ART – Artificial Reasoning Toolkit

Evolving a complex system

Marco Lamieri

lamieri@econ.unito.it

Spss training day 03-05-2004

Agenda:

• What is a genetic algorithm and how it works;

• Some improvement to the method, the ART project;

• Move to real world with an industry application: the Penelope project

• References

The idea

• Starting from “Survival of the fittest” [Darwin, 1959]

• Genetic Algorithms (GA) are evolutionary programs that manipulate a population of individuals represented by fixed-format strings of information.

• The background theory is the “artificial adaptation” discussed by Holland [Holland,1992].

• GA are used to solve real-world optimization problems within a very large solution space and “non well defined” problems.

How does a GA work

• An initial population of individuals (solutions) is generated;– individuals represent potential solutions to the given problem and

are described as binary strings;– each character in the individual’s data string is called a gene and

each possible value that the gene can take on is called an allele.

• Using a fitness proportional approach parents and individuals that are going to survive to the next generation are selected;

• The selected individuals are evolved by means of reproduction using two operators:– crossover, – mutation.

• Process go on untill the population converge to a specific individual.

Example (square root of 2)

• The solution space is bounded between 0 and 1.

• We use a binary representation on 10 digits.

• There are 1024 numbers [2^10], starting from 0 and ending at 1023 [2*10 -1].

Generate random population

• A population of solutions is generated randomly.

• For the square root problem, a fixed number of 10 character binary strings are generated randomly.

Define the fitness function

• Darwinian evolution of a population implies that the strongest individuals will probably survive.

• The fitness of an individual is a numerical assessment of that individual’s ability to solve the problem - it is the ability of the individual to satisfy the requirements of the environment.

• In terms of the square root problem, the perfect individual is the numerical value approximated by 1.414213562373.

• In economic problems,the profit can be used to generate a fitness function

Selection process (roulette wheel)

• To select individuals is used the roulette wheel technique.

• The roulette wheel implementation implicitly forces fitness-proportionate reproduction.

• Selection is divided in 2 steps:

1. Individuals that are going to survive to the next generation are selected;

2. Individuals that are going to reproduce are selected.

Crossover

• Crossover swaps some of the genetic material of two individuals, creating two new individuals (children), who are possibly better than their parents.

Mutation

• In order to recover from this loss of genetic material, the individuals are allowed to change their genes randomly.

Convergence

• John Holland’s Schema Theorem [Holland, 1992] is widely accepted as mathematical proof that the genetic algorithm, due to its fitness-proportionate reproduction, converges to better solutions.

• Via the convergence method is possible to solve non “well-defined” problems where the best solution is not known a priori.

Remarks

• There is no ultimate goal or problem that must be solved by natural evolution.

• Evolution itself does not guarantee the creation of fitter individuals.

• The GA use a fuzzy logic that not always lead to the best solution but to a good one.

• The algorithm is problem independent.

ART – Some improvement to the method

ART, starting from John Holland's work, introduces some extensions and innovations:

• extended alphabet: each gene can be represented by up to 32000 values. In a standard representation the genes have a binary alphabet and can become meaningless. With the extended alphabet each allele can be a meaningful part of the solution and the translation process is easier.

• multi genome: the multi genome schema give a high degree of freedom to the user in formalizing problems in which coexist different binded aspects.

• rescale fitness operator:the natural selection process has been modified in order to improve efficiency and manage negative fitness values.

• univocal genome: using this option each value of the alphabet is unique within the genome.

An industry application: the Penelope Project

• Penelope is an “optimizing automated production planning engine”.

• It is mainly applied to the textile industry.

• Penelope, consists of:

1. Enterprise Simulator (ES)a model of the firm's supply chain developed in Swarm.

2. Genetic algorithm (GA) searching the solutions space to find the best production plan.

The Enterprise Simulation

• Daily about 200 bulk orders arrive whit a defined delivery deadline

• Delay has economic value in term of customer satisfaction;

• There are 20 machines available for the process;

• Each machine can perform different operations with setup costs and setup time.

• A limited number of workers has to take care of:– machine set up;– patrolling;

Economic value of the production plan(fitness)

The algorithm

• Solution space is:

Evaluating this number of solutions via brute force would take millions of years.

• The GA solve it in about 20 minutes.

• The individual is defined by:• 1 univocal genome with order number;• 1 random genome with machine number; The priority is derived from the combination of the two

genomes

Results

• scheduling time reduction of nearly 80%:1. Random planning cost 1002. Fifo standard cost 603. Human planner cost 404. Penelope cost 25

• wider elaboration cases set (non obvious plan);

• best cost/time rate solution;

• disposer software costs reduction (50%);

• economic saving in terms of skilled resources;

• more knowledge on production process and precise prediction of production time give strong contractual power to the enterprise;

• overall increase of the performance of the company that can be more then 2% of the yearly value-added.

References

• ART project http://eco83.econ.unito.it/golem

• Penelope project http://www.penelopeproject.org

• This presentation is available at:

http://eco83.econ.unito.it/golem/ppt/20040503-spss-art.ppt

For any further information …

lamieri@econ.unito.it

Report 1

Questions ?