Dynamic Contribution-based Decomposition Method and Hybrid Genetic Algorithm for Multidisciplinary Engineering Optimisation

摘要

A novel decomposition method that is referred to as Contribution-based Decomposition is presented in this thesis. The influence of variables on the values of objective functions and/or constraints is interpreted as their contributions. Based on contributions of variables, a design problem is decomposed into a number of sub-problems so that variables have similar relative contributions within each sub-problem. The similarity in contributions among variables will lead to an even pressure on the variables when they are driven to better solutions during an optimisation process and, as a result, better solutions can be obtained. Due to nonlinearity of objectives and/ or constrains, variables’ contributions may vary significantly during the solution process. To cope with such variations, a Dynamic Contribution-based Decomposition (DCD) is proposed. By employing DCD, decomposition of system problems is carried out not only at the beginning, but also during the optimisation process, and as a result, the decomposition will always be consistent with the contributions of the current solutions. Further more, a random decomposition is also developed and presented to work in conjunction with the Dynamic Contribution-based Decomposition to introduce re-decompositions when it is required, aiming to increase the global exploring ability.To solve multidisciplinary engineering optimisation problems more efficiently, new solvers are also developed. These include a mixed discrete variable Pattern Search (MDVPS) algorithm and a mixed discrete variable Genetic Algorithm (MDVGA). Inside the MDVGA, new techniques including a flexible floating-point encoding method, a non-dominance ranking strategy and heuristic crossover and mutation operators are also developed to avoid premature convergence and enhance the GA’s search ability. Both MDVPS and MDVGA are able to handle optimisation problems having mixed discrete variables. The former algorithm is more capable of local searching and the latter has better global search ability. A hybrid solver is proposed, which incorporates the MDVPS and the MDVGA and takes advantage of both their strengths.Lastly, a Dynamic Sub-space Optimisation (DSO) method is developed by employing the proposed Dynamic Contribution-based Decomposition methods and the hybrid solver. By employing DSO, decomposed sub-problems can be solved without explicit coordination.To demonstrate the capability of the proposed methods and algorithms, a range of test problems have been exercised and the results are documented. Collectively the results show significant improvements over other published popular approaches.