On the Evolvability of Monotone Conjunctions with an Evolutionary Mutation Mechanism

A Bernoulli(p)n distribution Bn,p over {0, 1}n is a product distribution where each variable is satisfied with the same constant probability p. Diochnos (2016) showed that Valiant's swapping algorithm for monotone conjunctions converges efficiently under Bn,p distributions over {0, 1}n for any 0 < p < 1. We continue the study of monotone conjunctions in Valiant's framework of evolvability. In particular, we prove that given a Bn,p distribution characterized by some p ∈ (0, 1/3] ∪ {1/2}, then an evolutionary mechanism that relies on the basic mutation mechanism of a (1+1) evolutionary algorithm converges efficiently, with high probability, to an ε-optimal hypothesis. Furthermore, for 0 < α ≤ 3/13, a slight modification of the algorithm, with a uniform setup this time, evolves with high probability an ε-optimal hypothesis, for every Bn,p distribution such that p ∈ [α, 1/3 - 4α/9] ∪ {1/3} ∪ {1/2}.

Dynamic Harris Hawks Optimization with Mutation Mechanism for Satellite Image Segmentation

In this paper, a novel satellite image segmentation technique based on dynamic Harris hawks optimization with a mutation mechanism (DHHO/M) is proposed. Compared with the original Harris hawks optimization (HHO), the dynamic control parameter strategy and mutation operator used in DHHO/M can avoid falling into the local optimum and efficiently enhance the search capability. To evaluate the performance of the proposed method, a series of experiments are carried out on various satellite images. Eight advanced thresholding approaches are selected for comparison. Three criteria are adopted to determine the segmentation thresholds, namely Kapur’s entropy, Tsallis entropy, and Otsu between-class variance. Furthermore, four oil pollution images are used to further assess the practicality and feasibility of the proposed method on real engineering problem. The experimental results illustrate that the DHHO/M based thresholding technique is superior to others in the following three aspects: fitness function evaluation, image segmentation effect, and statistical tests.