Seeker optimization algorithm:a novel stochastic search algorithm for global numerical optimization

A novel heuristic search algorithm called seeker op- timization algorithm （SOA） is proposed for the real-parameter optimization. The proposed SOA is based on simulating the act of human searching. In the SOA, search direction is based on empir- ical gradients by evaluating the response to the position changes, while step length is based on uncertainty reasoning by using a simple fuzzy rule. The effectiveness of the SOA is evaluated by using a challenging set of typically complex functions in compari- son to differential evolution （DE） and three modified particle swarm optimization （PSO） algorithms. The simulation results show that the performance of the SOA is superior or comparable to that of the other algorithms.

GLOBAL OPTIMIZATION OF PUMP CONFIGURATION PROBLEM USING EXTENDED CROWDING GENETIC ALGORITHM

An extended crowding genetic algorithm (ECGA) is introduced for solvingoptimal pump configuration problem, which was presented by T. Westerlund in 1994. This problem hasbeen found to be non-convex, and the objective function contained several local optima and globaloptimality could not be ensured by all the traditional MINLP optimization method. The concepts ofspecies conserving and composite encoding are introduced to crowding genetic algorithm (CGA) formaintain the diversity of population more effectively and coping with the continuous and/or discretevariables in MINLP problem. The solution of three-levels pump configuration got from DICOPT++software (OA algorithm) is also given. By comparing with the solutions obtained from DICOPT++, ECPmethod, and MIN-MIN method, the ECGA algorithm proved to be very effective in finding the globaloptimal solution of multi-levels pump configuration via using the problem-specific information.

Global optimal path planning for mobile robot based onimproved Dijkstra algorithm and ant system algorithm

A novel method of global optimal path planning for mobile robot was proposed based on the improved Dijkstra algorithm and ant system algorithm. This method includes three steps: the first step is adopting the MAKLINK graph theory to establish the free space model of the mobile robot, the second step is adopting the improved Dijkstra algorithm to find out a sub-optimal collision-free path, and the third step is using the ant system algorithm to adjust and optimize the location of the sub-optimal path so as to generate the global optimal path for the mobile robot. The computer simulation experiment was carried out and the results show that this method is correct and effective. The comparison of the results confirms that the proposed method is better than the hybrid genetic algorithm in the global optimal path planning.

Global Convergence Analysis of Non-Crossover Genetic Algorithm and Its Application to Optimization

Selection, crossover, and mutation are three main operators of the canonical genetic algorithm (CGA). This paper presents a new approach to the genetic algorithm. This new approach applies only to mutation and selection operators. The paper proves that the search process of the non-crossover genetic algorithm (NCGA) is an ergodic homogeneous Markov chain. The proof of its convergence to global optimum is presented. Some nonlinear multi-modal optimization problems are applied to test the efficacy of the NCGA. NP-hard traveling salesman problem (TSP) is cited here as the benchmark problem to test the efficiency of the algorithm. The simulation result shows that NCGA achieves much faster convergence speed than CGA in terms of CPU time. The convergence speed per epoch of NCGA is also faster than that of CGA.

An adaptive genetic algorithm with diversity-guided mutation and its global convergence property

An adaptive genetic algorithm with diversity-guided mutation, which combines adaptive probabilities of crossover and mutation was proposed. By means of homogeneous finite Markov chains, it is proved that adaptive genetic algorithm with diversity-guided mutation and genetic algorithm with diversity-guided mutation converge to the global optimum if they maintain the best solutions, and the convergence of adaptive genetic algorithms with adaptive probabilities of crossover and mutation was studied. The performances of the above algorithms in optimizing several unimodal and multimodal functions were compared. The results show that for multimodal functions the average convergence generation of the adaptive genetic algorithm with diversity-guided mutation is about 900 less than that of (adaptive) genetic algorithm with adaptive probabilities and genetic algorithm with diversity-guided mutation, and the adaptive genetic algorithm with diversity-guided mutation does not lead to premature convergence. It is also shown that the better balance between overcoming premature convergence and quickening convergence speed can be gotten.

A composite particle swarm algorithm for global optimization of multimodal functions

During the last decade, many variants of the original particle swarm optimization （PSO） algorithm have been proposed for global numerical optimization, hut they usually face many challenges such as low solution quality and slow convergence speed on multimodal function optimization. A composite particle swarm optimization （CPSO） for solving these difficulties is presented, in which a novel learning strategy plus an assisted search mechanism framework is used. Instead of simple learning strategy of the original PSO, the proposed CPSO combines one particle＇s historical best information and the global best information into one learning exemplar to guide the particle movement. The proposed learning strategy can reserve the original search information and lead to faster convergence speed. The proposed assisted search mechanism is designed to look for the global optimum. Search direction of particles can be greatly changed by this mechanism so that the algorithm has a large chance to escape from local optima. In order to make the assisted search mechanism more efficient and the algorithm more reliable, the executive probability of the assisted search mechanism is adjusted by the feedback of the improvement degree of optimal value after each iteration. According to the result of numerical experiments on multimodal benchmark functions such as Schwefel, Rastrigin, Ackley and Griewank both with and without coordinate rotation, the proposed CPSO offers faster convergence speed, higher quality solution and stronger robustness than other variants of PSO.

