Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> Inventors' ideas: <s> This paper discusses the trade-off between accuracy, reliability and computing time in global optimization. Particular compromises provided by traditional methods (Quasi-Newton and Nelder-Mead's simplex methods) and genetic algorithms are addressed and illustrated by a particular application in the field of nonlinear system identification. Subsequently, new hybrid methods are designed, combining principles from genetic algorithms and "hill-climbing" methods in order to find a better compromise to the trade-off. Inspired by biology and especially by the manner in which living beings adapt themselves to their environment, these hybrid methods involve two interwoven levels of optimization, namely evolution (genetic algorithms) and individual learning (Quasi-Newton), which cooperate in a global process of optimization. One of these hybrid methods appears to join the group of state-of-the-art global optimization methods: it combines the reliability properties of the genetic algorithms with the accuracy of Quasi-Newton method, while requiring a computation time only slightly higher than the latter. <s> BIB001 </s> Hybridizing Differential Evolution and Particle Swarm Optimization to Design Powerful Optimizers: A Review and Taxonomy <s> Inventors' ideas: <s> We propose a hybrid algorithm for finding a set of nondominated solutions of a multi objective optimization problem. In the proposed algorithm, a local search procedure is applied to each solution (i.e., each individual) generated by genetic operations. Our algorithm uses a weighted sum of multiple objectives as a fitness function. The fitness function is utilized when a pair of parent solutions are selected for generating a new solution by crossover and mutation operations. A local search procedure is applied to the new solution to maximize its fitness value. One characteristic feature of our algorithm is to randomly specify weight values whenever a pair of parent solutions are selected. That is, each selection (i.e., the selection of two parent solutions) is performed by a different weight vector. Another characteristic feature of our algorithm is not to examine all neighborhood solutions of a current solution in the local search procedure. Only a small number of neighborhood solutions are examined to prevent the local search procedure from spending almost all available computation time in our algorithm. High performance of our algorithm is demonstrated by applying it to multi objective flowshop scheduling problems. <s> BIB002
The GA provides QN with starting points, and the fitness of any GA individual will be evaluated by that of its corresponding enhanced individual that is generated by QN. However, the GA will operate on the original individuals rather than the improved ones. The hybridization strategy is termed Inventors' ideas: The GA operates on the enhanced individuals that are improved by QN and provides QN with initial points. As opposed to GQD, the improvement of individuals in GQL is inherited into the chromosomes in the GA. The hybridization strategy is termed as Lamarckian learning in the research of MAs. Both GQD and GQL are expected to combine the advantage of the GA in exploration with that of QN in exploitation. 3) MOGLS (Multi-Objective Genetic Local Search) Proposed by Ishibuchi and Murata BIB002  A truncated LS is employed with the goal to alleviate the great burden of computation-intensive local exploitation and to achieve a better tradeoff between exploration and exploitation (Tr:Er&Ei). The LS is implemented by a shift mutation to solve the multiobjective flowshop scheduling problem. Except for some special techniques to handle multiple objectives (e.g., a random weighting technique) and the truncated LS, the MOGLS shares the same idea with the GQL that is proposed by Renders and Flasse BIB001 . In fact, both of them belong to the family of MAs. Inventors' ideas: Chaotic dynamics is incorporated into a PSO with adaptive inertia weight to enrich the searching behavior and avoid being trapped into local optimum. The global best particle in PSO is further improved and updated by CS. Note that the chaotic search is de facto an explorative TSM as it does not exploit local information. Liu et al. also employed a gbest-centered space contraction strategy to accelerate the exploration. Besides, in each generation, only a group of elite solutions will enter the new generation with the other solutions Inventors' ideas: The two MAs are de facto two frameworks to hybridize multiple LS methods (memes) with the GA in a meta-Lamarckian manner, which is primarily related to the topic of how to choose LSs according to their online performance. The core of MA-S1 is a subproblem decomposition strategy, which uses a distance metric to define the neighborhood of any individual. The LS for a given individual will be chosen from those employed by its neighbors according to their performance. In contrast, MA-S2 employs a biased roulette wheel scheme to bias the choice of LSs by accumulated knowledge on the performance of each LS candidate.  The GA provides SA with a set of initial solutions at each scheduled temperature. SA performs a Metropolis sampling for each solution until a predefined equilibrium condition is reached. The GA uses the solutions that are found by the SA to continue its parallel evolution. In fact, the SA here plays the role of an IM, carrying out a neighborhood search, though it has excellent exploration capability. Another well-known hybrid of the GA and SA was proposed by Mahfoud and Goldberg  . In this GASA, a temperatureregulated selection that originates from SA operates on parent and offspring solutions in the GA to choose the solutions for the next generation. Therefore, the SA in essence is embedded as a selection mechanism into the GA. Accordingly, this GASA can be categorized into E,P,N,D . 7) Simplex-GA Proposed by Yen et al.  : GA⊕CPS (  The hybrid implies a hierarchical fitnessranking-based division of the whole population. The GA evolves the whole population, and meanwhile, CPS operates on a group of top-ranking solutions. Besides, a part of the best solutions in the CPS subpopulation directly enter the next generation. The CPS is an exploitative optimizer that is expected to search the local space around some high-quality solutions. Inventors' ideas: DE/EDA combines global information that is extracted by the EDA with differential information that is obtained by DE to create promising solutions and explore the search space more effectively. In the DE/EDA offspringgeneration scheme, one part of a new solution is generated in the DE way, while the other part is sampled from a probability model based on elite solutions. In such a way, both global information and local information are used to guide the further search.