Shengxiang Yang

Evolutionary dynamic optimization: A survey of the state of the art

Optimization in dynamic environments is a challenging but important task since many real-world optimization problems are changing over time. Evolutionary computation and swarm intelligence are good tools to address optimization problems in dynamic environments due to their inspiration from natural self-organized systems and biological evolution, which have always been subject to changing environments. Evolutionary optimization in dynamic environments, or evolutionary dynamic optimization (EDO), has attracted a lot of research effort during the last 20 years, and has become one of the most active research areas in the field of evolutionary computation. In this paper we carry out an in-depth survey of the state-of-the-art of academic research in the field of EDO and other meta-heuristics in four areas: benchmark problems/generators, performance measures, algorithmic approaches, and theoretical studies. The purpose is to for the first time (i) provide detailed explanations of how current approaches work; (ii) review the strengths and weaknesses of each approach; (iii) discuss the current assumptions and coverage of existing EDO research; and (iv) identify current gaps, challenges and opportunities in EDO.

Experimental study on population-based incremental learning algorithms for dynamic optimization problems

Evolutionary algorithms have been widely used for stationary optimization problems. However, the environments of real world problems are often dynamic. This seriously challenges traditional evolutionary algorithms. In this paper, the application of population-based incremental learning (PBIL) algorithms, a class of evolutionary algorithms, for dynamic problems is investigated. Inspired by the complementarity mechanism in nature a Dual PBIL is proposed, which operates on two probability vectors that are dual to each other with respect to the central point in the genotype space. A diversity maintaining technique of combining the central probability vector into PBIL is also proposed to improve PBIL’s adaptability in dynamic environments. In this paper, a new dynamic problem generator that can create required dynamics from any binary-encoded stationary problem is also formalized. Using this generator, a series of dynamic problems were systematically constructed from several benchmark stationary problems and an experimental study was carried out to compare the performance of several PBIL algorithms and two variants of standard genetic algorithm. Based on the experimental results, we carried out algorithm performance analysis regarding the weakness and strength of studied PBIL algorithms and identified several potential improvements to PBIL for dynamic optimization problems.

Population-Based Incremental Learning With Associative Memory for Dynamic Environments

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.

A Clustering Particle Swarm Optimizer for Locating and Tracking Multiple Optima in Dynamic Environments

In the real world, many optimization problems are dynamic. This requires an optimization algorithm to not only find the global optimal solution under a specific environment but also to track the trajectory of the changing optima over dynamic environments. To address this requirement, this paper investigates a clustering particle swarm optimizer (PSO) for dynamic optimization problems. This algorithm employs a hierarchical clustering method to locate and track multiple peaks. A fast local search method is also introduced to search optimal solutions in a promising subregion found by the clustering method. Experimental study is conducted based on the moving peaks benchmark to test the performance of the clustering PSO in comparison with several state-of-the-art algorithms from the literature. The experimental results show the efficiency of the clustering PSO for locating and tracking multiple optima in dynamic environments in comparison with other particle swarm optimization models based on the multiswarm method.

A Grid-Based Evolutionary Algorithm for Many-Objective Optimization

Balancing convergence and diversity plays a key role in evolutionary multiobjective optimization (EMO). Most current EMO algorithms perform well on problems with two or three objectives, but encounter difficulties in their scalability to many-objective optimization. This paper proposes a grid-based evolutionary algorithm (GrEA) to solve many-objective optimization problems. Our aim is to exploit the potential of the grid-based approach to strengthen the selection pressure toward the optimal direction while maintaining an extensive and uniform distribution among solutions. To this end, two concepts-grid dominance and grid difference-are introduced to determine the mutual relationship of individuals in a grid environment. Three grid-based criteria, i.e., grid ranking, grid crowding distance, and grid coordinate point distance, are incorporated into the fitness of individuals to distinguish them in both the mating and environmental selection processes. Moreover, a fitness adjustment strategy is developed by adaptively punishing individuals based on the neighborhood and grid dominance relations in order to avoid partial overcrowding as well as guide the search toward different directions in the archive. Six state-of-the-art EMO algorithms are selected as the peer algorithms to validate GrEA. A series of extensive experiments is conducted on 52 instances of nine test problems taken from three test suites. The experimental results show the effectiveness and competitiveness of the proposed GrEA in balancing convergence and diversity. The solution set obtained by GrEA can achieve a better coverage of the Pareto front than that obtained by other algorithms on most of the tested problems. Additionally, a parametric study reveals interesting insights of the division parameter in a grid and also indicates useful values for problems with different characteristics.

A Self-Learning Particle Swarm Optimizer for Global Optimization Problems

Particle swarm optimization (PSO) has been shown as an effective tool for solving global optimization problems. So far, most PSO algorithms use a single learning pattern for all particles, which means that all particles in a swarm use the same strategy. This monotonic learning pattern may cause the lack of intelligence for a particular particle, which makes it unable to deal with different complex situations. This paper presents a novel algorithm, called self-learning particle swarm optimizer (SLPSO), for global optimization problems. In SLPSO, each particle has a set of four strategies to cope with different situations in the search space. The cooperation of the four strategies is implemented by an adaptive learning framework at the individual level, which can enable a particle to choose the optimal strategy according to its own local fitness landscape. The experimental study on a set of 45 test functions and two real-world problems show that SLPSO has a superior performance in comparison with several other peer algorithms.

Genetic algorithms with memory-and elitism-based immigrants in dynamic environments

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.

Genetic Algorithms With Immigrants and Memory Schemes for Dynamic Shortest Path Routing Problems in Mobile Ad Hoc Networks

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.

Non-stationary problem optimization using the primal-dual genetic algorithm

Genetic algorithms (GAs) have been widely used for stationary optimization problems where the fitness landscape does not change during the computation. However, the environments of real world problems may change over time, which puts forward serious challenge to traditional GAs. In this paper, we introduce the application of a new variation of GA called the primal-dual genetic algorithm (PDGA) for problem optimization in nonstationary environments. Inspired by the complementarity and dominance mechanisms in nature, PDGA operates on a pair of chromosomes that are primal-dual to each other in the sense of maximum distance in genotype in a given distance space. This paper investigates an important aspect of PDGA, its adaptability to dynamic environments. A set of dynamic problems are generated from a set of stationary benchmark problems using a dynamic problem generating technique proposed in this paper. Experimental study over these dynamic problems suggests that PDGA can solve complex dynamic problems more efficiently than traditional GA and a peer GA, the dual genetic algorithm. The experimental results show that PDGA has strong viability and robustness in dynamic environments.

Memory-based immigrants for genetic algorithms in dynamic environments

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 memory-based immigrants scheme efficiently improves the performance of genetic algorithms in dynamic environments.