Abstract—In recent years, interest in studying evolutionary algorithms (EAs) for dynamic optimization problems (DOPs) has grown due to its importance in real-world applications. Several approaches, such as the memory and multiple population schemes, have been developed for EAs to address dynamic problems. This paper investigates the application of the memory scheme for population-based incremental learning (PBIL) algorithms, a class of EAs, for DOPs. A PBIL-specific associative memory scheme, which stores best solutions as well as corresponding environmental information in the memory, is investigated to improve its adaptability in dynamic environments. In this paper, the interactions between the memory scheme and random immigrants, multipopulation, and restart schemes for PBILs in dynamic environments are investigated. In order to better test the performance of memory schemes for PBILs and other EAs in dynamic environments, this paper also proposes a dynamic environment generator that can systematically generate dynamic environments of different difficulty with respect to memory schemes. Using this generator, a series of dynamic environments are generated and experiments are carried out to compare the performance of investigated algorithms. The experimental results show that the proposed memory scheme is efficient for PBILs in dynamic environments and also indicate that different interactions exist between the memory scheme and random immigrants, multipopulation schemes for PBILs in different dynamic environments. Index Terms—Associative memory scheme, dynamic optimization problems (DOPs), immune system-based genetic algorithm (ISGA), memory-enhanced genetic algorithm, multipopulation scheme, population-based incremental learning (PBIL), random immigrants.

Investigating and enhancing the performance of genetic algorithms in dynamic environments have attracted a growing interest from the community of genetic algorithms in recent years. This trend reflects the fact that many real world problems are actually dynamic, which poses serious challenge to traditional genetic algorithms. Several approaches have been developed into genetic algorithms for dynamic optimization problems. Among these approches, random immigrants and memory schemes have shown to be beneficial in many dynamic problems. This paper proposes a hybrid memory and random immigrants scheme for genetic algorithms in dynamic environments. In the hybrid scheme, the best solution in memory is retrieved and acts as the base to create random immigrants to replace the worst individuals in the population. In this way, not only can diversity be maintained but it is done more efficiently to adapt the genetic algorithm to the changing environment. The experimental results based on a series of systematically constructed dynamic problems show that the proposed memorybased immigrants scheme efficiently improves the performance of genetic algorithms in dynamic environments.

Abstract. In recent years dynamic optimization problems have attracted a growing interest from the community of genetic algorithms with several approaches developed to address these problems, of which the memory scheme is a major one. In this paper an associative memory scheme is proposed for genetic algorithms to enhance their performance in dynamic environments. In this memory scheme, the environmental information is also stored and associated with current best individual of the population in the memory. When the environment changes the stored environmental information that is associated with the best re-evaluated memory solution is extracted to create new individuals into the population. Based on a series of systematically constructed dynamic test environments, experiments are carried out to validate the proposed associative memory scheme. The environmental results show the efficiency of the associative memory scheme for genetic algorithms in dynamic environments. 1

Abstract. Addressing dynamic optimization problems has been a challenging task for the genetic algorithm community. Over the years, several approaches have been developed into genetic algorithms to enhance their performance in dynamic environments. One major approach is to maintain the diversity of the population, e.g., via random immigrants. This paper proposes an elitism-based immigrants scheme for genetic algorithms in dynamic environments. In the scheme, the elite from previous generation is used as the base to create immigrants via mutation to replace the worst individuals in the current population. This way, the introduced immigrants are more adapted to the changing environment. This paper also proposes a hybrid scheme that combines the elitismbased immigrants scheme with traditional random immigrants scheme to deal with significant changes. The experimental results show that the proposed elitism-based and hybrid immigrants schemes efficiently improve the performance of genetic algorithms in dynamic environments. 1

Abstract In this paper a genetic algorithm is proposed where the worst individual and individuals with indices close to its index are replaced in every generation by randomly generated individuals for dynamic optimization problems. In the proposed genetic algorithm, the replacement of an individual can affect other individuals in a chain reaction. The new individuals are preserved in a subpopulation which is defined by the number of individuals created in the current chain reaction. If the values of fitness are similar, as is the case with small diversity, one single replacement can affect a large number of individuals in the population. This simple approach can take the system to a self-organizing behavior, which can be useful to control the diversity level of the population and hence allows the genetic algorithm to escape from local optima once the problem changes due to the dynamics.

