Three variants of three Stage Optimal Memetic Exploration for handling non-separable fitness landscapes

The file attached to this record is the authors final peer reviewed version. The publisher's final version can be found by following the DOI link.Three Stage Optimal Memetic Exploration (3SOME) is a recently proposed algorithmic framework which sequentially perturbs a single solution by means of three operators. Although 3SOME proved to be extremely successful at handling high-dimensional multi-modal landscapes, its application to non-separable fitness functions present some flaws. This paper proposes three possible variants of the original 3SOME algorithm aimed at improving its performance on non-separable problems. The first variant replaces one of the 3SOME operators, namely the middle distance exploration, with a rotation-invariant Differential Evolution (DE) mutation scheme, which is applied on three solutions sampled in a progressively shrinking search space. In the second proposed mechanism, a micro-population rotation-invariant DE is integrated within the algorithmic framework. The third approach employs the search logic (1+1)-Covariance Matrix Adaptation Evolution Strategy, aka (1+1)-CMA-ES. In the latter scheme, a Covariance Matrix adapts to the landscape during the optimization in order to determine the most promising search directions. Numerical results show that, at the cost of a higher complexity, the three approaches proposed are able to improve upon 3SOME performance for non-separable problems without an excessive performance deterioration in the other problems

The Importance of Being Structured: a Comparative Study on Multi Stage Memetic Approaches

The file attached to this record is the authors final peer reviewed version. The publisher's final version can be accessed via the DOI link.Memetic Computing (MC) is a discipline which studies optimization algorithms and sees them as structures of operators, the memes. Although the choice of memes is crucial for an effective algorithmic design, special attention should be paid also to the coordination amongst the memes. This paper presents a study on a basic sequential structure, namely Three Stage Optimal Memetic Exploration (3SOME). The 3SOME algorithm is composed of three operators (or memes) which progressively perturbs a single solution. The first meme, long distance exploration is characterized by a long search radius and is supposed to detect promising areas of the decision space. The second meme, middle distance exploration, is characterized by a moderate search radius and is supposed to focus the search in the the most promising basins of attraction. The third meme, short distance exploration, is characterized by a short search radius and had the role of performing the local optimal search in the areas detected by the first two memes. To assess the importance of the structure within MC we compare the performance of 3SOME with two modified versions of it over two complete benchmarks. In both cases, while retaining the 3SOME structure, we replace one of the three original components (short distance exploration) with an alternative deterministic local search, respectively Rosenbrock and Powell methods. Numerical results show that, regardless of the choice of the specific memes, as far as the 3SOME structure contains memes which perform long, middle, and short distance explorations a similar performance is achieved. These results remark that besides the intuitive finding that a proper choice of operators is fundamental for the algorithmic success, the structure composing them also plays a crucial role

Advanced optimization algorithms for applications in control engineering

In the last ten years optimization in industrial applications has obtained an increasing attention. In particular it has been demonstrated useful and effective in the solution of control problems. The implementation of an optimization algorithm on a real-time control platform must cope with the lack of a full power computer, thus it must use a very low amount of memory and computational power. On the other hand the presence of nonlinearities, sensors and approximations injects in the signals of the control loop some noise, resulting in a noisy fitness function to be optimized. In this work both issues are addressed in order to show how a novel algorithmic design can arise from the solution of these implementation problems, often underestimated in the theoretical approach. This thesis proposes a set of novel algorithmic solutions for facing complex real-world problems in control engineering. Two algorithms addressing the optimization in the presence of noise are discussed. In addition, a novel adaptation system inspired by estimation of distribution paradigm is proposed to handle highly multimodal fitness landscapes. A crucially important contribution contained in this thesis is the definition of compact Differential Evolution for optimization problems in presence of limited hardware. Finally an evolution of the latter algorithm in the fashion of Memetic Computing is proposed with reference to an industrial application problem

A Memetic Differential Evolution Approach in Noisy Optimization

This paper proposes amemetic approach for solving complex optimization problems characterized by a noisy fitness function. The proposed approach aims at solving highly multivariate and multi-modal landscapes which are also affected by a pernicious noise. The proposed algorithm employs a Differential Evolution framework and combines within this three additional algorithmic components. A controlled randomization of scale factor and crossover rate are employed which should better handle uncertainties of the problem and generally enhance performance of the Differential Evolution. Two combined local search algorithms applied to the scale factor, during offspring generation, should enhance performance of the Differential Evolution framework in the case of multi-modal and high dimensional problems. An on-line statistical test aims at assuring that only strictly necessary samples are taken and that all pairwise selections are properly performed. The proposed algorithm has been tested on a various set of test problems and its behavior has been studied, dependent on the dimensionality and noise level. A comparative analysis with a standard Differential Evolution, a modern version of Differential Evolution employing randomization of the control parameters and four metaheuristics tailored to optimization in a noisy environment has been carried out. One of these metaheuristics is a classical algorithm for noisy optimization while the other three are modern Differential Evolution based algorithms for noisy optimization which well represent the state-of-theart in the field. Numerical results show that the proposed memetic approach is an efficient and robust alternative for various and complex multivariate noisy problems and can be exported to real-world problems affected by a noise whose distribution can be approximated by a Gaussian distribution

Memetic compact differential evolution for cartesian robot control.

