Surrogate-Based Reduced-Dimension Global Optimization in Process Systems Engineering

A velocity-based butterfly optimization algorithm for high-dimensional optimization and feature selection

Memetic algorithms are effective algorithms to obtain reliable and accurate solutions for complex continuous optimization problems. Nowadays, high dimensional optimization problems are an interesting field of research. The high dimensionality introduces new problems for the optimization process, requiring more scalable algorithms that, at the same time, could explore better the higher domain space around each solution. In this work, we proposed a memetic algorithm, MA-SW-Chains, for large scale global optimization. This algorithm assigns to each individual a local search intensity that depends on its features, by chaining different local search applications. MA-SW-Chains is an adaptation to large scale optimization of a previous algorithm, MA-CMA-Chains, to improve its performance on high-dimensional problems. Finally, we present the results obtained by our proposal using the benchmark problems defined in the Special Session of Large Scale Global Optimization on the IEEE Congress on Evolutionary Computation in 2010.

Particle Swarm Optimization (PSO) is an evolution-nary computation technique. Separate adjustment to inertia weight and learning factors in PSO undermines the integrity and intelligent characteristic in the evolutionary process of particle swarm to some extent, thus it is not suitable for solving most complicated optimization problems. On the basis of previous researches, the aim of this study was to improve the computational efficiency of PSO and avoid premature convergence for multimodal, higher dimensional complicated optimization problems by considering the mutual influences of inertia weight and learning factors on the updates of particle's veloci-ties. A great number of experiment data provided evidence that the nonlinear adjustment to inertia weight, cognitive learning factor and social learning factor within a certain interval is a good selection. Moreover, the simulation results on four typical functions show that the improved strategy of PSO proposed in the paper is available for solving multimodal and higher dimensional complicated optimization problems, and can accelerate convergence speed, improve optimization quality effectively in comparison to the algorithms of standard PSO and existing relevant improved PSO.

Different kinds of sequential optimization strategies have been developed and employed for the design optimization of electromagnetic devices and systems in recent years, such as electrical machines and superconducting magnetic energy storage system. Besides the traditional low dimensional and single objective problems, they can be employed for high dimensional and multiobjective design optimization problems. Meanwhile, they can significantly reduce the computation cost of finite element analysis and improve the optimization efficiency. This paper aims to present a state of art of sequential optimization strategies for single and multi-objective electromagnetic optimization problems. Furthermore, a fast sequential sampling method is presented based on the framework of sequential optimization. Future work about sequential optimization and related research topics will be proposed as well.

Memetic algorithms arise as very effective algorithms to obtain reliable and high accurate solutions for complex continuous optimization problems. Nowadays, high dimensional optimization problems are an interesting field of research. The high dimensionality introduces new problems for the optimization process, making recommendable to test the behavior of the optimization algorithms to large-scale problems. The local search method must be applied with a higher intensity, specially to most promising solutions, to explore the higher domain space around each solution. In this work, we present a preliminar study of a memetic algorithm that assigns to each individual a local search intensity that depends on its features, by chaining different local search applications. This algorithm have obtained good results in continuous optimization and we study whether is a good algorithm for large scale optimizations problems. We make experiments of our proposal using the benchmark problems defined in the Special Session or Competition on Large Scale Global Optimisation, on the IEEE Congress on Evolutionary Computation in 2008. First, we test different local search methods to identify the best one. Then, we compare the proposed algorithm with the algorithms used into the competition, obtaining that our proposal is a very promising algorithm for this type of high-dimensional problems: with dimension 500 our proposal is the second best of the compared algorithms, and the best memetic algorithm.

Immune optimization algorithm for constrained nonlinear multiobjective optimization problems

A new filled function method for global optimization

Improved sequential optimization method (SOM) and dimension reduction optimization method (DROM) are presented for high dimensional optimization design problems of electromagnetic devices. Improved SOM can simultaneously optimize the statistical approximate models and optimization algorithms more efficiently compared with SOM. Using DROM, a high dimensional problem can be converted into a low dimensional problem with expert experience or some design of experiment techniques. Then two TEAM benchmark problems (Problem 22 and Problem 25) are investigated to illustrate the efficiency of the proposed methods. From the experimental results, we can see that the presented methods can obviously reduce the computational cost of finite element analysis, while the optimal results also satisfy design specification.

