An environment-driven hybrid evolutionary algorithm for dynamic multi-objective optimization problems

Abstract

In dynamic multi-objective optimization problems, the environmental parameters may change over time, which makes the Pareto fronts shifting. To address the issue, a common idea is to track the moving Pareto front once an environmental change occurs. However, it might be hard to obtain the Pareto optimal solutions if the environment changes rapidly. Moreover, it may be costly to implement a new solution. By contrast, robust Pareto optimization over time provides a novel framework to find the robust solutions whose performance is acceptable for more than one environment, which not only saves the computational costs for tracking solutions, but also minimizes the cost for switching solutions. However, neither of the above two approaches can balance between the quality of the obtained non-dominated solutions and the computation cost. To address this issue, environment-driven hybrid dynamic multi-objective evolutionary optimization method is proposed, aiming to fully use strengths of TMO and RPOOT under various characteristics of environmental changes. Two indexes, i.e., the frequency and intensity of environmental changes, are first defined. Then, a criterion is presented based on the characteristics of dynamic environments and the switching cost of solutions, to select an appropriate optimization method in a given environment. The experimental results on a set of dynamic benchmark functions indicate that the proposed hybrid dynamic multi-objective evolutionary optimization method can choose the most rational method that meets the requirements of decision makers, and balance the convergence and robustness of the obtained non-dominated solutions.

Robust Optimization Over Time: A Critical Review

“…Besides, an evolutionary multiobjective optimization method is used in this framework (MOEA/D [60] is used in [15]). This framework is also used in [16][17][18]61] for solving ROOT M Q problems. In [16], ensemble prediction methods are used in this framework to improve the prediction accuracy.…”

“…In [17] and [61], a grid-based multi-objective brain storming algorithm [62] with hybrid mutation operation and a modified version of non-dominated sorting genetic algorithm [63] were used as the optimization component in this framework, respectively. In [18], an alternative prediction component is used to estimate the future fitness values of the candidate solutions. In this method, instead of using time series of previous fitness values of candidate solutions for predicting their future fitness values, future environmental parameters (i.e., α-variables) are predicted.…”

“…where s′ max and h′ max are the largest s′ and h′ values among promising regions in C, respectively. The experimental results in [28,30] demonstrate that solutions chosen by (18), which considers both shift and height severity values, have longer survival times in comparison to the ones chosen by ( 16) and (17). Finally, in [14], a strategy is used that works based on the switching cost between the previous deployed solution s and the best-found positions in the promising regions in C:…”

“…To address the challenges of using the approximation component in providing the time series data for predicting the future fitness values of candidate solutions, α-variables (i.e., environmental parameters) are predicted in [18]. In this approach, using the baseline function f (•) and predicted αvariables, the fitness values of candidate solutions in future environments are calculated.…”

“…Among the various possible ROOT M problems, only the multi-objective ROOT M Q has been studied in the existing literature [15][16][17][18], where the set of deployed solutions consists of Pareto-optimal solutions (POS). However, it is important to note that ROOT M is not exclusively limited to multi-objective problems, and there are other classes of ROOT M problems, such as multimodal ones [19], where the search space contains multiple moving global optima [20,21].…”