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The gradient descent is one of the most common methods to modify the gradient parameters of the neural network, however, it may fall into the local optimum in the training process. As we all know, genetic algorithm can find the global optimal solution through global search, but it may not be efficient, always takes a lot of running time. These two methods are complementary in the running time and the cost, which inspired us to consider the combination of gradient descent and genetic algorithm. In this paper, a multi-start combinatorial optimization method based on the genetic algorithm and the gradient descent is proposed. First, the initial point is selected through the genetic algorithm. Then the combination of multi-start and gradient descent is used, which can quickly achieve the global search and improve the performance with relatively less running time and cost. Compared with the traditional genetic algorithm and gradient descent method, this proposed algorithm has a better performance in computing the global optimum efficiently.

George Leitmann's direct method permits to find the global minimum of a variational problem by use of a change of variables. In this article, we extend this method to a class of scalar, inequality constrained problems. An application example is given.

Boosting, one of the best off-the-shelf classification methods, has evoked widespread interest in machine learning and statistics. However, the original algorithm was developed for binary classification problems. In this paper, we study multi-class boosting algorithms under the ${\ell }_2$-loss framework, and devise two multi-class ${\ell }_2$-Boost algorithms. These are based on coordinate descent and gradient descent to minimize the multi-class ${\ell }_2$-loss function. We derive a scoring coding scheme using optimal scoring constraints to encode class labels and a simple decoder to recover the true class labels. Our boosting algorithms are easily implemented and their results converge to the global optimum. Experiments with synthetic and real-world datasets show that, compared with several state-of-art methods, our algorithms provide more accurate results.

An adaptive step length genetic algorithm (ASLGA) is presented, in this paper, to improve local search efficiency and to prevent premature convergence of the genetic algorithms (GAs). Step length of crossover and mutation are adaptively varied depending on the fitness values of the solutions to improve local search efficiency. Similar solutions are adaptively disrupted by multipoint mutation according to the livingness index of the population to prevent premature convergence. Three typical multimodal functions are used to verify the performance of the ASLGA. Experimental results demonstrate that the ASLGA has good local search efficiency and global search capacity.

Some types of equilibrium programming problem can be reduced to an implicit nonconvex mathematical programming problem. In general the reduced problem can have many locally optimal solutions. Only globally optimal solutions correspond to equilibrium points. In this paper we suggest a global optimization scheme based on concept of the nonlinear support function for solving equilibrium programming problems.

To solve the multi-variable, non-linear, and non-convex reactive power optimization problem, this study proposes a new intelligent optimization algorithm called Cell Membrane Optimization (CMO). This algorithm is based on the diffusion processes of the substance in cell. The substance (solutions) moves through free diffusion, facilitated diffusion and active transport according to its type which is classified by concentration, thereby increasing the speed of searching for the global optimal solution. In the process of reactive power optimization, based on the constraint conditions establish objective function of the minimum net loss using CMO. The algorithm is tested with IEEE 14-bus and IEEE 30-bus systems. Results show that the optimization ability of the algorithm is acceptable. This algorithm has parallelism naturally, which can avoid the local optimal solution.