Robust Optimization Over Time In Uncertain Environments Using Swarm Intelligence

Most real-world optimization problems are subject to various amounts of uncertainties.There are two general approaches to handling optimization in the presence of uncertainties in metaheuristics.One is to find robust optimal solutions,whose performance are expected to remain acceptable in the presence of uncertainties.The other is to track the moving optimum dynamically once there are any environmental changes.However,both approaches have shortcomings.The former assumes that the uncertainty is very small,but the uncertainty may be large sometimes in real-world problems,while the latter assumes that the algorithm can find the new optimal solution quickly.Unfortunately,frequently switching solutions is not allowed in many real-world problems,since switching solutions may incur costs.Thus,a new approach to solving dynamic optimization problems,called robust optimization over time(ROOT),has been proposed,which combines the merits of the above two methods.On the basis of ROOT,the following research is carried out in this thesis.(1)Since existing performance indicators for ROOT algorithms are based on predicted fitness values,which will degrade the accuracy of evaluation,three new indicators based on the real fitness function value for assessing the performance of ROOT algorithms are proposed and are empirically evaluated.Where the indicator “error” can be used to quantitatively measure the difference in robustness between the solution obtained by a ROOT algorithm and the actual one,the indicator “success” can be used to judge effectively whether the algorithm succeeds in identifying the ROOT solution in each environment.The indicator “success rate” can be used to measure the overall performance of the algorithm.Compared with the existing indicators,these proposed indicators can not only compare the performance among different algorithms,but also measure the performance of the algorithm for different parameter settings.(2)A new ROOT algorithm based on a swarm intelligence algorithm is proposed for solving constrained optimization problems.Firstly,a penalty function is constructed using the constraint conditions.Then,the penalty function and objective function are considered as two different fitness functions.A swarm intelligence algorithm is adopted to search for robust optimal solutions with the help of the new fitness functions and competitive selection.Finally,taking the optimization of the performance of carbon fiber precursor as an example,the proposed algorithm is tested and compared under different groups of parameters,and the results show the effectiveness of the proposed algorithm.Further,the influence of the prediction model on the performance of the algorithm is analyzed.The results show that the improvement of the prediction model is an important way to improve the performance of the algorithm.(3)Since switching solutions often incur cost in real-world applications,it is essential to consider the minimization of the switching cost in ROOT.Therefore,a framework for multi-objective robust optimization over time considering switching cost(ROOT/SC)is proposed,which is able to maximize the robustness and minimizes the switching cost simultaneously.An instantiation of the framework is also implemented,where a multi-objective particle swarm optimization algorithm is adopted as the optimizer and the cost for switching a solution is defined as the difference in the decision space between the solution used in the previous environment and the one in the current environment.Through a series of experimental tests,the effectiveness of the algorithm is verified,and the influence of each parameter on the performance of the algorithm is analyzed.Compared with other methods,the advantages of the proposed algorithm is that it not only takes into account the robustness,but also considers the optimization of the switching cost.(4)In order to consider the robustness and switching cost of the solutions simultaneously when switching the solution in a sequence of dynamic environments,a user-preferences-based method for ROOT is proposed.Firstly,the improved version of ROOT/SC algorithm,called ROOT/SCII,is proposed,inspired by the idea of “multiobjectivization”,a helper objective is introduced into the ROOT/SC algorithm to enhance its ability to search for Pareto optimal solutions.The experimental results show the effectiveness of the proposed algorithm.Secondly,the proposed method is achieved by combining ROOT/SCII that maximizes the robustness and minimizes the switching cost,and a switching policy that selects a solution from the non-dominated set obtained by ROOT/SCII to replace the solution currently in use.Finally,experimental results confirm that the proposed algorithm is able to switch solutions according to the user's preferences effectively.Compared with other methods,the proposed method takes into account the optimization of switching cost.In addition,the effects of robust thresholds,types of the dynamic environments and the dimension of the search space on the algorithm are examined by experiments.The advantages of the proposed method is that it can choose the right solution flexibly for switching according to the preferences of users and take into account the robustness requirements while optimizing the switching cost.Finally,the main results of the PhD work are summarized,and future research work is discussed.