Multiobjective Optimization and Multiple Constraint Handling with Evolutionary Algorithms

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

Multiobjective Optimization and Multiple Constraint Handling with Evolutionary Algorithms II: Application Example

The evolutionary approach to multiple function optimization formulated in the first part of the paper (1) is applied to the optimization of the low-pressure spool speed governor of a Pegasus turbine engine. This study illustrates how a technique such as the mUltiobjective Genetic Algorithm can be applied and exemplifies how design requirements can be defined as the algorithm runs. Several objective functions and associated goals express design concerns in direct form, i.e., as the designer would state them. While such a designer-orientated formulation is very attractive, its practical usefulness depends heavily on the ability to search and optimize cost surfaces in such a class much broader than usual, as already provided to a large extent by the Genetic Algorithm (GA). The two instances of the problem studied, demonstrate the need for preference articulation in cases where many and highly competing objects lead to a non dominated set too large for a finite population to sample effectively. Further, it is sown 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. The paper concludes with a discussion of the results

Multiobjective genetic algorithm strategies for electricity production from generation IV nuclear technology

Development of a technico-economic optimization strategy of cogeneration systems of electricity/hydrogen, consists in finding an optimal efficiency of the generating cycle and heat delivery system, maximizing the energy production and minimizing the production costs. The first part of the paper is related to the development of a multiobjective optimization library (MULTIGEN) to tackle all types of problems arising from cogeneration. After a literature review for identifying the most efficient methods, the MULTIGEN library is described, and the innovative points are listed. A new stopping criterion, based on the stagnation of the Pareto front, may lead to significant decrease of computational times, particularly in the case of problems involving only integer variables. Two practical examples are presented in the last section. The former is devoted to a bicriteria optimization of both exergy destruction and total cost of the plant, for a generating cycle coupled with a Very High Temperature Reactor (VHTR). The second example consists in designing the heat exchanger of the generating turbomachine. Three criteria are optimized: the exchange surface, the exergy destruction and the number of exchange modules

Comparison of Geometric Optimization Methods with Multiobjective Genetic Algorithms for Solving Integrated Optimal Design Problems

In this paper, system design methodologies for optimizing heterogenous power devices in electrical engineering are investigated. The concept of Integrated Optimal Design (IOD) is presented and a simplified but typical example is given. It consists in finding Pareto-optimal configurations for the motor drive of an electric vehicle. For that purpose, a geometric optimization method (i.e the Hooke and Jeeves minimization procedure) associated with an objective weighting sum and a Multiobjective Genetic Algorithm (i.e. the NSGA-II) are compared. Several performance issues are discussed such as the accuracy in the determination of Pareto-optimal configurations and the capability to well spread these solutions in the objective space

A Hierachical Evolutionary Algorithm for Multiobjective Optimization in IMRT

Purpose: Current inverse planning methods for IMRT are limited because they are not designed to explore the trade-offs between the competing objectives between the tumor and normal tissues. Our goal was to develop an efficient multiobjective optimization algorithm that was flexible enough to handle any form of objective function and that resulted in a set of Pareto optimal plans. Methods: We developed a hierarchical evolutionary multiobjective algorithm designed to quickly generate a diverse Pareto optimal set of IMRT plans that meet all clinical constraints and reflect the trade-offs in the plans. The top level of the hierarchical algorithm is a multiobjective evolutionary algorithm (MOEA). The genes of the individuals generated in the MOEA are the parameters that define the penalty function minimized during an accelerated deterministic IMRT optimization that represents the bottom level of the hierarchy. The MOEA incorporates clinical criteria to restrict the search space through protocol objectives and then uses Pareto optimality among the fitness objectives to select individuals. Results: Acceleration techniques implemented on both levels of the hierarchical algorithm resulted in short, practical runtimes for optimizations. The MOEA improvements were evaluated for example prostate cases with one target and two OARs. The modified MOEA dominated 11.3% of plans using a standard genetic algorithm package. By implementing domination advantage and protocol objectives, small diverse populations of clinically acceptable plans that were only dominated 0.2% by the Pareto front could be generated in a fraction of an hour. Conclusions: Our MOEA produces a diverse Pareto optimal set of plans that meet all dosimetric protocol criteria in a feasible amount of time. It optimizes not only beamlet intensities but also objective function parameters on a patient-specific basis