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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A multi-population based approach is proposed to realize the adapted ensemble of multiple strategies of differential evolution.The control parameters of each mutation strategy are adapted independently.Extensive experiments are conducted to test the performance of multi-population ensemble DE (MPEDE). Differential evolution (DE) is among the most efficient evolutionary algorithms (EAs) for global optimization and now widely applied to solve diverse real-world applications. As the most appropriate configuration of DE to efficiently solve different optimization problems can be significantly different, an appropriate combination of multiple strategies into one DE variant attracts increasing attention recently. In this study, we propose a multi-population based approach to realize an ensemble of multiple strategies, thereby resulting in a new DE variant named multi-population ensemble DE (MPEDE) which simultaneously consists of three mutation strategies, i.e., "current-to-pbest 1" and "current-to-rand 1" and "rand 1". There are three equally sized smaller indicator subpopulations and one much larger reward subpopulation. Each constituent mutation strategy has one indicator subpopulation. After every certain number of generations, the current best performing mutation strategy will be determined according to the ratios between fitness improvements and consumed function evaluations. Then the reward subpopulation will be allocated to the determined best performing mutation strategy dynamically. As a result, better mutation strategies obtain more computational resources in an adaptive manner during the evolution. The control parameters of each mutation strategy are adapted independently as well. Extensive experiments on the suit of CEC 2005 benchmark functions and comprehensive comparisons with several other efficient DE variants show the competitive performance of the proposed MPEDE (Matlab codes of MPEDE are available from http: guohuawunudt.gotoip2.com publications.html). Abstract The purpose of this paper is to present a new and an alternative differential evolution (ADE) algorithm for solving unconstrained global optimization problems. In the new algorithm, a new directed mutation rule is introduced based on the weighted difference vector between the best and the worst individuals of a particular generation. The mutation rule is combined with the basic mutation strategy through a linear decreasing probability rule. This modification is shown to enhance the local search ability of the basic DE and to increase the convergence rate. Two new scaling factors are introduced as uniform random variables to improve the diversity of the population and to bias the search direction. Additionally, a dynamic non-linear increased crossover probability scheme is utilized to balance the global exploration and local exploitation. Furthermore, a random mutation scheme and a modified Breeder Genetic Algorithm (BGA) mutation scheme are merged to avoid stagnation and or premature convergence. Numerical experiments and comparisons on a set of well-known high dimensional benchmark functions indicate that the improved algorithm outperforms and is superior to other existing algorithms in terms of final solution quality, success rate, convergence rate, and robustness. Mutation operators such as Gaussian, Levy and Cauchy have been used with evolutionary programming (EP). According to the no free lunch theorem, it is impossible for EP with a single mutation operator to outperform always. For example, Classical EP (CEP) with Gaussian mutation is better at searching in a local neighborhood while the Fast EP (FEP) with the Cauchy mutation performs better over a larger neighborhood. Motivated by these observations, we propose an ensemble approach where each mutation operator has its associated population and every population benefits from every function call. This approach enables us to benefit from different mutation operators with different parameter values whenever they are effective during different stages of the search process. In addition, the recently proposed Adaptive EP (AEP) using Gaussian (ACEP) and Cauchy (AFEP) mutations is also evaluated. In the AEP, the strategy parameter values are adapted based on the search performance in the previous few generations. The performance of ensemble is compared with a mixed mutation strategy, which integrates several mutation operators into a single algorithm as well as against the AEP with a single mutation operator. Improved performance of the ensemble over the single mutation-based algorithms and mixed mutation algorithm is verified using statistical tests. Mutations are required for adaptation, yet most mutations with phenotypic effects are deleterious. As a consequence, the mutation rate that maximizes adaptation will be some intermediate value. This abstract summarizes a previous publication in which we used Avida, a well-studied artificial life platform, to investigate the ability of natural selection to adjust and optimize mutation rates. Our initial experiments occurred in a previously studied environment with a complex fitness landscape ( Nature, 423, 2003) where Avidians were rewarded for performing any of nine logic tasks. We assessed the optimal mutation rate by empirically determining which unchanging mutation rate produced the highest rate of adaptation. Then, we allowed mutation rates to evolve and we evaluated their proximity to the optimum. Although we chose conditions favorable for mutation rate optimization (asexual organisms not yet adapted to a new environment), the evolved rates were invariably far below the optimum across a wide range of experimental parameter settings (Fig. 1). We hypothesized that the reason mutation rates evolved to be suboptimal was the ruggedness of fitness landscapes. To test this hypothesis, we created a simplified 'counting ones' landscape without any fitness valleys and found that, in such conditions, populations evolved near-optimal mutation rates (Fig. 2, top row). In contrast, once moderate fitness valleys were added to this simple landscape, the ability of evolving populations to find the optimal mutation rate was lost (Fig. 2, bottom two rows). Additional experiments revealed that lowering the rate at which mutation rates evolved did not preclude the evolution of suboptimal mutation rates (see original manuscript). We conclude that rugged fitness landscapes can prevent the evolution of mutation rates that are optimal for long-term adaptation because of the short-term costs of traversing fitness valleys. This finding has important implications for evolutionary research in both biological and computational realms.