On the Impact of Mutation-Selection Balance on the Runtime of Evolutionary Algorithms

The interplay between mutation and selection plays a fundamental role in the behaviour of evolutionary algorithms (EAs). However, this interplay is still not completely understood. This paper presents a rigorous runtime analysis of a non-elitist population-based EA that uses the linear ranking selection mechanism. The analysis focuses on how the balance between parameter $\eta$, controlling the selection pressure in linear ranking, and parameter $\chi$ controlling the bit-wise mutation rate, impacts the runtime of the algorithm. The results point out situations where a correct balance between selection pressure and mutation rate is essential for finding the optimal solution in polynomial time. In particular, it is shown that there exist fitness functions which can only be solved in polynomial time if the ratio between parameters $\eta$ and $\chi$ is within a narrow critical interval, and where a small change in this ratio can increase the runtime exponentially. Furthermore, it is shown quantitatively how the appropriate parameter choice depends on the characteristics of the fitness function. In addition to the original results on the runtime of EAs, this paper also introduces a very useful analytical tool, i.e., multi-type branching processes, to the runtime analysis of non-elitist population-based EAs

Self-adaptation of Mutation Rates in Non-elitist Populations

The runtime of evolutionary algorithms (EAs) depends critically on their parameter settings, which are often problem-specific. Automated schemes for parameter tuning have been developed to alleviate the high costs of manual parameter tuning. Experimental results indicate that self-adaptation, where parameter settings are encoded in the genomes of individuals, can be effective in continuous optimisation. However, results in discrete optimisation have been less conclusive. Furthermore, a rigorous runtime analysis that explains how self-adaptation can lead to asymptotic speedups has been missing. This paper provides the first such analysis for discrete, population-based EAs. We apply level-based analysis to show how a self-adaptive EA is capable of fine-tuning its mutation rate, leading to exponential speedups over EAs using fixed mutation rates.Comment: To appear in the Proceedings of the 14th International Conference on Parallel Problem Solving from Nature (PPSN

Statistical and Computational Tradeoff in Genetic Algorithm-Based Estimation

When a Genetic Algorithm (GA), or a stochastic algorithm in general, is employed in a statistical problem, the obtained result is affected by both variability due to sampling, that refers to the fact that only a sample is observed, and variability due to the stochastic elements of the algorithm. This topic can be easily set in a framework of statistical and computational tradeoff question, crucial in recent problems, for which statisticians must carefully set statistical and computational part of the analysis, taking account of some resource or time constraints. In the present work we analyze estimation problems tackled by GAs, for which variability of estimates can be decomposed in the two sources of variability, considering some constraints in the form of cost functions, related to both data acquisition and runtime of the algorithm. Simulation studies will be presented to discuss the statistical and computational tradeoff question.Comment: 17 pages, 5 figure

Towards Smart Hybrid Fuzzing for Smart Contracts

Smart contracts are Turing-complete programs that are executed across a blockchain network. Unlike traditional programs, once deployed they cannot be modified. As smart contracts become more popular and carry more value, they become more of an interesting target for attackers. In recent years, smart contracts suffered major exploits, costing millions of dollars, due to programming errors. As a result, a variety of tools for detecting bugs has been proposed. However, majority of these tools often yield many false positives due to over-approximation or poor code coverage due to complex path constraints. Fuzzing or fuzz testing is a popular and effective software testing technique. However, traditional fuzzers tend to be more effective towards finding shallow bugs and less effective in finding bugs that lie deeper in the execution. In this work, we present CONFUZZIUS, a hybrid fuzzer that combines evolutionary fuzzing with constraint solving in order to execute more code and find more bugs in smart contracts. Evolutionary fuzzing is used to exercise shallow parts of a smart contract, while constraint solving is used to generate inputs which satisfy complex conditions that prevent the evolutionary fuzzing from exploring deeper paths. Moreover, we use data dependency analysis to efficiently generate sequences of transactions, that create specific contract states in which bugs may be hidden. We evaluate the effectiveness of our fuzzing strategy, by comparing CONFUZZIUS with state-of-the-art symbolic execution tools and fuzzers. Our evaluation shows that our hybrid fuzzing approach produces significantly better results than state-of-the-art symbolic execution tools and fuzzers