Solutions (encodings)

Author:

Antonio J. Nebro

Version:

1.0

Date:

2022-11-30

One of the first decisions that have to be taken when using metaheuristics is to define how to encode or represent the tentative solutions of the problem to solve. Representations strongly depend on the problem (e.g., continuous, binary, permutation, etc.) and they may restrict, on the one hand, the algorithms that can be used (for example, particle swarm optimization and differential evolution are designed to solve continuous problems) and, on the other hand, the specific operators that can be applied, as the crossover and mutation operators in the case of evolutionary algorithms.

The base class of all the solution encodings in jMetal is the Solution interface, which located in the org.uma.jmetal.solution package (jmetal-auto sub-project):

package org.uma.jmetal.solution;

/**
 * Interface representing a Solution
 *
 * @author Antonio J. Nebro <antonio@lcc.uma.es>
 * @param <T> Type (Double, Integer, etc.)
 */
public interface Solution<T> extends Serializable {
  List<T> variables() ;
  double[] objectives() ;
  double[] constraints() ;
  Map<Object,Object> attributes() ;

  Solution<T> copy() ;
}

Any solution contains a list of decision variables, an array of objective values, and array of constraint values (i.e., the constraint violation degree per each of the problem side constraints), and a map of attributes (e.g., to assign properties such as ranking, strength, etc., which are usually algorithm dependant). The variable values are assigned when a solution is created (typically, when invoking the createSolution() method of a problem), whereas the objective and constraint values are usually assigned when evaluating a solution.

jMetal provides currently the following interfaces representing encodings (all of them extending Solution):

• BinarySolution

• IntegerSolution

• DoubleSolution

• PermutationSolution

• SequenceSolution

• CompositeSolution

These interfaces are intended to allow different implementations of a given encoding, although we currently provide a default implementation for most of them:

• DefaultBinarySolution: The solution chromosome is a list of binary strings. The number of solution variables is the number of strings.

• DefaultIntegerSolution: The solution chromosome is a list of integer values bounded by a lower and upper bound. Each integer value is stored in a solution variable.

• DefaultDoubleSolution: The solution chromosome is a list of double values bounded by a lower and upper bound. Each double value is stored in a solution variable.

• IntegerPermutationSolution: The encoding is a list of N integer numbers with are arrange as a permutation of size N. Each value of the permutation is stored in a solution variable.

• CharSequenceSolution: The encoding a list of N char values.

• CompositeSolution: A solution is composed of list of solutions, thus allowing to mix different types of encodings in a single solution. Each solution variable contains a solution.

Of course, you can define your own encodings if none of the available ones suit your needs.