# Mutational Chemotaxis Motion Driven MdpI for Engineering Applications
###### Abstract
[51] proposed an enhanced MFO, which added a simulate-annealing strategy to enhance the local exploitation and introduced the idea of a quantum-revolving gate to enhance its global exploration ability. [PERSON] et al. [52] added inertia weight to balance the algorithm performance and introduced a small probability mutation in the position-update stage to enhance the ability of the algorithm to escape from the local optimal space. [PERSON] et al. [53] defined a hybrid phase in the MFO algorithm to balance the exploration and exploitation of the algorithm, and adopted the dynamic-crossover mechanism to the flame to enhance population diversity. [PERSON] et al. [54] proposed a novel variant of MFO, whose main optimization idea was to adopt differential evolution and opposite-learning strategies to the generation of flame. The improved shuffle-frog-jump algorithm was used as the local-search algorithm, and the individuals with poor fitness were eliminated through the death mechanism. [PERSON] et al. [55] proposed a dual-evolutionary learning MFO. The two optimization strategies in the algorithm were differential-evolutionary- flame generation and dynamic-flame-guidance strategy, which aimed to generate a high-quality flame to guide the moth to fly toward the optimal direction. [PERSON] et al. [56] initialized the moth population by chaotic mapping, processed the cross-border individuals, and adjusted the distance parameters to improve the performance of MFO. The statistical results showed that chaotic mapping promotes the algorithm's performance. [PERSON] et al. [57] added a cultural-learning mechanism to MFO and performed a Gaussian mutation of the optimal flame, which increased the population diversity and enhanced the search ability of the algorithm. In order to overcome the problem of premature convergence of MFO, [PERSON] et al. [58] used opposition learning, Cauchy mutation and evolutionary-boundary-constraint-processing technology. Experiments showed that the enhanced MFO improved both in convergence and escape from local stagnation. Although many scholars have proposed optimization strategies for MFO from different perspectives, it still needs to be strengthened in terms of jumping out of the local optimal space and optimization accuracy. To overcome the problem that the traditional MFO is prone to local optimality and poor optimization accuracy, this paper proposes a novel MFO-variant algorithm called HMCMMFO. To deal with the problem that MFO is vulnerable to deceptive optimality, this paper proposes a hybrid-mutation strategy that assigns dynamic weights to Cauchy and Gaussian mutation, which are applied to the individuals adaptively with the deepening of the optimization process. At the same time, to improve the optimization accuracy of the algorithm, chemotaxis-motion mechanism is proposed to better mine the solutions in the local space and improve the search efficiency. Based on the classical IEEE CEC2017 functions, experiments, such as mechanism combination, balanced-diversity analysis, and comparison of novel and advanced algorithms, were conducted to demonstrate the optimization effect of the MFO variant named HMCMMFO, of which the effectiveness and superiority were verified, and was then applied to engineering problems to realize its potential value better. Note that the main contributions of this study are as follows. 1. A hybrid-mutation strategy is proposed to enhance the exploration ability of the algorithm and the ability to jump out of the local optimum. 2. Chemotaxis-motion mechanism is proposed to guide the direction of the population to approach optimal solution and improve the algorithm's local-exploitation capability. 3. HMCMMFO can obtain high-quality optimal solutions within the CEC 2017 test functions. 4. HMCMMFO is applied to five typical engineering cases to solve the constraint problems effectively.