Genetic Algorithm Calibration for ABM

Summary

Ben Said et al. (2002) use genetic algorithms to calibrate the CUBES consumer agent population. Each GA chromosome encodes an agent’s behavioral and socio-economic characteristics (6 genes). The GA evolves a population of agent configurations through fitness-proportionate selection, arithmetic crossover, and mutation, evaluated by a Result-Analysis Module that compares simulated market outcomes to observed data. This approach enables automated discovery of realistic agent population parameters.

Overview

Genetic algorithms (Holland 1975) have been used for evolving complex systems including neural networks and cellular automata. Ben Said et al. apply GA to the specific problem of calibrating ABM agent populations — finding the parameter values for individual agents that, when combined in a simulation, reproduce observed market phenomena.

Main Content

Chromosome Encoding

Definition: Consumer Agent Chromosome (Ben Said et al. 2002)

Each consumer agent is represented by a chromosome encoding 6 characteristics:

1. BA characteristics: The behavioral attitude intensity values (mistrust, opportunism, conditioning, innovativeness, imitation)
2. Age: The consumer agent’s age
3. Number of acquaintances: Size of the agent’s social network
4. Social class: The social class to which the consumer agent belongs
5. Professional and educational levels: Socio-economic status
6. Product necessity: How essential the product is for this consumer

Most parameters are real numbers, encoded using a value-encoding technique.

GA Procedure

The GA follows a standard evolutionary loop with specific design choices:

Step 1: Fitness Evaluation

For each consumer agent chromosome $C_i$ ($i\in [1,N]$):

• A fitness value $f_i$ is calculated by the Result-Analysis Module (RAM)
• The RAM associates a fitness score to each individual agent by comparing their simulated behavior to macro-level observed results
• See GA Fitness Evaluation and the RAM for details

Step 2: Elite Selection

A portion of consumer agent chromosomes having the highest fitness (elite) are copied without modification into the next generation.

• Elite rate: 10% of the population size

Step 3: Selection, Crossover, and Mutation

Selection: Fitness-proportionate (Roulette Wheel selection method)

• Individuals with higher fitness have proportionally higher probability of being selected as parents

Crossover: Arithmetic crossover with a random mixing parameter $p\in [0,1]$:

Definition: Arithmetic Crossover (Ben Said et al. 2002)

Given two parent chromosomes $(a_1,b_1,p{c}_1,c_1,p{d}_1,d_1)$ and $(a_2,b_2,p{c}_2,c_2,p{d}_2,d_2)$, the two offspring are:

• Child 1: $(p{a}_1+(1-p)a_2,p{b}_1+(1-p)b_2,pp{c}_1+(1-p)p{c}_2,p{c}_1+(1-p)c_2,pp{d}_1+(1-p)p{d}_2,p{d}_1+(1-p)d_2)$
• Child 2: $(p{a}_2+(1-p)a_1,p{b}_2+(1-p)b_1,pp{c}_2+(1-p)p{c}_1,p{c}_2+(1-p)c_1,pp{d}_2+(1-p)p{d}_1,p{d}_2+(1-p)d_1)$

Crossover rate: 85%

Mutation: Random perturbation within the definition range of the chosen gene

• Mutation rate: 1%
• Picks a random value within the gene’s valid range

Step 4: Termination

Two termination criteria (combined):

1. The proportion of individuals whose fitness exceeds a fixed value reaches a certain percentage
2. The global fitness of the population does not vary during a fixed number of GA iterations (convergence)

GA Parameters Summary

Parameter	Value
Population size	N consumer agents (thousands)
Elite rate	10%
Selection method	Roulette Wheel (fitness-proportionate)
Crossover type	Arithmetic
Crossover rate	85%
Mutation rate	1%
Encoding	Value encoding (real numbers)
Termination	Dual criterion (fitness threshold + convergence)

Convergence Results

The average population fitness over 45 generations (Figure 5 in paper) shows:

• Rapid improvement in the first ~10 generations
• Gradual convergence over generations 10-30
• Near-plateau after ~35 generations
• Population of 5000 consumer agents achieves realistic behavioral patterns

Connections

• The fitness evaluation is detailed in GA Fitness Evaluation and the RAM
• The chromosomes encode properties from Behavioral Attitudes in CUBES and the CUBES Simulator Architecture
• GA calibration is one approach discussed in ABM Calibration Overview
• The calibrated population produces the emergent phenomena in Market Share Equilibrium and Lock-In

See Also

• GA Fitness Evaluation and the RAM — how fitness is computed
• ABM Calibration Overview — broader context of ABM calibration
• Behavioral Attitudes in CUBES — the attitudes encoded in chromosomes
• ABM Methodology and Principles — the foundational ABM framework that defines why calibration is needed