A new hybrid algorithm for global optimization and slope stability evaluation

A new hybrid optimization algorithm was presented by integrating the gravitational search algorithm （GSA） with the sequential quadratic programming （SQP）, namely GSA-SQP, for solving global optimization problems and minimization of factor of safety in slope stability analysis. The new algorithm combines the global exploration ability of the GSA to converge rapidly to a near optimum solution. In addition, it uses the accurate local exploitation ability of the SQP to accelerate the search process and find an accurate solution. A set of five well-known benchmark optimization problems was used to validate the performance of the GSA-SQP as a global optimization algorithm and facilitate comparison with the classical GSA. In addition, the effectiveness of the proposed method for slope stability analysis was investigated using three ease studies of slope stability problems from the literature. The factor of safety of earth slopes was evaluated using the Morgenstern-Price method. The numerical experiments demonstrate that the hybrid algorithm converges faster to a significantly more accurate final solution for a variety of benchmark test functions and slope stability problems.

Finding Global Minima with a New Dynamical Evolutionary Algorithm

A new dynamical evolutionary algorithm (DEA) based on the theory of statistical mechanics is presented. This algorithm is very different from the traditional evolutionary algorithm and the two novel features are the unique of selecting strategy and the determination of individuals that are selected to crossover and mutate. We use DEA to solve a lot of global optimization problems that are nonlinear, multimodal and multidimensional and obtain satisfactory results.

Multi-swingby optimization of mission to Saturn using global optimization algorithms

Based on the trajectory design of a mission to Saturn, this paper discusses four different trajectories in various swingby cases. We assume a single impulse to be applied in each case when the spacecraft approaches a celestial body. Some optimal trajectories ofEJS, EMS, EVEJS and EVVEJS flying sequences are obtained using five global optimization algorithms： DE, PSO, DP, the hybrid algorithm PSODE and another hybrid algorithm, DPDE. DE is proved to be supe- rior to other non-hybrid algorithms in the trajectory optimi- zation problem. The hybrid algorithm of PSO and DE can improve the optimization performance of DE, which is vali- dated by the mission to Saturn with given swingby sequences. Finally, the optimization results of four different swingby sequences are compared with those of the ACT of ESA.

AN ANALYSIS ABOUT BEHAVIOR OF EVOLUTIONARY ALGORITHMS:A KIND OF THEORETICAL DESCRIPTION BASED ON GLOBAL RANDOM SEARCH METHODS

Evolutionary computation is a kind of adaptive non--numerical computation method which is designed tosimulate evolution of nature. In this paper, evolutionary algorithm behavior is described in terms of theconstruction and evolution of the sampling distributions over the space of candidate solutions. Iterativeconstruction of the sampling distributions is based on the idea of the global random search of generationalmethods. Under this frame, propontional selection is characterized as a gobal search operator, and recombination is characerized as the search process that exploits similarities. It is shown-that by properly constraining the search breadth of recombination operators, weak convergence of evolutionary algorithms to aglobal optimum can be ensured.

ANew Theoretical Framework forAnalyzing Stochastic Global Optimization Algorithms

In this paper, we develop a new theoretical framework by means of the absorbing Markov process theory for analyzing some stochastic global optimization algorithms. Applying the framework to the pure random search, we prove that the pure random search converges to the global minimum in probability and its time has geometry distribution. We also analyze the pure adaptive search by this framework and turn out that the pure adaptive search converges to the global minimum in probability and its time has Poisson distribution.

A New Stochastic Algorithm of Global Optimization ——Region's Walk and Contraction

This paper presents a new stochastic algorithm for box constrained global optimization problem. Bacause the level set of objective function is always not known, the authors designed a region containing the current minimum point to replace it, and in order to fit the level set well, this region would be walking and contracting in the running process. Thus, the new algorithm is named as region's walk and contraction(RWC). Some numerical experiments for the RWC were conducted, which indicate good property of the algorithm.

Neural network and genetic algorithm based global path planning in a static environment

Mobile robot global path planning in a static environment is an important problem. The paper proposes a method of global path planning based on neural network and genetic algorithm. We constructed the neural network model of environmental information in the workspace for a robot and used this model to establish the relationship between a collision avoidance path and the output of the model. Then the two-dimensional coding for the path via-points was converted to one-dimensional one and the fitness of both the collision avoidance path and the shortest distance are integrated into a fitness function. The simulation results showed that the proposed method is correct and effective.

