Sliding Window 3-Objective Pareto Optimization for Problems with Chance Constraints

Multi-objective formulations have been widely used to solve single-objective optimization problems. The initial study carried out by Knowles et al. [8] for the H-IFF and the traveling salesperson problem shows that such formulations can significantly reduce the number of local optima in the search space and uses the term multi-objectivization for such approaches. Using multi-objective formulations to solve constrained single-objective optimization problems by evolutionary multi-objective optimization using the constraint as an additional objective has shown to be highly beneficial for a wide range of problems [4,9,12]. Using the constraint as an additional objective for such problems allows simple evolutionary multi-objective algorithms such as GSEMO mimic a greedy behaviour and as a consequence allows us to achieve theoretically best possible performance guarantees for a wide range of constrained submodular optimization problems [17-19]. Such approaches have been widely studied recently under the term Pareto optimization in the artificial intelligence and machine learning literature [22]. In the context of problems with stochastic constraints, it has recently been shown that 3-objective formulations where the given constraint is relaxed into a third objective lead to better performance than 2-objective formulations that optimize the expected value and variance of the given stochastic components under the given constraint [14, 15].