Evolutionary Computation Advanced Algorithms and Operators Chapter 1

Evolutionary Computation: Advanced Algorithms and Operators Chapter 1 -6 Jang, Ha. Young March 28, 2011

Contents Introduction to fitness evaluation Encoding and decoding functions Competitive fitness evaluation Complexity-based fitness evaluation Multiobjective optimization Introduction to constraint-handling techniques

Contents Introduction to fitness evaluation Encoding and decoding functions Competitive fitness evaluation Complexity-based fitness evaluation Multiobjective optimization Introduction to constraint-handling techniques

Fitness Evaluation Optimization problem as follows: Fitness evaluation function as follows: In binary coding,

Contents Introduction to fitness evaluation Encoding and decoding functions Competitive fitness evaluation Complexity-based fitness evaluation Multiobjective optimization Introduction to constraint-handling techniques

Binary Strings N object variables x = (x 1, x 2, …, xn) into a binary string Decoding scheme Decoding function linearly maps the decoded integer value of the binary substring in the desired interval [ui, vi)

Gray Coded Strings Encoding binary string into Gray code Decoding Gray code into binary string

Messy Coding Gene position and the corresponding bit values are coded in a string

Floating Point Coding Mantissa and exponent of a floating-point parameter Decoding

Coding for … Binary Variables Presence or absence Permutation problems TSP Control problems Time or frequency dependent function of some control variables

Contents Introduction to fitness evaluation Encoding and decoding functions Competitive fitness evaluation Complexity-based fitness evaluation Multiobjective optimization Introduction to constraint-handling techniques

Competitive Fitness Evaluation Objective Fitness Is ‘absolute objective’ or complete ordering is always possible? Relative Fitness Direct comparison to some other solution either evolved or provided as a component of the environment Competitive Fitness Sensitive to the contents of the population

Contents Introduction to fitness evaluation Encoding and decoding functions Competitive fitness evaluation Complexity-based fitness evaluation Multiobjective optimization Introduction to constraint-handling techniques

Model Selection Criteria Minimal description length criterion Tradeoff between residual error Model complexity including a structure estimation term for the final model Number of bits necessary to encode the observations Number of bits needed to encode the parameters of the model

Model Selection Criteria Akaike information criterion Approximation of the idealized Kullback-Leibler distance between the true data and the model Minimum message length Inferred estimates of the unknown parameters Data using an optimal code based on the data probability distribution

Minimum Descirption Legnth based Fitness Evaluation for Genetic Programming Six multiplexor problem

Minimum Descirption Legnth based Fitness Evaluation for Genetic Programming

Contents Introduction to fitness evaluation Encoding and decoding functions Competitive fitness evaluation Complexity-based fitness evaluation Multiobjective optimization Introduction to constraint-handling techniques

Contents Introduction to fitness evaluation Encoding and decoding functions Competitive fitness evaluation Complexity-based fitness evaluation Multiobjective optimization Introduction to constraint-handling techniques

Search Space and Feasible and Infeasible Parts

Constraint Handling Techniques Penalize infeasible individiuals Change the topology of the search space Repair infeasible solution Start with an initial population of feasible individuals Process solutions and constraints separately Locate feasible solutions