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In this paper, an adaptive modification rate artificial bee colony (AMR‐ABC) algorithm is proposed by incorporating a novel adaptive modification rate to adaptively balance exploration and exploitation to determine which parameters (or the number of parameters) to be updated in a solution during each iteration. The performance of the AMR‐ABC algorithm is compared to those the standard ABC algorithm and its two variants, and the Parks–McClellan algorithm for designing Type 3 (orders: 14, 26, and 38) and Type 4 (orders: 13, 25, and 37) linear phase FIR differentiators to evaluate their design capabilities. Design results have shown that the proposed AMR‐ABC algorithm (i) outperforms four other design algorithms with the lowest p‐norm error in each of the six differentiator designs and (ii) is robust such that the same p‐norm error solution with an equiripple amplitude response in each of the six differentiator designs can be obtained by repeating a design with a different population of randomly generated initial solutions. The filter coefficients of six linear phase FIR differentiator designs are given as benchmarks to compare the p‐norm error performance of the AMR‐ABC algorithm to other algorithms. The AMR‐ABC algorithm is attractive to be used for optimisation in this and other design problems.

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