L1-norm optimization of problems with arbitrary column rank by Whale method and its improved algorithm for outlier detection

Abstract In this contribution L1-norm target function is minimized by Whale algorithm for the first time. It is a meta-heuristic optimization method which mimics the social behavior of humpback whales. The Whale algorithm is simple and flexible. It takes advantage of a derivation-free mechanism. L1-norm is an efficient tool for outlier detection, nevertheless, its implementation is complex since after formulation of L1-norm minimization for a certain problem, one must solve a linear programming problem by a cumbersome search method while here we only need to set the corresponding L1-norm cost function. During this contribution we also investigate other advantages of the proposed method over traditional methods numerically. As the Whale algorithm cannot deal with rank deficient problems, it must be improved. Thus the second algorithm of this contribution is an improved Whale algorithm which is developed here. Three geodetic applications approve the robustness of the proposed approach.