One of the major distinguishing features of the dynamic multiobjective optimization problems (DMOPs) is that optimization objectives will change over time, thus tracking the varying Pareto-optimal front becomes a challenge. One of the promising solutions is reusing “experiences” to construct a prediction model via statistical machine learning approaches. However, most existing methods neglect the nonindependent and identically distributed nature of data to construct the prediction model. In this paper, we propose an algorithmic framework, called transfer learning-based dynamic multiobjective evolutionary algorithm (EA), which integrates transfer learning and population-based EAs to solve the DMOPs. This approach exploits the transfer learning technique as a tool to generate an effective initial population pool via reusing past experience to speed up the evolutionary process, and at the same time any population-based multiobjective algorithms can benefit from this integration without any extensive modifications. To verify this idea, we incorporate the proposed approach into the development of three well-known EAs, nondominated sorting genetic algorithm II, multiobjective particle swarm optimization, and the regularity model-based multiobjective estimation of distribution algorithm. We employ 12 benchmark functions to test these algorithms as well as compare them with some chosen state-of-the-art designs. The experimental results confirm the effectiveness of the proposed design for DMOPs.
The increasing diversity methods tend to add variety to the population by using a certain type of methodology when the environment change was detected. For example, Cobb proposed the triggered hypermutation method @cite_34 , and the basic idea of this method is that when change is identified, the mutation rate would be increased immediately, and this would make the converged population divergent again. This approach calls for some improvements, and one of them is that the mutation rate is in a state of uncontrolled change during the whole process, and this ultimately results in reduced performance of the algorithm. Therefore, Vavak @cite_33 presented a mutation operator, called variable local search (VLS), to address the problem. The strategy that the VLS adopted was to gradually increase the mutation rate. Yen @cite_2 proposed a dynamic EA which relocates the individuals based on their change in function value due to the change in the environment and the average sensitivities of their decision variables to the corresponding change in the objective space. This approach can avoid the drawbacks of previous methods to a certain extent.
@cite_34 @cite_33 @cite_2
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Abstract : Previous studies of Genetic Algorithm (GA) optimization in nonstationary environments focus on discontinuous, Markovian switching environment. This study introduces the problem of GA optimization in continuous, nonstationary environments where the state of the environment is a function of time. The objective of the GA in such an environment is to select a sequence of values over time that minimize, or maximize, the time-average of the environmental evaluations. In this preliminary study, we explore the use of mutation as a control strategy for having the GA increase or maintain the time- average best-of-generation performance. Given this context, the paper presents a set of short experiments using a simple, unimodal function. Each generation, the domain value mapping into the optimum changes so that the movement follows a sinusoidal path. In one of the experiments, we demonstrate the use of a simple adaptive mutation operator. During periods where the time-averaged best performance of the GA worsens, the GA enters hypermutation (a large increase in mutation); otherwise, the GA maintains a low level of mutation. (kr) In this paper we examine a modification to the genetic algorithm — a new adaptive operator was developed for two industrial applications using genetic algorithm based on-line control systems. The aim is to enable the control systems to track optima of a time-varying dynamic system whilst not being detrimental to its ability to provide sound results for the stationary environments. When compared with the hypermutation operator, the new operator matched the level of diversity introduced into the population with the “degree” of the environmental changes better because it increases population diversity only gradually. Although the new technique was developed for the control application domain where real variables are mostly used, a possible generalization of the method is also suggested. It is believed that the technique has the potential to be a further contribution in making genetic algorithm based techniques more readily usable in industrial control applications. Many real-world optimization problems have to be solved under the presence of uncertainties. A significant number of these uncertainty problems falls into the dynamic optimization category in which the fitness function varies through time. For this class of problems, an evolutionary algorithm is expected to perform satisfactorily in spite of different degrees and frequencies of change in the fitness landscape. In addition, the dynamic evolutionary algorithm should warrant an acceptable performance improvement to justify the additional computational cost. Effective reuse of previous evolutionary information is a must as it facilitates a faster convergence after a change has occurred. This paper proposes a new dynamic evolutionary algorithm that uses variable relocation to adapt already converged or currently evolving individuals to the new environmental condition. The proposed algorithm relocates those individuals based on their change in function value due to the change in the environment and the average sensitivities of their decision variables to the corresponding change in the objective space. The relocation occurs during the transient stage of the evolutionary process, and the algorithm reuses as much information as possible from the previous evolutionary history. As a result, the algorithm shows improved adaptation and convergence. The newly adapted population is shown to be fitter to the new environment than the original or most randomly generated population. The algorithm has been tested by several dynamic benchmark problems and has shown competitive results compared to some chosen state-of-the-art dynamic evolutionary approaches.