Modified evolutionary algorithm for global optimization

A modification of evolutionary programming or evolution strategies for ndimensional global optimization is proposed. Based on the ergodicity and inherentrandomness of chaos, the main characteristic of the new algorithm which includes two phases is that chaotic behavior is exploited to conduct a rough search of the problem space in order to find the promising individuals in Phase I. Adjustment strategy of steplength and intensive searches in Phase II are employed. The population sequences generated by the algorithm asymptotically converge to global optimal solutions with probability one. The proposed algorithm is applied to several typical test problems. Numerical results illustrate that this algorithm can more efficiently solve complex global optimization problems than evolutionary programming and evolution strategies in most cases.

Ant Colony System Algorithm for Real-Time Globally Optimal Path Planning of Mobile Robots

为活动机器人计划的即时全球性最佳的路径的一个新奇方法基于蚂蚁殖民地系统(交流) 被建议算法。这个方法包括三步：第一步正在利用 MAKLINK 图理论建立活动机器人的空间模型，第二步正在利用 Dijkstra 算法发现一条非最优的没有碰撞的路径，并且第三步正在利用 ACS 算法优化非最优的路径的地点以便产生全球性最佳的路径。建议方法是有效的并且能在即时路径被使用活动机器人计划的计算机模拟实验表演的结果。建议方法比与优秀人材模型一起基于基因算法计划方法的路径处于集中速度，答案变化，动态集中行为，和计算效率有更好的性能，这被验证了。

Global optimization by small-world optimization algorithm based on social relationship network

A fast global convergence algorithm, small-world optimization (SWO), was designed to solve the global optimization problems, which was inspired from small-world theory and six degrees of separation principle in sociology. Firstly, the solution space was organized into a small-world network model based on social relationship network. Secondly, a simple search strategy was adopted to navigate into this network in order to realize the optimization. In SWO, the two operators for searching the short-range contacts and long-range contacts in small-world network were corresponding to the exploitation and exploration, which have been revealed as the common features in many intelligent algorithms. The proposed algorithm was validated via popular benchmark functions and engineering problems. And also the impacts of parameters were studied. The simulation results indicate that because of the small-world theory, it is suitable for heuristic methods to search targets efficiently in this constructed small-world network model. It is not easy for each test mail to fall into a local trap by shifting into two mapping spaces in order to accelerate the convergence speed. Compared with some classical algorithms, SWO is inherited with optimal features and outstanding in convergence speed. Thus, the algorithm can be considered as a good alternative to solve global optimization problems.

THE GLOBALIZATION OF DURAND-KERNER ALGORITHM

Making use of the theory of continuous homotopy and the relation betweensymmetric polynomtal and polynomtal in one variable the arthors devoted ims article to constructing a regularly homotopic curve with probability one. Discrete tracingalong this honlotopic curve leads 10 a class of Durand-Kerner algorithm with stepparameters. The convergernce of this class of algorithms is given, which solves theconjecture about the global property of Durand-Kerner algorithm. The.problem forsteplength selection is thoroughly discussed Finally, sufficient numerical examples areused to verify our theory

MERIT FUNCTION AND GLOBAL ALGORITHMFOR BOX CONSTRAINED VARIATIONALINEQUALITIES

The authors consider optimization methods for box constrained variational inequalities. First, the authors study the KKT-conditions problem based on the original problem. A merit function for the KKT-conditions problem is proposed, and some desirable properties of the merit function are obtained. Through the merit function, the original problem is reformulated as minimization with simple constraints. Then, the authors show that any stationary point of the optimization problem is a solution of the original problem. Finally, a descent algorithm is presented for the optimization problem, and global convergence is shown.

The Algorithms for Achieving Global States and Self-Stabilization for Communication Protocols

This paper discusses the algorithms for achieving global states and self-stabilizationfor communication protocols. It first describes a primary algorithm including its suitability forachieving global states and limitation of self-stabilization for communication protocols, and thenpresents an improved algorithm that can be suitable to achieve global states and can be also usedto self-stabilizing communication protocols. Filially, it gives the proof of correctness and analysis ofcomplexity of the improved algorithm, and verifies its availability and efficiency by illustrating anexample protocol.

An Algorithm for Global Optimization Using Formula Manupulation

Constrained nonlinear optimization problems are well known as very difficult problems. In this paper, we present a new algorithm for solving such problems. Our proposed algorithm combines the Branch-and-Bound algorithm and Lipschitz constant to limit the search area effectively;this is essential for solving constrained nonlinear optimization problems. We obtain a more appropriate Lipschitz constant by applying the formula manipulation system of each divided area. Therefore, we obtain a better approximate solution without using a lot of searching points. The efficiency of our proposed algorithm has been shown by the results of some numerical experiments.