Noisy combinatorial optimisation with evolutionary algorithms

The determination of the efficient evolutionary optimisation approaches in solving noisy combinatorial problems is the main focus in this research. Initially, we present an empirical study of a range of evolutionary algorithms applied to various noisy combinatorial optimisation problems. There are four sets of experiments. The first looks at several toy problems, such as OneMax and other linear problems. We find that Univariate Marginal Distribution Algorithm (UMDA) and the Paired-Crossover Evolutionary Algorithm (PCEA) are the only ones able to cope robustly with noise, within a reasonable fixed time budget. In the second stage, UMDA and PCEA are then tested on more complex noisy problems: SubsetSum, Knapsack and SetCover. Both perform well under increasing levels of noise, with UMDA being the better of the two. In the third stage, we consider two noisy multi-objective problems (CountingOnesCountingZeros and a multi-objective formulation of SetCover). We compare several adaptations of UMDA for multi-objective problems with the Simple Evolutionary Multi-objective Optimiser (SEMO) and NSGA-II. In the last stage of empirical analysis, a realistic problem of the path planning for the ground surveillance with Unmanned Aerial Vehicles is considered. We conclude that UMDA, and its variants, can be highly effective on a variety of noisy combinatorial optimisation, outperforming many other evolutionary algorithms. Next, we study the use of voting mechanisms in populations, and introduce a new Voting algorithm which can solve OneMax and Jump in O(n log n), even for gaps as large as O(n). More significantly, the algorithm solves OneMax with added posterior noise in O(n log n), when the variance of the noise distribution is sigma$^2$ = O(n) and in O(sigma$^2$ log n) when the noise variance is greater than this. We assume only that the noise distribution has finite mean and variance and (for the larger noise case) that it is unimodal. Building upon this promising performance, we consider other noise models prevalent in optimisation and learning and show that the Voting algorithm has efficient performance in solving OneMax in presence of these noise variants. We also examine the performance on arbitrary linear and monotonic functions. The Voting algorithm fails on LeadingOnes but we give a variant which can solve the problem in O(n log n). We empirically study the use of voting in population based algorithms (UMDA, PCEA and cGA) and show that this can be effective for large population sizes

Application of fuzzy consensus for oral pre-cancer and cancer susceptibility assessment

Health questionnaire data assessment conventionally relies upon statistical analysis in understanding disease susceptibility using discrete numbers and fails to reflect physician’s perspectives and missing narratives in data, which play subtle roles in disease prediction. In addressing such limitations, the present study applies fuzzy consensus in oral health and habit questionnaire data for a selected Indian population in the context of assessing susceptibility to oral pre-cancer and cancer. Methodically collected data were initially divided into age based small subgroups and fuzzy membership function was assigned to each. The methodology further proposed the susceptibility to oral precancers (viz. leukoplakia, oral submucous fibrosis) and squamous cell carcinoma in patients considering a fuzzy rulebase through If-Then rules with certain conditions. Incorporation of similarity measures using the Jaccard index was used during conversion into the linguistic output of fuzzy set to predict the disease outcome in a more accurate manner and associated condition of the relevant features. It is also expected that this analytical approach will be effective in devising strategies for policy making through real-life questionnaire data handling