Multiobjective Optimization and Multiple Constraint Handling with Evolutionary Algorithms

Abstract

In this talk, fitness assignment in multiobjective evolutionary algorithms
is interpreted as a multi-criterion decision process. A suitable decision 
making framework based on goals and priorities is formulated in terms of a
relational operator, characterized, and shown to encompass a number of
simpler decision strategies, including constraint satisfaction,
lexicographic optimization, and a form of goal programming. Then, the
ranking of an arbitrary number of candidates is considered, and the effect
of preference changes on the cost surface seen by an evolutionary algorithm
is illustrated graphically for a simple problem.

The formulation of a multiobjective genetic algorithm based on the proposed
decision strategy is also discussed. Niche formation techniques are used to
promote diversity among preferable candidates, and progressive articulation
of preferences is shown to be possible as long as the genetic algorithm can
recover from abrupt changes in the cost landscape.

Finally, an application to the optimization of the low-pressure spool speed
governor of a Pegasus gas turbine engine is described, which illustrates how
a technique such as the Multiobjective Genetic Algorithm can be applied, and
exemplifies how design requirements can be refined as the algorithm runs.   

The two instances of the problem studied demonstrate the need for preference
articulation in cases where many and highly competing objectives lead to a  
non-dominated set too large for a finite population to sample effectively.  
It is shown that only a very small portion of the non-dominated set is of   
practical relevance, which further substantiates the need to supply
preference information to the GA.