Several common general purpose optimization algorithms are compared for finding A-and D-optimal designs for different types of statistical models of varying complexity, including high dimensional models with five and more factors. The algorithms of interest include exact methods, such as the interior point method, the Nelder-Mead method, the active set method, the sequential quadratic programming, and metaheuristic algorithms, such as particle swarm optimization, simulated annealing and genetic algorithms. Several simulations are performed, which provide general recommendations on the utility and performance of each method, including hybridized versions of metaheuristic algorithms for finding optimal experimental designs. A key result is that general-purpose optimization algorithms, both exact methods and metaheuristic algorithms, perform well for finding optimal approximate experimental designs.

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The density-peak clustering algorithm, which we refer to as DPC, is a novel and efficient density-based clustering approach. The method has the advantage of allowing non-convex clusters, and clusters of variable size and density, to be grouped together, but it also has some limitations, such as the visual location of centers and the parameter tuning. This paper describes an optimization-based methodology for automatic parameter/center selection applicable both to the DPC and to other algorithms derived from it. The objective function is an internal/external cluster validity index, and the decisions are the parameterization of the algorithm and the choice of centers. The internal validation measures lead to an automatic parameter-tuning process, and the external validation measures lead to the so-called optimal rules, which are a tool to bound the performance of a given algorithm from above on the set of parameterizations. A numerical experiment with real data was performed for the DPC and for the fuzzy weighted k-nearest neighbor (FKNN-DPC) which validates the automatic parameter-tuning methodology and demonstrates its efficiency compared to the state of the art.

Most parallel surrogate-based optimization algorithms focus only on the mechanisms for generating multiple updating points in each cycle, and rather less attention has been paid to producing them through the cooperation of several algorithms. For this purpose, a surrogate-based cooperative optimization framework is here proposed. Firstly, a class of parallel surrogate-based optimization algorithms is developed, based on the idea of viewing the infill sampling criterion as a bi-objective optimization problem. Each algorithm of this class is called a Sequential Multipoint Infill Sampling Algorithm (SMISA) and is the combination resulting from choosing a surrogate model, an exploitation measure, an exploration measure and a multiobjective optimization approach to its solution. SMISAs are the basic algorithms on which collaboration mechanisms are established. Many SMISAs can be defined, and the focus has been on scalar approaches for bi-objective problems such as the -constrained method, revisiting the Parallel Constrained Optimization using Response Surfaces (CORS-RBF) method and the Efficient Global Optimization with Pseudo Expected Improvement (EGO-PEI) algorithm as instances of SMISAs. In addition, a parallel version of the Lower Confidence Bound-based (LCB) algorithm is given as a member within the SMISA class. Secondly, we propose a cooperative optimization framework between the SMISAs. The cooperation between SMISAs occurs in two ways: (1) they share solutions and their objective function values to update their surrogate models and (2) they use the sampled points obtained from different SMI-SAs to guide their own search process. Some convergence results for this cooperative framework are given under weak conditions. A numerical comparison between EGO-PEI, Parallel CORS-RBF and a cooperative method using both, named CPEI, shows that CPEI improves the performance of the baseline algorithms. The numerical results were derived from 17 analytic tests and they show the reduction of wallclock time with respect to the increase in the number of processors.

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