Fitness is a score for how well a candidate solution meets a goal. Think of judging a packed knapsack: its contents may be valuable, but the packing fails if the bag is too heavy. A fitness function turns that judgment into a number an optimization algorithm can use to compare candidates. Depending on the goal, a better score may be higher or lower. section 4.7 section 4.2
Scoring a knapsack
Suppose the bag holds at most 9 kg. Pearls weigh 3 kg and are worth $4; a crown weighs 4 kg and is worth $5; a ring weighs 2 kg and is worth $5. Packing all three weighs 9 kg and scores 14—the sum of their values. Gold and a crown weigh 11 kg, so that packing breaks the limit. One simple fitness rule gives an overweight bag a score of 0, however valuable its contents look. section 4.2 section 4.7
To score a population of candidate knapsacks:
- Represent each packing as a chromosome: a string of genes, with 1 for an included item and 0 for an excluded item. section 4.4
- For each chromosome, add the weights and values of its included items. Return 0 if the weight exceeds the limit; otherwise, return the total value. section 4.7
- Use the scores to favor stronger candidates when selecting parents, while still allowing less-fit candidates a chance. Repeat scoring as new generations appear. section 4.8 section 4.3
def calculate_individual_fitness(individual, maximum_weight):
total_individual_weight = 0
total_individual_value = 0
for gene_index in range(len(individual)): #A
gene_switch = individual[gene_index]
if gene_switch == '1': #B
total_individual_weight
➥+= knapsack_items[gene_index][KNAPSACK_ITEM_WEIGHT_INDEX] #C
total_individual_value
➥+= knapsack_items[gene_index][KNAPSACK_ITEM_VALUE_INDEX] #C
if total_individual_weight > maximum_weight: #D
return 0
return total_individual_value #E
The Python function shows the rule directly: inspect each gene, accumulate weight and value for included items, then return either 0 or the total value. section 4.7
The rule must match the real objective. Maximizing packed value is different from minimizing unused space, and an inaccurate score steers selection toward the wrong solutions. A refinery problem needs a more involved rule: it must account for extraction time as well as item value to measure value per hour. Fitness measures solution quality, not how quickly the computer found the solution. section 4.7 section 5.12 section 4.2
Fitness also helps decide when to stop: an algorithm can stop at a desired score or when its best score barely changes across generations. Outside genetic algorithms, particle swarm optimization scores each particle after it moves and tracks its best result. In the drone-material example, lower scores are better because the search minimizes a function associated with drag and wobble. The practical question is always the same: does the number reward what you actually want? section 4.19 section 7.7 section 7.3
