            

            

              
What You're Looking At

              
A noisy resource allocation problem. Your unit has a limited training budget. Choose 3-4 of 5 events, allocate hours, and maximize total readiness.

              
The Setup

              
Each event follows a diminishing-returns payoff curve. Some event combinations unlock hidden synergies. Unselected events suffer atrophy. A 4th event costs 5-15 points of overhead. Every evaluation adds noise.

              
Why It's Hard

              
The search space is large (discrete event selection + continuous hour allocation), the fitness landscape is noisy, and synergies are hidden. Brute-force search is impractical. This is exactly the kind of problem a genetic algorithm can solve.

              
How to Interact

              
Select events and set hours in the sidebar. Press Sim x1/x10/x50 to see noisy outcomes. The payoff curves show what you can observe in isolation. Toggle atrophy and noise bands to see the full picture.

              
Related Topics

              

                
                  Bias-Variance Tradeoff
                  noise and estimation error
                
              

            

          

        

        

          

            
What is a Chromosome?

            

              

                A genetic algorithm represents each candidate solution as a
                chromosome
                . Each chromosome has 10 genes:
              

              
    
                
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                  Genes 1-5:
                   binary (0 = no, 1 = yes). 3 or 4 must be selected (4 incurs overhead).
                
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                  Genes 6-10:
                   hours allocated to each event. Must sum to the budget.
                
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  • Unselected events have weight genes but they are zeroed out in decoding.
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Example Chromosome

            

              

              

              

            

            
          

          
          

            

              
◆ THE BLUEPRINT

              
            

            

              
What You're Looking At

              
A 10-gene chromosome that encodes a candidate solution to the resource allocation problem.

              
The Encoding

              
Genes 1-5 are binary selection genes (0 = skip, 1 = select). Genes 6-10 are hour-weight genes. Decoding normalizes the active weights so hours sum to the budget. Unselected events have their weight genes zeroed out.

              
Why This Encoding

              
Separating discrete choices (which events) from continuous choices (how many hours) lets crossover and mutation operate naturally on both. A repair operator enforces the 3-or-4 constraint after genetic operations.

              
How to Interact

              
Press Generate New Example to see a random chromosome. Trace how the raw genes map to an allocation and a fitness score. Notice how two chromosomes with different weight genes can decode to the same allocation if their ratios are identical.

            

          

        

        

          

            

              

                
How Selection Works

                

                  
Selection decides which individuals get to be parents for the next generation.
         Better solutions should be chosen more often, but not always. Some randomness
         preserves diversity and prevents premature convergence.

                  

                

                
              

              

                

                  

                    
Population Fitness

                    

                      

                      

                    

                    
                  

                

                

                  

                    

                      

                    

                    

                      

                    

                    
                  

                

              

            

            
            
            
          

          
          

            

              
◆ THE BLUEPRINT

              
            

            

              
What You're Looking At

              
Three selection methods for choosing parents from a population. Selection pressure controls the tradeoff between exploiting the best solutions and exploring new ones.

              
The Methods

              
Tournament: pick k random individuals, the fittest wins. Roulette: selection probability proportional to fitness. Rank: selection probability proportional to rank, not raw fitness. Rank-based selection prevents a single dominant individual from monopolizing reproduction.

              
Selection Pressure

              
Stronger pressure (larger tournament size, or roulette with spread-out fitness) converges faster but risks losing diversity. Weaker pressure preserves exploration but converges slowly. Elitism guarantees the best individuals survive regardless of selection method.

              
How to Interact

              
Try each method and press Select a Parent. Watch how elites (blue) always pass through. Compare tournament sizes. Toggle elitism on and off to see its effect on the population bar chart.

            

          

        

        

          

            

              Genetic Operators
              
            

            

              

                

                  

                    

                      
How Crossover Works

                      

                        

                          Crossover combines two parents to produce
                          one child
                          .
                        

                        

                      

                      
                    

                    

                      
Parent 1 + Parent 2 = Child

                      

                        

                      

                      
                    

                    

                      
Decoded Allocations

                      

                        

                      

                      
                    

                  

                  
                  
                  
                

              

              

                

                  

                    

                      
How Mutation Works

                      

                        

                      

                      
                    

                    

                      
Before and After

                      

                        

                      

                      
                    

                    

                      

                        

                          
Where Did the Draws Land?

