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ABSTRACT

When used for global optimization, Evolutionary Algorithms (EAs) can be seen as unconstrained optimization techniques. Therefore, they require an additional mechanism to incorporate constraints of any kind (i.e., inequality, equality, linear, nonlinear) into their fitness function. Although the use of penalty functions (very popular with mathematical programming techniques) may seem an obvious choice, this sort of approach requires a careful fine tuning of the penalty factors to be used. Otherwise, an EA may be unable to reach the feasible region (if the penalty is too low) or may reach quickly the feasible region but being unable to locate solutions that lie in the boundary with the infeasible region (if the penalty is too severe). This has motivated the development of a number of approaches to incorporate constraints into the fitness function of an EA. This tutorial will cover the main proposals in current use, including novel approaches such as the use of tournament rules based on feasibility, multiobjective optimization concepts, hybrids with mathematical programming techniques (e.g., Lagrange multipliers), cultural algorithms, and artificial immune systems, among others. Other topics such as the importance of maintaining diversity, current benchmarks and the use of alternative search engines (e.g., particle swarm optimization, differential evolution, evolution strategies, etc.) will be also discussed (as time allows).

INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.6 Optimization
          Subjects: Constrained optimization

General Terms:
Algorithms

Keywords:
constraints, evolutionary algorithms