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.

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.

Abstract — Addressing dynamic optimization problems (DOPs) has been a challenging task for the genetic algorithm (GA) community. One approach is to maintain the diversity of the population via introducing immigrants. This paper intensively examines several design decisions when employing immigrants schemes, and from these observations an environmental information-based immigrants scheme is derived for GAs to deal with DOPs. In the scheme, the environmental information (e.g., the allele distribution over the population in this paper) from previous generation is used to create immigrants to replace the worst individuals in the current population. In this way, the introduced immigrants are more adapted to the changing environment. A hybrid scheme combining immigrants based on current environmental information and its complementation is also proposed in this paper to address different degrees of changes. Experimental results validate the efficacy of the proposed environmental information-based and hybrid environmental information-based immigrants schemes. I.

Abstract. This paper proposes a memory scheme based on abstraction for evolutionary algorithms to address dynamic optimization problems. In this memory scheme, the memory does not store good solutions as themselves but as their abstraction, i.e., their approximate location in the search space. When the environment changes, the stored abstraction information is extracted to generate new individuals into the population. Experiments are carried out to validate the abstraction based memory scheme. The results show the efficiency of the abstraction based memory scheme for evolutionary algorithms in dynamic environments. 1

Abstract Dynamic optimization problems challenge traditional evolutionary algorithms seriously since they, once converged, cannot adapt quickly to environmental changes. This paper investigates the application of memetic algorithms, a class of hybrid evolutionary algorithms, for dynamic optimization problems. An adaptive hill climbingmethodisproposedasthe localsearchtechnique in the framework of memetic algorithms, which combinesthefeaturesofgreedycrossover-basedhillclimbing and steepest mutation-based hill climbing. In order to address the convergence problem, two diversity maintaining methods, called adaptive dual mapping and triggered random immigrants respectively, are also introduced into the proposed memetic algorithm for dynamic optimization problems. Based on a series of dynamic problems generated from several stationary benchmark problems, experiments are carried out to investigate the performance of the proposed memetic algorithm in comparisonwith some peer evolutionaryalgorithms.The experimental results show the efficiency of the proposed memetic algorithm in dynamic environments. Keywords Geneticalgorithm,memeticalgorithm,local search,crossover-basedhill climbing, mutation-based hill climbing, dual mapping, triggered random immigrants, dynamic optimization problems 1

Abstract — Using diploidy and dominance is one method to enhance the performance of genetic algorithms in dynamic environments. For diploidy genetic algorithms, there are two key design factors: the cardinality of genotypic alleles and the uncertainty in the dominance scheme. This paper investigates the effect of these two factors on the performance of diploidy genetic algorithms in dynamic environments. A generalized diploidy and dominance scheme is proposed for diploidy genetic algorithms, where the cardinality of genotypic alleles and/or the uncertainty in the dominance scheme can be easily tuned and studied. The experimental results show the efficiency of increasing genotypic cardinality rather than introducing uncertainty in the dominance scheme. I.

Abstract—In recent years, the static shortest path (SP) problem has been well addressed using intelligent optimization techniques, e.g., artificial neural networks, genetic algorithms (GAs), particle swarm optimization, etc. However, with the advancement in wireless communications, more and more mobile wireless networks appear, e.g., mobile networks [mobile ad hoc networks (MANETs)], wireless sensor networks, etc. One of the most important characteristics in mobile wireless networks is the topology dynamics, i.e., the network topology changes over time due to energy conservation or node mobility. Therefore, the SP routing problem in MANETs turns out to be a dynamic optimization problem. In this paper, we propose to use GAs with immigrants and memory schemes to solve the dynamic SP routing problem in MANETs. We consider MANETs as target systems because they represent new-generation wireless networks. The experimental results show that these immigrants and memory-based GAs can quickly adapt to environmental changes (i.e., the network topology changes) and produce high-quality solutions after each change. Index Terms—Dynamic optimization problem (DOP), dynamic shortest path routing problem (DSPRP), genetic algorithm (GA), immigrants scheme, memory scheme, mobile ad hoc network (MANET). I.

Abstract Recently, there has been an increasing concern from the evolutionary computation community on dynamic optimization problems since many real-world optimization problems are dynamic. This paper investigates a particle swarm optimization (PSO) based memetic algorithm that hybridizes PSO with a local search technique for dynamic environments. Within the framework of the proposed algorithm, a local version of PSO with a ring-shape topology structure is used as the global search operator and a fuzzy cognition local search method is proposed as the local search technique. In addition, a self-organized random immigrants scheme is extended into our proposed algorithm in order to further enhance its exploration capacity for new peaks in the search space. Experimental study over the moving peaks benchmark problem shows that the proposed PSO-based memetic algorithm is robust and adaptable in dynamic environments. 1

In recent years, the static shortest path (SP) problem has been well addressed using intelligent optimization techniques, e.g., artificial neural networks, genetic algorithms (GAs), particle swarm optimization, etc. However, with the advancement in wireless communications, more and more mobile wireless networks appear, e.g., mobile networks [mobile ad hoc networks (MANETs)], wireless sensor networks, etc. One of the most important characteristics in mobile wireless networks is the topology dynamics, i.e., the network topology changes over time due to energy conservation or node mobility. Therefore, the SP routing problem in MANETs turns out to be a dynamic optimization problem. In this paper, we propose to use GAs with immigrants and memory schemes to solve the dynamic SP routing problem in MANETs. We consider MANETs as target systems because they represent new-generation wireless networks. The experimental results show that these immigrants and memory-based GAs can quickly adapt to environmental changes (i.e., the network topology changes) and produce high-quality solutions after each change.

Abstract — Using diploid representation with dominance scheme is one of the approaches developed for genetic algorithms to address dynamic optimization problems. This paper proposes an adaptive dominance mechanism for diploid genetic algorithms in dynamic environments. In this scheme, the genotype to phenotype mapping in each gene locus is controlled by a dominance probability, which is learnt adaptively during the searching progress. The proposed dominance scheme is experimentally compared to two other schemes for diploid genetic algorithms. Experimental results validate the efficiency of the dominance learning scheme. I.