Genetic algorithms in economics
The genetic algorithm in economics is an algorithm used to model the learning behaviour of economic agents. The term "genetic algorithm" is often abbreviated as GA. The genetic algorithm is a particular class of evolutionary algorithm inspired by evolutionary biology. A genetic algorithm is defined as basic if it only contains a method for reproduction and experimentation. It is defined as augmented if it contains a selection operator as well.
Genetic algorithms are implemented as a computer simulation in which a population of abstract representations (called chromosomes or strings) of candidate solutions (called individuals, or agents) to an optimization problem evolves toward better solutions. Traditionally, solutions are represented in binary as strings of 0s and 1s, but other encodings are also possible. The evolution usually starts from a population of randomly generated individuals and happens in generations. In each generation, the fitness of every individual in the population is evaluated, multiple individuals are stochastically selected from the current population (based on their fitness), and modified (mutated or recombined) to form a new population. The new population is then used in the next iteration of the algorithm.
The Genetic Algorithm has increasingly been applied to economics over the last two decades. It has been used to characterize a variety of models including the cobweb model, the overlapping generations model, game theory and asset pricing
Design
The genetic algorithm generally consists of a population of n agents with m strings. These strings are often initially randomly generated but are then updated every g periods. Each string is assigned a fitness value through a defined method which is used as a measure of performance. The strings are updated through a series of operators. The basic genetic algorithm generally consists of three unique operators: the reproduction operator, which attempts to imitate successful agents and the two experimentation operators, crossover and mutation, which are implemented to bring diversity into the system. The augmented genetic algorithm includes an election operator, which adds a selection criteria.
Reproduction
The first operator, reproduction, works by attempting to imitate. In general, it selects another agent to observe it's fitness value. If it's fitness value is greater than it's own, then it elects to adopt the other agent's string. Otherwise, it perserves it own. These strings are then placed into an offspring pool to undergo the mutation operators, crossover and mutation. Most functions are stochastic and designed so that a small proportion of less fit solutions are selected. This helps keep the diversity of the population large, preventing premature convergence on poor solutions. Popular and well-studied selection methods include roulette wheel selection and tournament selection.
Crossover
Mutation
Election
These processes ultimately result in the offspring pool of strings that is different from the initial parent pool. The election operator then works by comparing the fitness of the parent strings to the potential fitness of the offspring pool. If the offspring string has a higher fitness value, it will replace the parent string in the population. Otherwise, the parent string will stay. Generally the average fitness will have increased by this procedure for the population, since only the best strings are selected.
See Also
References
- J Arifovic, 'Genetic Algorithm Learning and the Cobweb Model ', Journal of Economic Dynamics and Control, vol. 18, Issue 1, (January 1994), 3-28.