29,538 research outputs found
High-dimensional Black-box Optimization via Divide and Approximate Conquer
Divide and Conquer (DC) is conceptually well suited to high-dimensional
optimization by decomposing a problem into multiple small-scale sub-problems.
However, appealing performance can be seldom observed when the sub-problems are
interdependent. This paper suggests that the major difficulty of tackling
interdependent sub-problems lies in the precise evaluation of a partial
solution (to a sub-problem), which can be overwhelmingly costly and thus makes
sub-problems non-trivial to conquer. Thus, we propose an approximation
approach, named Divide and Approximate Conquer (DAC), which reduces the cost of
partial solution evaluation from exponential time to polynomial time.
Meanwhile, the convergence to the global optimum (of the original problem) is
still guaranteed. The effectiveness of DAC is demonstrated empirically on two
sets of non-separable high-dimensional problems.Comment: 7 pages, 2 figures, conferenc
Algorithms Applied to Global Optimisation – Visual Evaluation
Evaluation and assessment of various search and optimisation algorithms is subject of large research efforts. Particular interest of this study is global optimisation and presented approach is based on observation and visual evaluation of Real-Coded Genetic Algorithm, Particle Swarm Optimisation, Differential Evolution and Free Search, which are briefly described and used for experiments. 3D graphical views, generated by visualisation tool VOTASA, illustrate essential aspects of global search process such as divergence, convergence, dependence on initialisation and utilisation of accidental events. Discussion on potential benefits of visual analysis, supported with numerical results, which could be used for comparative assessment of other methods and directions for further research conclude presented study
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Incremental evolution strategy for function optimization
This paper presents a novel evolutionary approach for function optimization Incremental Evolution Strategy (IES). Two strategies are proposed. One is to evolve the input variables incrementally. The whole evolution consists of several phases and one more variable is focused in each phase. The number of phases is equal to the number of variables in maximum. Each phase is composed of two stages: in the single-variable evolution (SVE) stage, evolution is taken on one independent variable in a series of cutting planes; in the multi-variable evolving (MVE) stage, the initial population is formed by integrating the populations obtained by the SVE and the MVE in the last phase. And the evolution is taken on the incremented variable set. The other strategy is a hybrid of particle swarm optimization (PSO) and evolution strategy (ES). PSO is applied to adjust the cutting planes/hyper-planes (in SVEs/MVEs) while (1+1)-ES is applied to searching optima in the cutting planes/hyper-planes. The results of experiments show that the performance of IES is generally better than that of three other evolutionary algorithms, improved normal GA, PSO and SADE_CERAF, in the sense that IES finds solutions closer to the true optima and with more optimal objective values
State Transition Algorithm
In terms of the concepts of state and state transition, a new heuristic
random search algorithm named state transition algorithm is proposed. For
continuous function optimization problems, four special transformation
operators called rotation, translation, expansion and axesion are designed.
Adjusting measures of the transformations are mainly studied to keep the
balance of exploration and exploitation. Convergence analysis is also discussed
about the algorithm based on random search theory. In the meanwhile, to
strengthen the search ability in high dimensional space, communication strategy
is introduced into the basic algorithm and intermittent exchange is presented
to prevent premature convergence. Finally, experiments are carried out for the
algorithms. With 10 common benchmark unconstrained continuous functions used to
test the performance, the results show that state transition algorithms are
promising algorithms due to their good global search capability and convergence
property when compared with some popular algorithms.Comment: 18 pages, 28 figure
Adaptive multimodal continuous ant colony optimization
Seeking multiple optima simultaneously, which multimodal optimization aims at, has attracted increasing attention but remains challenging. Taking advantage of ant colony optimization algorithms in preserving high diversity, this paper intends to extend ant colony optimization algorithms to deal with multimodal optimization. First, combined with current niching methods, an adaptive multimodal continuous ant colony optimization algorithm is introduced. In this algorithm, an adaptive parameter adjustment is developed, which takes the difference among niches into consideration. Second, to accelerate convergence, a differential evolution mutation operator is alternatively utilized to build base vectors for ants to construct new solutions. Then, to enhance the exploitation, a local search scheme based on Gaussian distribution is self-adaptively performed around the seeds of niches. Together, the proposed algorithm affords a good balance between exploration and exploitation. Extensive experiments on 20 widely used benchmark multimodal functions are conducted to investigate the influence of each algorithmic component and results are compared with several state-of-the-art multimodal algorithms and winners of competitions on multimodal optimization. These comparisons demonstrate the competitive efficiency and effectiveness of the proposed algorithm, especially in dealing with complex problems with high numbers of local optima
Adaptive intelligence applied to numerical optimisation
The article presents modification strategies theoretical comparison and experimental results achieved by adaptive heuristics applied to numerical optimisation of several non-constraint test functions. The aims of the study are to identify and compare how adaptive search heuristics behave within heterogeneous search space without retuning of the search parameters. The achieved results are summarised and analysed, which could be used for comparison to other methods and further investigation
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