A dynamic state transition algorithm with application to sensor network localization

The sensor network localization (SNL) problem is to reconstruct the positions of all the sensors in a network with the given distance between pairs of sensors and within the radio range between them. It is proved that the computational complexity of the SNL problem is NP-hard, and semi-definite programming or second-order cone programming relaxation methods are only able to solve some special problems of this kind. In this study, a stochastic global optimization method called the state transition algorithm is introduced to solve the SNL problem without additional assumptions and conditions of the problem structure. To transcend local optimality, a novel dynamic adjustment strategy called "risk and restoration in probability" is incorporated into the state transition algorithm. An empirical study is investigated to appropriately choose the "risk probability" and "restoration probability", yielding the dynamic state transition algorithm, which is further improved by gradient-based refinement. The dynamic state transition algorithm with refinement is applied to the SNL problem, and satisfactory experimental results have testified the effectiveness of the proposed approach.Comment: 22 page

Discrete State Transition Algorithm for Unconstrained Integer Optimization Problems

A recently new intelligent optimization algorithm called discrete state transition algorithm is considered in this study, for solving unconstrained integer optimization problems. Firstly, some key elements for discrete state transition algorithm are summarized to guide its well development. Several intelligent operators are designed for local exploitation and global exploration. Then, a dynamic adjustment strategy ``risk and restoration in probability" is proposed to capture global solutions with high probability. Finally, numerical experiments are carried out to test the performance of the proposed algorithm compared with other heuristics, and they show that the similar intelligent operators can be applied to ranging from traveling salesman problem, boolean integer programming, to discrete value selection problem, which indicates the adaptability and flexibility of the proposed intelligent elements.Comment: 14 pages, 13 figure

A Rolling PID Control Approach and its Applications

The canonical proportional-integral-derivative (PID) control approach has been widely used in industrial application due to their simplicity and ease of use. However, its corresponding controller parameters are hard to be adjusted, especially for nonlinear systems. The optimization-based method provides a general framework to find optimal PID controller parameters; nevertheless, several disadvantages exist, for example, it is nontrivial to select an appropriate sample size and it is necessary to obtain the global optimal solution but the optimization problem is non-convex, making it hard to achieve. To alleviate the aforementioned limitations, a rolling PID control approach is proposed in this study, in which, at each rolling period, the PID controller parameters are updated using observable data, which can be classified to data-driven control method. The effectiveness of the proposed approach has been validated by experiments

A matlab toolbox for continuous state transition algorithm

State transition algorithm (STA) has been emerging as a novel stochastic method for global optimization in recent few years. To make better understanding of continuous STA, a matlab toolbox for continuous STA has been developed. Firstly, the basic principles of continuous STA are briefly described. Then, a matlab implementation of the standard continuous STA is explained, with several instances given to show how to use to the matlab toolbox to minimize an optimization problem with bound constraints. In the same while, a link is provided to download the matlab toolbox via available resources.Comment: 6 page

Global solutions to a class of CEC benchmark constrained optimization problems

This paper aims to solve a class of CEC benchmark constrained optimization problems that have been widely studied by nature-inspired optimization algorithms. Global optimality condition based on canonical duality theory is derived. Integrating the dual solutions with the KKT conditions, we are able to obtain the approximate solutions or global solutions easily

A Statistical Study on Parameter Selection of Operators in Continuous State Transition Algorithm

State transition algorithm (STA) has been emerging as a novel metaheuristic method for global optimization in recent few years. In our previous study, the parameter of transformation operator in continuous STA is kept constant or decreasing itself in a periodical way. In this paper, the optimal parameter selection of the STA is taken in consideration. Firstly, a statistical study with four benchmark two-dimensional functions is conducted to show how these parameters affect the search ability of the STA. Based on the experience gained from the statistical study, then, a new continuous STA with optimal parameters strategy is proposed to accelerate its search process. The proposed STA is successfully applied to twelve benchmarks with 20, 30 and 50 dimensional space. Comparison with other metaheuristics has also demonstrated the effectiveness of the proposed method.Comment: 10 page

A Comparative Study of STA on Large Scale Global Optimization

State transition algorithm has been emerging as a new intelligent global optimization method in recent few years. The standard continuous STA has demonstrated powerful global search ability for global optimization problems whose dimension is no more than 100. In this study, we give a test report to present the performance of standard continuous STA for large scale global optimization when compared with other state-of-the-art evolutionary algorithms. From the experimental results, it is shown that the standard continuous STA still works well for almost all of the test problems, and its global search ability is much superior to its competitors.Comment: arXiv admin note: substantial text overlap with arXiv:1604.0084

Improved Canonical Dual Algorithms for the Maxcut Problem

By introducing a quadratic perturbation to the canonical dual of the maxcut problem, we transform the integer programming problem into a concave maximization problem over a convex positive domain under some circumstances, which can be solved easily by the well-developed optimization methods. Considering that there may exist no critical points in the dual feasible domain, a reduction technique is used gradually to guarantee the feasibility of the reduced solution, and a compensation technique is utilized to strengthen the robustness of the solution. The similar strategy is also applied to the maxcut problem with linear perturbation and its hybrid with quadratic perturbation. Experimental results demonstrate the effectiveness of the proposed algorithms when compared with other approaches

A Comparative Study of State Transition Algorithm with Harmony Search and Artificial Bee Colony

We focus on a comparative study of three recently developed nature-inspired optimization algorithms, including state transition algorithm, harmony search and artificial bee colony. Their core mechanisms are introduced and their similarities and differences are described. Then, a suit of 27 well-known benchmark problems are used to investigate the performance of these algorithms and finally we discuss their general applicability with respect to the structure of optimization problems

Spherical tϵt_\epsilon-Designs for Approximations on the Sphere

A spherical $t$-design is a set of points on the sphere that are nodes of a positive equal weight quadrature rule having algebraic accuracy $t$ for all spherical polynomials with degrees $\le t$. Spherical $t$-designs have many distinguished properties in approximations on the sphere and receive remarkable attention. Although the existence of a spherical $t$-design is known for any $t\ge 0$, a spherical design is only known in a set of interval enclosures on the sphere \cite{chen2011computational} for $t\le 100$. It is unknown how to choose a set of points from the set of interval enclosures to obtain a spherical $t$-design. In this paper we investigate a new concept of point sets on the sphere named spherical $t_\epsilon$-design ($0<\epsilon<1$), which are nodes of a positive weight quadrature rule with algebraic accuracy $t$. The sum of the weights is equal to the area of the sphere and the mean value of the weights is equal to the weight of the quadrature rule defined by the spherical $t$-design. A spherical $t_\epsilon$-design is a spherical $t$-design when $\epsilon=0,$ and a spherical $t$-design is a spherical $t_\epsilon$-design for any $0<\epsilon <1$. We show that any point set chosen from the set of interval enclosures \cite{chen2011computational} is a spherical $t_\epsilon$-design. We then study the worst-case errors of quadrature rules using spherical $t_\epsilon$-designs in a Sobolev space, and investigate a model of polynomial approximation with the $l_1$-regularization using spherical $t_\epsilon$-designs. Numerical results illustrate good performance of spherical $t_\epsilon$-designs for numerical integration and function approximation on the sphere