JADE is an state-of-the-art adaptive differential evolution algorithm which implements “DE/current-to-pbest” as its mutation strategy, adapts its mutation factor and crossover rate, and uses an optional external archive to keep track of potential removed individuals in previous generations. This paper proposes MPADE, which extends JADE by using a multi-populated approach to solve high dimensional real-parameter optimization problems. This mechanism helps preventing the two well-known problems affecting the differential evolution algorithm performance, which are premature convergence and stagnation. The algorithm was tested using the benchmark functions in IEEE Congress on Evolutionary Computation 2014 test suite. MPADE was compared using Wilcoxon test to JADE algorithm and with other state-of-the-art algorithms that either use a multi-population approach or adapt their parameters. The experimental results show that the proposed new algorithm improves significantly its precursor and it is also suggested that other state-of-the-art algorithms could benefit from the multi-populated based approach.

Aiming at the premature convergence problem of particle swarm optimization algorithm, a new particle swarm Optimization algorithm with dynamic adaptive inertia weigh was presented to solve the typical multi-peak, high dimensional function optimization problems. The dynamic adaptive strategy was introduced in this new algorithm and the change of inertia weight was formulated as an adjust function of this factor according to its impact on the search performance of the swarm. In each iteration process, the inertia weight was timely changed based on the current the swarm diversity and congregate degree, which provides the algorithm with effective dynamic adaptability. The experiments show that the proposed strategy is effectiveness.

The main objective of this paper is to solve the inverse convection heat transfer problems with particle swarm optimization method. An enhanced particle swarm optimization (EPSO) algorithm is proposed to overcome the shortcoming of earlier convergence of standard PSO algorithms. The performance of EPSO is tested by some benchmark functions; it is shown that EPSO has a strong antilocal trap capability especially for high dimensional multimodal optimization problems. At last, EPSO is used to identify the unknown boundary heat flux in a channel flow. According to the computational results of four test problems, it is clear that the proposed EPSO algorithm is able to estimate the unknown heat flux accurately even when the input data contain measurement error.

This paper presents the application of mixed-integer programming (MIP) approach for solving the hydro-thermal self scheduling (HTSS) problem of generating units. In the deregulated environment, the generation companies schedule their generators to maximize their profit while satisfying loads is not an obligation. The HTSS is a high dimensional mixed-integer optimization problem. Therefore, in the large-scale power systems, solving the HTSS is very difficult. In this paper, MIP formulation is adopted for precise modeling of dynamic ramp rate limits, prohibited operating zones, operating services, valve loading effects, variable fuel cost, non-linear start-up cost functions of thermal units, fuel and emission limits of thermal units, multi head power-discharge characteristics of hydro plants and spillage of reservoir. The modified IEEE 118-bus system is used to demonstrate the performance of the proposed method.

Current training methods for deep neural networks boil down to very high dimensional and non-convex optimization problems which are usually solved by a wide range of stochastic gradient descent methods. While these approaches tend to work in practice, there are still many gaps in the theoretical understanding of key aspects like convergence and generalization guarantees, which are induced by the properties of the optimization surface (loss landscape). In order to gain deeper insights, a number of recent publications proposed methods to visualize and analyze the otimization surfaces. However, the computational cost of these methods are very high, making it hardly possible to use them on larger networks. In this paper, we present the GradVis Toolbox, an open source library for efficient and scalable visualization and analysis of deep neural network loss landscapes in Tesorflow and PyTorch. Introducing more efficient mathematical formulations and a novel parallelization scheme, GradVis allows to plot 2d and 3d projections of optimization surfaces and trajectories, as well as high resolution second order gradient information for large networks.

In order to overcome the basic glowworm swarm optimization (GSO) algorithm in the high dimension space function optimization effect is poor defects. This paper, we introduce the idea of the traditional complex method, with the complex method the worst part of the glowworm guidance for reflection be good glowworm swarm, so as to continuously make the worst glowworm swarm become the better glowworm swarm. Finally, an improved artificial glowworm algorithm solves high dimension space of function optimization effect improvement. And through the and basic glowworm swarm algorithm, artificial fish algorithm (AFSA) and particle swarm optimization (PSO) to eight test function optimization results are compared. The show that the efficiency of the method.

Teaching-learning-based optimization algorithm (TLA) is a recently developed heuristic algorithm based on the natural phenomenon of teaching-learning process. Aiming at the shortage of easily fall into local optimum when solving high dimensional complex optimization problems, in this paper, an improved teaching-learning-based optimization algorithm is proposed for economic load dispatch problems (ELD). The sub-population with reverse-learning strategy, the adaptive teaching factor and the differential evolution based Student phase were adopted to improve the basic TLA. Two test systems with thirteen and forty units are used to illustrate the effectiveness and accuracy of the proposed method. The results show that the proposed algorithm is a challenging method for ELD and is validated by comparing with the basic TLA.