                          

                            

                          

                          
                        

                      

                      

                        

                          
Fitness Impact

                          

                            

                          

                          
                        

                      

                    

                  

                  
                  
                  
                

              

            

            
          

          
          

            

              
◆ THE BLUEPRINT

              
            

            

              
What You're Looking At

              
Two genetic operators that create variation. Crossover combines two parents into a child. Mutation perturbs individual genes.

              
Crossover

              
Single-point: one cut, child gets P1 before and P2 after. Two-point: two cuts, middle segment from P2. Uniform: each gene independently from P1 or P2 with equal probability. Purple genes show where the repair operator flipped selection bits to enforce the 3-or-4 constraint.

              
Mutation

              
Each gene has a chance of being mutated. Selection genes flip on/off. Weight genes get Gaussian nudges controlled by sigma. Paired transfers move weight between two events, preserving the budget. Unpaired nudges are independent and can violate the budget.

              
How to Interact

              
On the Crossover tab, try each method and watch how the child inherits genes. On the Mutation tab, compare paired vs unpaired. Watch the hour sums: paired always matches the budget, unpaired can drift.

            

          

        

        

          

            

              

                

                  

                    
Convergence

                    

                      

                    

                    
                  

                

                

                  

                    
Best Allocation So Far

                    

                      

                    

                    
                  

                

              

              

                

                  

                    
Population Diversity

                    

                      

                    

                    
                  

                

                

                  

                    
Current Generation's Best

                    

                      

                    

                    
                  

                

              

            

            
            
            
          

          
          

            

              
◆ THE BLUEPRINT

              
            

            

              
What You're Looking At

              
A full GA run. The convergence plot tracks best, generation-best, and mean fitness over generations. The diversity plot shows how similar the population becomes over time.

              
The Ceiling

              
The dashed line is the theoretical optimum given noise. The GA estimates fitness by averaging N noisy simulations. Even the true-best allocation will score below its deterministic value when evaluated this way.

              
What the Plots Show

              
Overall Best (blue) never decreases. Generation Best (green) can fluctuate. Generation Mean (purple, dotted) reflects population quality. When all three converge, the population has settled.

              
The allocation bar chart compares the GA's best solution to the true optimum. The breakdown chart shows per-event scores for the current generation's best individual.

              
How to Interact

              
Press Run and watch convergence. Press Pause to freeze and inspect. Use Step to advance one generation at a time. Reset reinitializes the population.

              
Try increasing mutation rate if the GA plateaus early. Try larger populations for smoother convergence. Reduce simulations per evaluation to speed up each generation at the cost of noisier fitness estimates.

              
Related Topics

              

                
                  Bias-Variance Tradeoff
                  noise and estimation error
                
              

            

          

        

        

          

            

              

                
                

                  

                    

                      
What to Look For

                      

                        
Each config runs independently on the same problem. Compare:

                        
    
                          
  • How fast does each config approach the optimum?
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  • Does it plateau early or keep improving?
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Convergence Comparison

                      

                        

                      

                      
                    

                    

                      
Results Summary

                      

                        

                      

                      
                    

                  

                

              

            

            
            
            
          

          
          

            

              
◆ THE BLUEPRINT

              
            

            

              
What You're Looking At

              
Multiple GA configurations racing on the same problem. Each config runs independently with its own population, selection, and mutation parameters.

              
What to Compare

              
Convergence speed: how quickly does each config approach the ceiling? Final score: how close does it get? Diversity: does the population collapse early or maintain variation? Higher mutation rates explore more. Larger populations converge more smoothly. More simulations per evaluation reduce noise but cost more compute per generation.

              
Quick Lessons

              
The preset buttons set up classic comparisons. Mutation Rate shows the exploration-exploitation tradeoff. Population Size shows the effect of population diversity. Elitism shows guaranteed survival vs. pure selection. Noise shows how simulation count affects fitness estimation.

              
How to Interact

              
Pick a preset or customize configs manually. Press Run All Configs and compare the convergence curves. The dashed line is the theoretical ceiling. The results table shows final scores as a percentage of that ceiling.