In the field of evolutionary multi-criterion optimization, the hypervolume indicator is the only single set quality measure that is known to be strictly monotonic with regard to Pareto dominance: whenever a Pareto set approximation entirely dominates another one, then the indicator value of the dominant set will also be better. This property is of high interest and relevance for problems involving a large number of objective functions. However, the high computational effort required for hypervolume calculation has so far prevented the full exploitation of this indicator's potential; current hypervolume-based search algorithms are limited to problems with only a few objectives. This paper addresses this issue and proposes a fast search algorithm that uses Monte Carlo simulation to approximate the exact hypervolume values. The main idea is not that the actual indicator values are important, but rather that the rankings of solutions induced by the hypervolume indicator. In detail, we present HypE, a hypervolume estimation algorithm for multi-objective optimization, by which the accuracy of the estimates and the available computing resources can be traded off; thereby, not only do many-objective problems become feasible with hypervolume-based search, but also the runtime can be flexibly adapted. Moreover, we show how the same principle can be used to statistically compare the outcomes of different multi-objective optimizers with respect to the hypervolume—so far, statistical testing has been restricted to scenarios with few objectives. The experimental results indicate that HypE is highly effective for many-objective problems in comparison to existing multi-objective evolutionary algorithms. HypE is available for download at http://www.tik.ee.ethz.ch/sop/download/supplementary/hype/ .

Static analyzers help find bugs early by warning about recurring bug categories. While fixing these bugs still remains a mostly manual task in practice, we observe that fixes for a specific bug category often are repetitive. This paper addresses the problem of automatically fixing instances of common bugs by learning from past fixes. We present Getafix, an approach that produces human-like fixes while being fast enough to suggest fixes in time proportional to the amount of time needed to obtain static analysis results in the first place. Getafix is based on a novel hierarchical clustering algorithm that summarizes fix patterns into a hierarchy ranging from general to specific patterns. Instead of an expensive exploration of a potentially large space of candidate fixes, Getafix uses a simple yet effective ranking technique that uses the context of a code change to select the most appropriate fix for a given bug. Our evaluation applies Getafix to 1,268 bug fixes for six bug categories reported by popular static analyzers for Java, including null dereferences, incorrect API calls, and misuses of particular language constructs. The approach predicts exactly the human-written fix as the topmost suggestion between 12% and 91% of the time, depending on the bug category. The top-5 suggestions contain fixes for 526 of the 1,268 bugs. Moreover, we report on deploying the approach within Facebook, where it contributes to the reliability of software used by billions of people. To the best of our knowledge, Getafix is the first industrially-deployed automated bug-fixing tool that learns fix patterns from past, human-written fixes to produce human-like fixes. CCS Concepts: • Software and its engineering → Software testing and debugging.

Abstract-Assuming that evolutionary multiobjective optimization (EMO) mainly deals with set problems, one can identify three core questions in this area of research: (i) how to formalize what type of Pareto set approximation is sought, (ii) how to use this information within an algorithm to efficiently search for a good Pareto set approximation, and (iii) how to compare the Pareto set approximations generated by different optimizers with respect to the formalized optimization goal. There is a vast amount of studies addressing these issues from different angles, but so far only few studies can be found that consider all questions under one roof. This paper is an attempt to summarize recent developments in the EMO field within a unifying theory of set-based multiobjective search. It discusses how preference relations on sets can be formally defined, gives examples for selected user preferences, and proposes a general, preference-independent hill climber for multiobjective optimization with theoretical convergence properties. Furthermore, it shows how to use set preference relations for statistical performance assessment and provides corresponding experimental results. The proposed methodology brings together preference articulation, algorithm design, and performance assessment under one framework and thereby opens up a new perspective on EMO.

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