The Weights Can Be Harmful: Pareto Search versus Weighted Search in Multi-objective Search-based Software Engineering

Abstract

In presence of multiple objectives to be optimized in Search-Based Software Engineering (SBSE), Pareto search has been commonly adopted. It searches for a good approximation of the problem’s Pareto optimal solutions, from which the stakeholders choose the most preferred solution according to their preferences. However, when clear preferences of the stakeholders (e.g., a set of weights which reflect relative importance between objectives) are available prior to the search, weighted search is believed to be the first choice since it simplifies the search via converting the original multi-objective problem into a single-objective one and enable the search to focus on what only the stakeholders are interested in. This paper questions such a “weighted search first” belief. We show that the weights can, in fact, be harmful to the search process even in the presence of clear preferences. Specifically, we conduct a large scale empirical study which consists of 38 systems/projects from three representative SBSE problems, together with two types of search budget and nine sets of weights, leading to 604 cases of comparisons. Our key finding is that weighted search reaches a certain level of solution quality by consuming relatively less resources at the early stage of the search; however, Pareto search is at the majority of the time (up to 77% of the cases) significantly better than its weighted counterpart, as long as we allow a sufficient, but not unrealistic search budget. This is a beneficial result, as it discovers a potentially new “rule-of-thumb” for the SBSE community: even when clear preferences are available, it is recommended to always consider Pareto search by default for multi-objective SBSE problems provided that solution quality is more important. Weighted search, in contrast, should only be preferred when the resource/search budget is limited, especially for expensive SBSE problems. This, together with other findings and actionable suggestions in the paper, allows us to codify pragmatic and comprehensive guidance on choosing weighted and Pareto search for SBSE under the circumstance that clear preferences are available. All code and data can be accessed at: https://github.com/ideas-labo/pareto-vs-weight-for-sbse.

Multi-objective search for gender-fair and semantically correct word embeddings

“…3: d). These result are in line with those by Chen and Li [95], who showed that Pareto search is preferred over weighted search for problems in the Search-Based Software Engineering domain.…”

Regularization-free multicriteria optimization of polymer viscoelasticity model

“…For the sake of practical illustration, though, the solutions with nearly equal regression residuals for both storage and loss moduli we obtained are numerically close to that reported in the referenced literature. In particular, we were able to approximately reproduce the results obtained by the mentioned monobjective EA [17] for the LDPE material with respect to both regression errors and number of model parameters (indeed, the literature [31] suggests that multiobjective optimization methods can outperform monobjective analogs in virtue of the lower scale sensitivity and susceptibility to local-optima traps-although subject to the limitations of the intrinsic experimental errors in the data sample). Like in the said experiment, the solutions produced by MOAD/D have similar or lower regression residuals than those yielded by deterministic methods reported in the literature (Section 1.2), and with a lower number of parameters.…”

Hierarchical clustering-based framework for a posteriori exploration of Pareto fronts: application on the bi-objective next release problem

“…When information about preferences is lacking, building a significant preference model can be difficult, and it could take many executions with different preference settings in order to find a compliant solution. Furthermore, even when preferences are clear and certain, recent studies show that a priori approaches based on weights can be harmful to the search (Chen and Li, 2022).…”