Few for Many: A Non-Pareto Approach for Many Objective Optimization

Description

In various real-world applications, it is very often that many objectives should be considered at the same time. Examples include multi-task learning where different tasks should be solved simultaneously, and engineering manufacturing where a number of quality metrics should be optimized. The most widely used approach is to optimize an aggregation of all these individual objectives and produce one single optimal solution. However, it is very difficult, if not impossible, for one single solution to accommodate all the objectives. Recently, much effort has been made to model these applications as many objective Pareto optimization problems and attempt to find or approximate the whole Pareto front. A major drawback of the Pareto approach is that its computational overhead can often be prohibitively high, particularly when the number of objectives is large. A too large and complicated solution set can also cause information overflow and make it difficult for decision-makers to use. In this project, we will develop and investigate non-Pareto methods for many objective optimization. We consider applications where different objectives are highly correlated, thus it is feasible to explore common patterns of these objectives and produce a ‘simple’ set of optimal solutions for users to use. We will propose and solve two set optimization problems for addressing these applications. One is to find a small number of optimal solutions, and the other is to find a finite set of optimal solutions with many common components. Both of them are to optimize a well-defined quality metric. We will combine ideas and techniques from modern heuristics, evolutionary computation, traditional optimization, and machine learning to develop efficient algorithms for solving these problems. We will apply our proposed methods to algorithm configuration problems.