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This paper presents a simplified algorithm for the profiling of the rack gear tool to generate the active profile associated with rolling centrodes. The algorithm is based on the enveloping surfaces principles and reduces the computational problem by proposing an approximate representation of tool’s profile using only three or four points on the profile to be generated by using Bezier representations of the surfaces. The algorithm computes the coefficients of a Bezier substitution polynomial instead of computing hundreds of points on the active profile. This simplifies the solution methodology and requires only a limited number of points along the profile to be generated. The algorithm is computationally efficient and can also be used in the case when the active profile to be generated is physically measured at a few points. Examples include mill tools, splined shafts, and gears. [ABSTRACT FROM AUTHOR]

Abstract  Dynamic optimization problems challenge traditional evolutionary algorithms seriously since they, once converged, cannot adapt quickly to environmental changes. This paper investigates the application of memetic algorithms, a class of hybrid evolutionary algorithms, for dynamic optimization problems. An adaptive hill climbing method is proposed as the local search technique in the framework of memetic algorithms, which combines the features of greedy crossover-based hill climbing and steepest mutation-based hill climbing. In order to address the convergence problem, two diversity maintaining methods, called adaptive dual mapping and triggered random immigrants, respectively, are also introduced into the proposed memetic algorithm for dynamic optimization problems. Based on a series of dynamic problems generated from several stationary benchmark problems, experiments are carried out to investigate the performance of the proposed memetic algorithm in comparison with some peer evolutionary algorithms. The experimental results show the efficiency of the proposed memetic algorithm in dynamic environments. [ABSTRACT FROM AUTHOR]

Abstract  In this paper, a memetic algorithm (MA) based on differential evolution (DE), namely MADE, is proposed for the multi-objective no-wait flow-shop scheduling problems (MNFSSPs). Firstly, a largest-order-value rule is presented to convert individuals in DE from real vectors to job permutations so that the DE can be applied for solving flow-shop scheduling problems (FSSPs). Secondly, the DE-based parallel evolution mechanism is applied to perform effective exploration, and several local searchers developed according to the landscape of multi-objective FSSPs are applied to emphasize local exploitation. Thirdly, a speed-up computing method is developed based on the property of the no-wait FSSPs. In addition, the concept of Pareto dominance is used to handle the updating of solutions in sense of multi-objective optimization. Due to the well balance between DE-based global search and problem-dependent local search as well as the utilization of the speed-up evaluation, the MNFSSPs can be solved effectively and efficiently. Simulation results and comparisons demonstrate the effectiveness and efficiency of the proposed MADE. [ABSTRACT FROM AUTHOR]

In this paper, we use the Ehlich-Zeller-G9ärtel inequality to derive an algorithm for finding the global minima of polynomials over hyperrectangles as well as to provide a bounding method for the branch-and-bound algorithm. The latter application of the inequality results in an improved algorithm which gives simultaneously a decreasing upper bound and an increasing lower bound for the global minimum at each iteration. The algorithm can be used also to find the Lipschitz constant of a polynomial. [ABSTRACT FROM AUTHOR]