Continuation Methods for the Numerical Treatment of Multi- and Many Objective Optimization Problems
讲座名称：
Continuation Methods for the Numerical Treatment of Multi- and Many Objective Optimization Problems
讲座时间：
2019-10-25
讲座人：
Oliver Scheutze
形式：
校区：
兴庆校区
实践学分：
讲座内容：
讲座题目：Continuation Methods for the Numerical Treatment of Multi- and Many Objective Optimization Problems
讲座时间：2019年10月25日（星期五）上午8：30- 10：00
讲座地点：航天学院 第四会议室
讲座人：Oliver Scheutze
讲座简介：
In many applications the problem arises that several objectives have to be optimized concurrently leading to multi-objective optimization problems (MOPs). As a general example, two common goals in product design are certainly to maximize the quality of the product and to minimize its cost. Since these two goals are typically contradicting, it comes as no surprise that the solution set -- the so-called Pareto set -- of a MOP does in general not consist of one single solution but rather of an entire set of solutions. More precisely, the Pareto set of a continuous MOP typically forms at least locally a (k-1)-dimensional manifold, where k is the number of objectives involved in the problem.
In this talk, we will address continuation methods that make use of this geometric property of the Pareto set. Given an initial solution of a MOP, continuation methods perform a movement along the solution set and are thus the most effective local solvers for such problems. First, we will address the treatment of problems with few objectives (say, k from 2 to 4), and will afterwards propose possible strategies to cope with so-called many objective optimization problems (i.e., MOPs where k is larger than 4). The applicability and usefulness of all methods will be demonstrated on benchmark problems as well as on two applications from industrial laundry design and injection molding.
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