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The conventional robust optimization methods usually focus on problems with unimodal random variables. In real applications, input random variables may follow multimodal distributions with multiple peaks in their probability density. When multimodal random variables are involved, the conventional methods, such as the mean-variance-based methods, will be not accurate. This paper presents an efficient robust optimization method, which provides a potential computational tool for engineering problems involving multimodal random variables. A robustness metric is formulated by introducing the concept of accepting/rejecting the limit to calculate the failure probability of the performance response, which can directly capture the multimodal characteristics of the performance. A second-order higher moment method is presented to efficiently conduct the probability calculation in the inner loop of design optimization. The proposed decoupling strategy drives the probability calculation and the design optimization sequentially and alternately. This method is applied to the three micromachine design problems, including a sweat-rate sensor, a piezoelectric sensor, and an image sensing module. The numerical results show that the method has excellent engineering practicality due to the comprehensive performance in terms of efficiency, accuracy, and convergence.

Shopper buying behaviour is essential for the retailers to segment the shoppers in accordance to their disruptive attitude and perception for better innovative strategies which may lead to higher profits. The major purpose of this study to categorize the shoppers into distinct groups based on their risk-based perception for the organized retail outlets in Bangladesh. Seven hundred eighty-five respondents were responding on 21 variables related to store which influence their buying behaviour. In the present study, the shoppers were classified into three segments such as value seekers and disruptive to please shoppers, quality and style-driven shoppers, sensory-driven, and not interested shoppers by using innovative k-means cluster analysis. The results of the study help to retailers in understanding the various disruptive segments of shoppers in relation to their importance for store attributes affected by their demographic characteristics and guide the retailers to take necessary actions regard redesign of retail mix to provide innovative value to the shoppers.

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