This article deals with optimization problems to be solved in the absence of a full power computer device. The goal is to solve a complex optimization problem by using a control card related to portable devices, e.g. for the control of commercial robots. In order to handle this class of optimization problems, a novel Memetic Computing approach is presented. The proposed algorithm employs a Differential Evolution framework which instead of processing an actual population of candidate solutions, makes use of a statistical representation of the population which evolves over time. In addition, the framework uses a stochastic local search algorithm which attempts to enhance the performance of the elite. In this way, the memetic logic of performing the optimization by observing the decision space from complementary perspectives can be integrated within computational devices characterized by a limited memory. The proposed algorithm, namely Memetic compact Differential Evolution (McDE), has been tested and compared with other algorithms belonging to the same category for a real-world industrial application, i.e. the control system design of a cartesian robot for variable mass movements. For this real-world application, the proposed McDE displays high performance and has proven to considerably outperform other compact algorithms representing the current state-of-the-art in this sub-field of computational intelligence

Composed compact differential evolution

This paper proposes a novel algorithm for solving continuous complex optimization problems with a relatively low memory consumption. The proposed approach, namely Composed compact Differential Evolution, consists of a set of compact Differential Evolution units which simultaneously search the decision space from various perspectives. A randomization in the virtual population allows the algorithm to behave, on one hand, as a multiple local search with a multi-start logic integrated within it. On the other hand, the compact units communicate among each other by means of a ring topology and propagation of information. More specifically, the most promising elite solutions and scale factor values of each compact unit are migrated to the neighbour unit so that the search of the global optimum is performed. In other words, while each single compact unit performs a local search by exploiting the direction suggested by each elite solution, the entire structure combines the achievement of each local search operation towards the direction of the global search. The proposed algorithm is characterized by a limited memory consumption and is memory-wise equivalent to a population-based algorithm with a small population. Numerical results show that the proposed approach outperforms other compact algorithms and various modern population-based structures

Disturbed exploitation compact differential evolution for limited memory optimization problems

This paper proposes a novel and unconventional Memetic Computing approach for solving continuous optimization problems characterized by memory limitations. The proposed algorithm, unlike employing an explorative evolutionary framework and a set of local search algorithms, employs multiple exploitative search within the main framework and performs a multiple step global search by means of a randomized perturbation of the virtual population corresponding to a periodical randomization of the search for the exploitative operators. The proposed Memetic Computing approach is based on a populationless (compact) evolutionary framework which, instead of processing a population of solutions, handles its statistical model. This evolutionary framework is based on a Differential Evolution which cooperatively employs two exploitative search operators: the first is based on a standard Differential Evolution mutation and exponential crossover, and the second is the trigonometric mutation. These two search operators have an exploitative action on the algorithmic framework and thus contribute to the rapid convergence of the virtual population towards promising candidate solutions. The action of these search operators is counterbalanced by a periodical stochastic perturbation of the virtual population, which has the role of ‘‘disturbing’’ the excessively exploitative action of the framework and thus inhibits its premature convergence. The proposed algorithm, namely Disturbed Exploitation compact Differential Evolution, is a simple and memory-wise cheap structure that makes use of the Memetic Computing paradigm in order to solve complex optimization problems. The proposed approach has been tested on a set of various test problems and compared with state-of-the-art compact algorithms and with some modern population based meta-heuristics. Numerical results show that Disturbed Exploitation compact Differential Evolution significantly outperforms all the other compact algorithms present in literature and reaches a competitive performance with respect to modern population algorithms, including some memetic approaches and complex modern Differential Evolution based algorithms. In order to show the potential of the proposed approach in real-world applications, Disturbed Exploitation compact Differential Evolution has been implemented for performing the control of a space robot by simulating the implementation within the robot micro-controller. Numerical results show the superiority of the proposed algorithm with respect to other modern compact algorithms present in literature

Compact Differential Evolution

This paper proposes the compact differential evolution (cDE) algorithm. cDE, like other compact evolutionary algorithms, does not process a population of solutions but its statistic description which evolves similarly to all the evolutionary algorithms. In addition, cDE employs the mutation and crossover typical of differential evolution (DE) thus reproducing its search logic. Unlike other compact evolutionary algorithms, in cDE, the survivor selection scheme of DE can be straightforwardly encoded. One important feature of the proposed cDE algorithm is the capability of efficiently performing an optimization process despite a limited memory requirement. This fact makes the cDE algorithm suitable for hardware contexts characterized by small computational power such as micro-controllers and commercial robots. In addition, due to its nature cDE uses an implicit randomization of the offspring generation which corrects and improves the DE search logic. An extensive numerical setup has been implemented in order to prove the viability of cDE and test its performance with respect to other modern compact evolutionary algorithms and state-of-the-art population-based DE algorithms. Test results show that cDE outperforms on a regular basis its corresponding population-based DE variant. Experiments have been repeated for four different mutation schemes. In addition cDE outperforms other modern compact algorithms and displays a competitive performance with respect to state-of-the-art population-based algorithms employing a DE logic. Finally, the cDE is applied to a challenging experimental case study regarding the on-line training of a nonlinear neuralnetwork-based controller for a precise positioning system subject to changes of payload. The main peculiarity of this control application is that the control software is not implemented into a computer connected to the control system but directly on the micro-controller. Both numerical results on the test functions and experimental results on the real-world problem are very promising and allow us to think that cDE and future developments can be an efficient option for optimization in hardware environments characterized by limited memory