ART – Artificial Reasoning Toolkit Evolving a complex system Marco Lamieri Spss training day

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 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 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: t he 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 Fifo standard  cost Human planner  cost 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 Penelope project This presentation is available at: art.ppt art.ppt For any further information …

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