Table 5 - uploaded by Saúl Domínguez-Isidro
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Fesibility Rate (FR) and Success Performance (SP) for C01 to C09 test problems at 10D and 30D. Boldface remarks those best values.
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Citations
... In order to test the five ε control mechanisms, this work proposes a Multimeme Differential Evolution, MDE for short, which incorporates three optimizers as local search operators: 1) Hooke-Jeeves (HJ), 2) Hill Climber (HC), and 3) Nelder-Mead (NM). For details of the operation of the three local optimizers, the reader is referred to [23]. The optimizers are selected randomly, such as in [9] through an user-defined parameter named local search activation frequency f req, see Fig. 1. ...
Memetic approaches are composed of three general processes, a global optimizer, a set of local-search operators, and a coordination mechanism; which are defined depending on the problem to be optimized. For constrained optimization problems (COPs), memetic algorithms require the incorporation of a constraint handler that guides the search to the feasible regions of the search space. In this regard, the epsilon-constrained method has demonstrated to operate correctly in memetic approaches by transforming a COP into an unconstrained problem during a certain period of the search process. This constraint handler uses a tolerance level that promotes the exploration, mainly in COPs where there are disjoint feasible regions or equality constraints. Nevertheless, epsilon-constrained depends on a set of parameters that determine its behavior, so five variants have emerged in the control of its tolerance, (1) static, (2) dynamic, (3) truncated, (4) threshold, and (5) adaptive. This study focuses on determining the most appropriate control technique in a memetic approach and its relation to the performance and final results of the algorithm. For the study, a memetic differential evolution (MDE) is implemented, whose coordination mechanism controls the activation of three local search methods. Each epsilon-level control mechanism is incorporated separately within the MDE and is tested in eighteen well-known test problems. The results suggest that there is a benefit through the use of adaptive/dynamic mechanisms while reducing the budget for fitness evaluations. Likewise, its advantage is exhibited in functions with non-separable equality constraints. Finally, results determine that there is no benefit relationship between how to control the epsilon-level and the performance of the local optimizers used in this study.
... Every LSO uses a maximum allowable fitness evaluation budget for each application. All three methods have been shown to have a competitive performance in constrained problems [19,145]. Whereas HJ, through its exploratory and pattern movements, obtains search directions approaching the gradient subspace, HC provides randomness in its exploration process, and NM can generate contraction and expansion movements in the search space through the initial simplex. ...
... Update β hj using Equation 6.1 34: end if 35: if β nm < rand(0, 1) then 36: Randomly select r ∈ [1, (P max * 0. parameter for LSO coordinations which were obtained by analyzing each LSO performance for a set of test functions inspired in [145]: ...
The object of study of this dissertation is Memetic Differential Evolution Algorithms (MDEs) for constrained numerical optimization problems (CNOPs). MDEs are one of the most used approaches to improve the performance of the standard differential evolution (DE) for the solution of numerical optimization problems, which are present in real-world applications, often in engineering problems. As it is well known, memetic approaches are characterized by the inclusion of search operators within the cycle of an evolutionary algorithm, improving the search process on a broader range of problems, due to the synergy between the global and local search operator. However, the coordination among the algorithmic components is an issue in the design part of a memetic algorithm, since the excessive use of the local search operator could affect the efficiency of the algorithm. Therefore, three main studies of the effects of local search operators in MDE schemes are carried out. The first study analyzes the relationship between the performance of the local search operator within an MDE and its final results in CNOPs by adopting an improvement index measure, which indicates the rate of fitness improvement made by the local search operator. The second study analyzes the influence of the depth of direct local search methods within MDE when solving CNOPs. Finally, the third study analyzes the Baldwin effect and Lamarckian learning on an MDE that solves CNOPs. Derived from the assessments mentioned above, we propose a coordination mechanism of multiple local search operators for a multimeme scheme based on Differential Evolution (MmDE) that solves CNOPs. The proposed approach associates a pool of direct local search operators within the standard Differential Evolution. The coordination mechanism consists of a probabilistic method based on a cost-benefit scheme, and it is aimed to regulate the activation probability of every local search operator during the evolutionary cycle of the global search. For all implementations, the epsilon-constrained method is used as constraint-handling technique. All experiments are tested on thirty-six well-known benchmark problems.
Cooperative Co-evolutionary algorithms are very popular to solve large-scale problems. A significant part of these algorithms is the decomposition of the problems according to the variables interaction. In this paper, an approach based on a memetic scheme, where its local stage (and not the global stage) is guided by the decomposition method (Local Cooperative Search LoCoS), is presented to solve large-scale constrained optimization problems. Two decomposition methods are tested: the improved version of the Variable Interdependence Identification for Constrained problems and Differential Grouping version 2. A recently-proposed benchmark with eighteen test problems with different features is solved to assess the performance of LoCoS when compared against a similar memetic algorithm but without decomposition and also against a state-of-the-art cooperative co-evolutionary algorithm. The results show a faster convergence, better final results and higher feasibility ratio by LoCosS with respect to the values provided by the compared algorithms.
This chapter reviews applications of Memetic Algorithms in the areas of business analytics and data science. This approach originates from the need to address optimization problems that involve combinatorial search processes. Some of these problems were from the area of operations research, management science, artificial intelligence and machine learning. The methodology has developed considerably since its beginnings and now is being applied to a large number of problem domains. This work gives a historical timeline of events to explain the current developments and, as a survey, gives emphasis to the large number of applications in business and consumer analytics that were published between January 2014 and May 2018.
