Evolving Dynamic Multi-Objective Optimization Problems with Objective Replacement

Abstract

This paper studies the strategies for multi-objective optimization in a dynamic environment. In particular, we focus on problems with objective replacement, where some objectives may be replaced with new objectives during evolution. It is shown that the Pareto-optimal sets before and after the objective replacement share some common members. Based on this observation, we suggest the inheritance strategy. When objective replacement occurs, this strategy selects good chromosomes according to the new objective set from the solutions found before objective replacement, and then continues to optimize them via evolution for the new objective set. The experiment results showed that this strategy can help MOGAs achieve better performance than MOGAs without using the inheritance strategy, where the evolution is restarted when objective replacement occurs. More solutions with better quality are found during the same time span.

Benchmarks for dynamic multi-objective optimisation algorithms

“…Guan et al [2005] suggested creating DMOOPs by replacing objective functions with new objective functions over time. The advantage of Guan et al's approach is that the new objective function(s) can cause a severe change in the DMOOP, and by selecting the objective functions carefully, various types of changes can be incorporated into the DMOOP.…”

“…When objective functions are changed over time, as in the approaches followed by Guan et al [2005] and Wang and Li, the objective functions should be selected carefully to ensure that the resulting objective functions hinder the algorithm in finding the POF in various ways, as discussed in Section 3. Another approach was followed by Jin and Sendhoff [2004], where a two-objective DMOOP is constructed from a three-objective MOO function.…”

Performance measures for dynamic multi-objective optimisation algorithms

“…Guan et al [28] introduced a set coverage measure that is based on the S and D metrics introduced by Zitzler [71]. The HV of the objective space that is dominated by POF * but not by POF ′ , referred to as the D-metric, is defined as…”

Dynamic Multi-Objective Optimization Using PSO

“…An approach to reformulate a three-objective optimisation test function to define a dynamic two-objective optimisation problem was presented by Jin and Sendhof [14]. Guan et al [11] presented an approach to create DMOOPs by replacing objective functions with new ones at specific times. DMOOPs based on the static MOO twoobjective ZDT functions [26] and the scalable DTLZ functions [5] was presented by Farina et al [7].…”