On Easiest Functions for Mutation Operators in Bio-Inspired Optimisation

Understanding which function classes are easy and which are hard for a given algorithm is a fundamental question for the analysis and design of bio-inspired search heuristics. A natural starting point is to consider the easiest and hardest functions for an algorithm. For the (1+1) EA using standard bit mutation (SBM) it is well known that OneMax is an easiest function with unique optimum while Trap is a hardest. In this paper we extend the analysis of easiest function classes to the contiguous somatic hypermutation (CHM) operator used in artificial immune systems. We define a function MinBlocks and prove that it is an easiest function for the (1+1) EA using CHM, presenting both a runtime and a fixed budget analysis. Since MinBlocks is, up to a factor of 2, a hardest function for standard bit mutations, we consider the effects of combining both operators into a hybrid algorithm. We rigorously prove that by combining the advantages of k operators, several hybrid algorithmic schemes have optimal asymptotic performance on the easiest functions for each individual operator. In particular, the hybrid algorithms using CHM and SBM have optimal asymptotic performance on both OneMax and MinBlocks. We then investigate easiest functions for hybrid schemes and show that an easiest function for an hybrid algorithm is not just a trivial weighted combination of the respective easiest functions for each operator.publishersversionPeer reviewe

Expected Fitness Gains of Randomized Search Heuristics for the Traveling Salesperson Problem.

Randomized search heuristics are frequently applied to NP-hard combinatorial optimization problems. The runtime analysis of randomized search heuristics has contributed tremendously to their theoretical understanding. Recently, randomized search heuristics have been examined regarding their achievable progress within a fixed time budget. We follow this approach and present a fixed budget analysis for an NP-hard combinatorial optimization problem. We consider the well-known Traveling Salesperson problem (TSP) and analyze the fitness increase that randomized search heuristics are able to achieve within a given fixed time budget. In particular, we analyze Manhattan and Euclidean TSP instances and Randomized Local Search (RLS), (1 + 1) EA and (1 + λ) EA algorithms for the TSP in a smoothed complexity setting and derive the lower bounds of the expected fitness gain for a specified number of generations

Adaptive Hypermutation for Search-Based System Test Generation: A Study on REST APIs with EvoMaster

REST web services are widely popular in industry, and search techniques have been successfully used to automatically generate system-level test cases for those systems. In this article, we propose a novel mutation operator which is designed specifically for test generation at system-level, with a particular focus on REST APIs. In REST API testing, and often in system testing in general, an individual can have a long and complex chromosome. Furthermore, there are two specific issues: (1) fitness evaluation in system testing is highly costly compared with the number of objectives (e.g., testing targets) to optimize for; and (2) a large part of the genotype might have no impact on the phenotype of the individuals (e.g., input data that has no impact on the execution flow in the tested program). Due to these issues, it might be not suitable to apply a typical low mutation rate like 1/n (where n is the number of genes in an individual), which would lead to mutating only one gene on average. Therefore, in this article, we propose an adaptive weight-based hypermutation, which is aware of the different characteristics of the mutated genes. We developed adaptive strategies that enable the selection and mutation of genes adaptively based on their fitness impact and mutation history throughout the search. To assess our novel proposed mutation operator, we implemented it in the EvoMaster tool, integrated in the MIO algorithm, and further conducted an empirical study with three artificial REST APIs and four real-world REST APIs. Results show that our novel mutation operator demonstrates noticeable improvements over the default MIO. It provides a significant improvement in performance for six out of the seven case studies, where the relative improvement is up to +12.09% for target coverage, +12.69% for line coverage, and +32.51% for branch coverage.publishedVersio