Abstract — In recent years the study of dynamic optimization problems has attracted an increasing interest from the community of genetic algorithms and researchers have developed a variety of approaches into genetic algorithms to solve these problems. In order to compare their performance an important issue is the construction of standardized dynamic test environments. Based on the concept of problem difficulty this paper proposes a new dynamic environment generator using a decomposable trap function. With this generator it is posssible to systematically construct dynamic environments with changing and bounding difficulty and hence we can test different genetic algorithms under dynamic environments with changing but controllable difficulty levels. I.

Abstract. In recent years, there has been an increasing concern from the evolutionary computation community on dynamic optimization problems since many real-world optimization problems are time-varying. In this paper, a triggered memory scheme is introduced into the particle swarm optimization to deal with dynamic environments. The triggered memory scheme enhances traditional memory scheme with a triggered memory generator. Experimental study over a benchmark dynamic problem shows that the triggered memory-based particle swarm optimization algorithm has stronger robustness and adaptability than traditional particle swarm optimization algorithms, both with and without traditional memory scheme, for dynamic optimization problems. 1

Abstract- Several approaches have been developed into evolutionary algorithms to deal with dynamic optimization problems, of which memory and random immigrants are two major schemes. This paper investigates the application of a direct memory scheme for univariate marginal distribution algorithms (UMDAs), a class of evolutionary algorithms, for dynamic optimization problems. The interaction between memory and random immigrants for UMDAs in dynamic environments is also investigated. Experimental study shows that the memory scheme is efficient for UMDAs in dynamic environments and that the interactive effect between memory and random immigrants for UMDAs in dynamic environments depends on the dynamic environments. 1

Abstract: Dynamic optimization problems are a kind of optimization problems that involve changes over time. They pose a serious challenge to traditional optimization methods as well as conventional genetic algorithms since the goal is no longer to search for the optimal solution(s) of a fixed problem but to track the moving optimum over time. Dynamic optimization problems have attracted a growing interest from the genetic algorithm community in recent years. Several approaches have been developed to enhance the performance of genetic algorithms in dynamic environments. One approach is to maintain the diversity of the population via random immigrants. This paper proposes a hybrid immigrants scheme that combines the concepts of elitism, dualism and random immigrants for genetic algorithms to address dynamic optimization problems. In this hybrid scheme, the best individual, i.e., the elite, from the previous generation and its dual individual are retrieved as the bases to create immigrants via traditional mutation scheme. These elitism-based and dualism-based immigrants together with some random immigrants are substituted into the current population, replacing the worst individuals in the population. These three kinds of immigrants aim to address environmental changes of slight, medium and significant degrees respectively and hence efficiently adapt genetic algorithms to dynamic environments that are subject to different severities of changes. Based on a series of systematically constructed dynamic test problems, experiments are carried out to investigate the performance of genetic algorithms with the hybrid immigrants scheme and traditional random immigrants scheme. Experimental results validate the efficiency of the proposed hybrid immigrants scheme for improving the performance of genetic algorithms in dynamic environments. Keywords: Genetic algorithms, random immigrants, elitism-based immigrants, dualism, dynamic optimization problems.

In recent years the genetic algorithm community has shown a growing interest in studying dynamic optimization problems. Several approaches have been devised. The random immigrants and memory schemes are two major ones. The random immigrants scheme addresses dynamic environments by maintaining the population diversity while the memory scheme aims to adapt genetic algorithms quickly to new environments by reusing historical information. This paper investigates a hybrid memory and random immigrants scheme, called memory-based immigrants, and a hybrid elitism and random immigrants scheme, called elitism-based immigrants, for genetic algorithms in dynamic environments. In these schemes, the best individual from memory or the elite from the previous generation is retrieved as the base to create immigrants into the population by mutation. This way, not only can diversity be maintained but it is done more efficiently to adapt genetic algorithms to the current environment. Based on a series of systematically constructed dynamic problems, experiments are carried out to compare genetic algorithms with the memory-based and elitism-based immigrants schemes against genetic algorithms with traditional memory and random immigrants schemes and a hybrid memory and multi-population scheme. The sensitivity analysis regarding some key parameters is also carried out. Experimental results show that the memory-based and elitism-based immigrants schemes efficiently improve the performance of genetic algorithms in dynamic environments.