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Data clustering is the task of separating data samples into a set of clusters. $K$-means is a popular partitional clustering algorithm. However, it has a lot of weaknesses, including sensitivity to initialization and the ability to become stuck in local optima. Hence, nature-inspired optimization algorithms were applied to the clustering problem to overcome the limitations of the $K$-means algorithm. However, due to the high-dimensionality of a search space, the nature-inspired optimization algorithm suffers from local optima and poor convergence rates. To address the mentioned issues, this paper presents a simplex method-based bacterial colony optimization (SMBCO) algorithm. The simplex method is a stochastic variant approach that improves population diversity while increasing the algorithm’s local searching ability. The potential and effectiveness of the proposed SMBCO clustering algorithm are assessed using a variety of benchmark machine learning datasets and the generated groups were evaluated using different performance measures. When compared to several well-known nature-inspired algorithms, the experimental results reveal that the SMBCO model produces superior clustering efficiency and a faster convergence rate.

The Biot model is widely used to model poroelastic media. Several authors have studied its applicability to cancellous bone. In this article the feasibility of determining the Biot parameters of cancellous bone by acoustic interrogation using frequencies in the 5–15 kHz range is studied. It is found that the porosity of the specimen can be determined with a high degree of accuracy. The degree to which other parameters can be determined accurately depends upon porosity.

In a precursor to this article the Biot model was used to model poroelastic media. The question this article addresses is whether the sort of experiments described by McKelvie and Palmer, Williams, and Hosokawa and Otani can be used to determine the parameters of the Biot model. A method of computing acoustic pressure in the low 100 kHz range was developed in Buchanan and Gilbert, "Determination of the parameters of cancellous bone using high frequency acoustic measurements," which appeared in Math. Comput. Modelling. In the present work a parameter recovery algorithm which uses parallel processing is developed and tested. It is found that when it is assumed that the agreement between calculated and measured data is about two digits, porosity can be determined to within about 1–2% and permeability, pore size and the bulk moduli to within about 40%, but in most cases less than 20%.

To overcome the poor population diversity and slow convergence rate of grey wolf optimizer (GWO), this paper introduces the elite opposition-based learning strategy and simplex method into GWO, and proposes a hybrid grey optimizer using elite opposition (EOGWO). The diversity of grey wolf population is increased and exploration ability is improved. The experiment results of 13 standard benchmark functions indicate that the proposed algorithm has strong global and local search ability, quick convergence rate and high accuracy. EOGWO is also effective and feasible in both low-dimensional and high-dimensional case. Compared to particle swarm optimization with chaotic search (CLSPSO), gravitational search algorithm (GSA), flower pollination algorithm (FPA), cuckoo search (CS) and bat algorithm (BA), the proposed algorithm shows a better optimization performance and robustness.

A linear program (LP) Minimizec^txsubject toAx = b, x ≥ 0 (null column vector), where A is an m×n real matrix, c and b are n- and m-vectors, respectively is a problem of great importance in numerous physical problems involving linear optimization such as diet problems, transport problems, industrial production problems. The algorithms such as simplex method, self-dual parametric algorithm, decomposition algorithm, primal-dual algorithm to solve an LP have been non-polynomial time. In order to appreciate the recent advances in this area the present chapter provides a background based on the simplex methods which completely ruled the scene during sixties, seventies and early eighties. Although the simplex methods are non-polynomial-time in the worst case, they did perform excellently in most real-world problems and behaved like a fast (polynomial-time) algorithm. The chapter then focuses on the development of several fast (polynomial-time) algorithms during the last two decades. It then briefly highlights heuristic and evolutionary approach to solve LPs including errorfree implementation.

The goal is to give some theoretical explanation for the efficiency of the simplex method of George Dantzig. Fixing the number of constraints and using Dantzig's self-dual parametric algorithm, we show that the number of pivots required to solve a linear programming problem grows in proportion to the number of variables on the average.

Although several anti-cycling pivot selection rules exist for the simplex method for a general linear program (LP), none is known to avoid stalling (an exponential sequence of degenerate pivots). In this paper we develop a pivot selection rule that prevents stalling when the coefficient matrix of the LP is totally unimodular. For an LP with m constraints and totally unimodular coefficient matrix, our pivot selection rule guarantees that the simplex method performs at most m consecutive degenerate pivots or declares that the current solution is optimal. This extends a corresponding result available for minimum cost flows.