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In this article, an improved Gaussian distribution based quantum-behaved particle swarm optimization (IG-QPSO) algorithm is proposed to solve engineering shape design problems with multiple constraints. In this algorithm, the Gaussian distribution is employed to generate the sequence of random numbers in the QPSO algorithm. By decreasing the variance of the Gaussian distribution linearly, the algorithm is able not only to maintain its global search ability during the early search stages, but can also obtain gradually enhanced local search ability in the later search stages. Additionally, a weighted mean best position in the IG-QPSO is employed to achieve a good balance between local search and global search. The proposed algorithm and some other well-known PSO variants are tested on ten standard benchmark functions and six well-studied engineering shape design problems. Experimental results show that the IG-QPSO algorithm can optimize these problems effectively in terms of precision and robustness compared to its competitors. [ABSTRACT FROM AUTHOR]