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The joint order batching and picker routing problem (JOBPRP) is a combinatorial optimization problem that occurs during in the order-picking operation of warehouse management. It consists of simultaneous assignment of customer orders to batches and routing of picking operations in the batches such that the total travel distance is minimized. In this paper, we develop a memetic algorithm with fuzzy-based population control (MA-FPC) to solve the JOBPRP. MA-FPC takes advantage of the hierarchical nature of the problem to design a batch exchange crossover (BEX) operator and a two-level local improvement procedure. BEX transfers complete batches from parent solutions to offsprings. Local improvement systematically employs a combined heuristic and exact routing approach to solve the picker routing problem. Furthermore, fuzzy-based population control is used to dynamically regulate population diversity during the search, which removes individuals from or adds individuals to the population. In numerical experiments, MA-FPC significantly outperforms state-of-the-art point-based and population-based algorithms developed for the order batching problem and JOBPRP with respect to solution quality in reasonable running times. Our algorithm improves the previous best-known solutions for 57 of the 64 benchmark instances. [ABSTRACT FROM AUTHOR]

In practical FIR digital filter applications it is often necessary to represent the filter coefficients with a finite number of bits. The finite wordlength coefficient restriction reduces the filter quality and increases the filter deviation. This increase can be reduced substantially if the optimal finite wordlength coefficients are used. Computing these coefficients is more difficult and can be slow. It was shown before that the computation time can be significantly reduced with the help of a lower bound on the deviation increase. Derivation of a new algorithm that uses a much better lower bound is the purpose of this paper. We consider the general case of a length N filter with a discrete set of allowable real coefficients and demonstrate the effectiveness of the new algorithm on a set of filter design cases. The results show that this algorithm reduces the computation times up to 3 times when compared with the previously best results. • Practical FIR filter implementations often require low bit filter coefficients. • Quantization of FIR filter coefficients reduces the filter quality. • Optimal finite wordlength FIR filter coefficients are much better. • Computing the optimal low bit coefficients can be computationally demanding. • A new faster algorithm for optimal finite wordlength FIR design is a solution. [ABSTRACT FROM AUTHOR]