## Multi-Objective Optimization Using Evolutionary AlgorithmsEvolutionary algorithms are relatively new, but very powerful techniques used to find solutions to many real-world search and optimization problems. Many of these problems have multiple objectives, which leads to the need to obtain a set of optimal solutions, known as effective solutions. It has been found that using evolutionary algorithms is a highly effective way of finding multiple effective solutions in a single simulation run. - Comprehensive coverage of this growing area of research
- Carefully introduces each algorithm with examples and in-depth discussion
- Includes many applications to real-world problems, including engineering design and scheduling
- Includes discussion of advanced topics and future research
- Can be used as a course text or for self-study
- Accessible to those with limited knowledge of classical multi-objective optimization and evolutionary algorithms
The integrated presentation of theory, algorithms and examples will benefit those working and researching in the areas of optimization, optimal design and evolutionary computing. This text provides an excellent introduction to the use of evolutionary algorithms in multi-objective optimization, allowing use as a graduate course text or for self-study. |

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### Contents

Prologue | 1 |

MultiObjective Optimization | 13 |

Classical Methods | 49 |

Evolutionary Algorithms | 81 |

NonElitist MultiObjective Evolutionary Algorithms | 171 |

Elitist MultiObjective Evolutionary Algorithms | 239 |

Constrained MultiObjective Evolutionary Algorithms | 289 |

Salient Issues of MultiObjective Evolutionary Algorithms | 315 |

Applications of MultiObjective Evolutionary Algorithms | 447 |

Epilogue | 481 |

489 | |

509 | |

### Common terms and phrases

ashare assigned fitness best non-dominated better calculated choose chosen clusters computational complexity constraint violation convergence convex corresponding created crossover operator decision variable space discussed distribution dominated solutions elitist equation Euclidean distance evaluated evolution strategy evolutionary algorithms external population feasible solution find multiple genetic algorithm genetic operations global goal programming hypercube infeasible solutions local search mating pool maximum method metric Minimize minimum MOEAs multi-objective optimization problem mutation operator mutation strength niche count non-dominated front non-dominated set non-dominated solutions nonconvex NPGA NSGA NSGA-II number of solutions objective function values objective space objective vector obtained solutions offspring population optimum parent solutions Pareto Pareto-optimal region Pareto-optimal set Pareto-optimal solutions performed population members random real-parameter schema search space selection operator set of solutions shown in Figure shows solving SPEA Step strategy string studies subpopulation suggested technique test problems tournament selection trade-off solutions true Pareto-optimal front VEGA WBGA weight vector

### Popular passages

Page 508 - Zitzler E, Deb K, Thiele L (2000) Comparison of multiobjective evolutionary algorithms: Empirical results.

Page 489 - T 1996 Evolutionary Algorithms in Theory and Practice (New York: Oxford University Press...

Page 494 - Fogel, LJ., Angeline, PJ and Fogel, DB (1995). An Evolutionary Programming Approach to Self-Adaptation on Finite State Machines.