stochastic algorithm
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Author(s):  
Fukui Li ◽  
Jingyuan He ◽  
Mingliang Zhou ◽  
Bin Fang

Local search algorithms are widely applied in solving large-scale distributed constraint optimization problem (DCOP). Distributed stochastic algorithm (DSA) is a typical local search algorithm to solve DCOP. However, DSA has some drawbacks including easily falling into local optima and the unfairness of assignment choice. This paper presents a novel local search algorithm named VLSs to solve the issues. In VLSs, sampling according to the probability corresponding to assignment is introduced to enable each agent to choose other promising values. Besides, each agent alternately performs a greedy choice among multiple parallel solutions to reduce the chance of falling into local optima and a variance adjustment mechanism to guide the search into a relatively good initial solution in a periodic manner. We give the proof of variance adjustment mechanism rationality and theoretical explanation of impact of greed among multiple parallel solutions. The experimental results show the superiority of VLSs over state-of-the-art DCOP algorithms.


Author(s):  
Julián Andrés Gómez-Salazar ◽  
Jennifer Patlán-González ◽  
María Elena Sosa-Morales ◽  
Juan Gabriel Segovia-Hernandez ◽  
Eduardo Sánchez-Ramírez ◽  
...  

Author(s):  
Renbo Zhao

We develop stochastic first-order primal-dual algorithms to solve a class of convex-concave saddle-point problems. When the saddle function is strongly convex in the primal variable, we develop the first stochastic restart scheme for this problem. When the gradient noises obey sub-Gaussian distributions, the oracle complexity of our restart scheme is strictly better than any of the existing methods, even in the deterministic case. Furthermore, for each problem parameter of interest, whenever the lower bound exists, the oracle complexity of our restart scheme is either optimal or nearly optimal (up to a log factor). The subroutine used in this scheme is itself a new stochastic algorithm developed for the problem where the saddle function is nonstrongly convex in the primal variable. This new algorithm, which is based on the primal-dual hybrid gradient framework, achieves the state-of-the-art oracle complexity and may be of independent interest.


Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3043
Author(s):  
Manuel L. Esquível ◽  
Nadezhda P. Krasii ◽  
Pedro P. Mota ◽  
Nélio Machado

We propose a stochastic algorithm for global optimisation of a regular function, possibly unbounded, defined on a bounded set with regular boundary; a function that attains its extremum in the boundary of its domain of definition. The algorithm is determined by a diffusion process that is associated with the function by means of a strictly elliptic operator that ensures an adequate maximum principle. In order to preclude the algorithm to be trapped in a local extremum, we add a pure random search step to the algorithm. We show that an adequate procedure of parallelisation of the algorithm can increase the rate of convergence, thus superseding the main drawback of the addition of the pure random search step.


Processes ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 2060
Author(s):  
Jiaxing Chen ◽  
Qiguo Yang ◽  
Guomin Cui ◽  
Zhongkai Bao ◽  
Guanhua Zhang

Facing the current energy structure urgently needs to be transformed, heat exchanger network (HEN) can implement heat recovery and cost reduction by the arrangement for heat exchanges between cold and hot streams. The plenty of integer and continuous variables involved in HEN synthesis cause the results to be easily trapped in local optima. To avoid this situation, the mechanism of accepting imperfect solutions is added in a novel algorithm called Random Walk Algorithm with Compulsive Evolution. However, several potential solutions maybe abandoned by accepting imperfect solutions. To maintain the global searching ability, and at the same time, protecting the potential solutions during the optimization process, the limitations of accepting imperfect solutions are investigated in this work, then a back substitution strategy and elite optimization strategy based on algorithm are proposed. The former is to identify and adjust the inferior individuals in long-term stagnation while the latter is to keep and perform a fine search for the better solutions. Furthermore, a modified stage-wised superstructure is also developed to implement the flexible placement of utilities, which efficiently enlarges the solution domain. The validation of strategies and model is implemented by three cases, the results are lower, with 2219 $/year, 1280 $/year, and 2M $/year than the best published result, revealing the strong abilities of the proposed method in designing more economical HENs.


2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Irina Shalimova ◽  
Karl K. Sabelfeld

Abstract We further develop in this study the Random Walk on Spheres (RWS) stochastic algorithm for solving systems of coupled diffusion-recombination equations first suggested in our recent article [K. Sabelfeld, First passage Monte Carlo algorithms for solving coupled systems of diffusion–reaction equations, Appl. Math. Lett. 88 2019, 141–148]. The random walk on spheres process mimics the isotropic diffusion of two types of particles which may recombine to each other. Our motivation comes from the transport problems of free and bound exciton recombination. The algorithm is based on tracking the trajectories of the diffusing particles exactly in accordance with the probabilistic distributions derived from the explicit representation of the relevant Green functions for balls and spheres. Therefore, the method is mesh free both in space and time. In this paper we implement the RWS algorithm for solving the diffusion-recombination problems both in a steady-state and transient settings. Simulations are compared against the exact solutions. We show also how the RWS algorithm can be applied to calculate exciton flux to the boundary which provides the electron beam-induced current, the concentration of the survived excitons, and the cathodoluminescence intensity which are all integral characteristics of the solution to diffusion-recombination problem.


2021 ◽  
Author(s):  
Wali Khan ◽  
Faiz Ur Rehaman ◽  
Habib Shah

Abstract Teaching learning based optimization (TLBO) is a stochastic algorithm which was first proposed for unconstrained optimization problems. It is population based, nature-inspired, and meta-heuristic that imitates teaching learning process. It has two phases, teacher and learner. In teacher phase, the teacher who is well-learned person transfers his/her knowledge to the learners to raise their grades/results; while in learner phase, learners/pupils learn and refine their knowledge through mutual interconnection. To solve constrained optimization problems (COPs) through TLBO we need to merge it with some constraint handling technique (CHT). Superiority of feasibility (SF) is a concept for making CHTs, existed in different forms based on various decisive factors. Most commonly used decision making factors in SF are number of constraints violated (NCV) and weighted mean (WM) values for comparing solutions. In this work, SF based on number of constraints violated (NCVSF) and weighted mean (WMSF) are incorporated in the framework of TLBO. These are tested upon CEC-2006 constrained suit with the remark that single factor used for the decision making of winner is not a wise idea. Mentioned remark leads us to made a single CHT that carries the capabilities of both discussed CHTs. It laid the foundation of hybrid superiority of feasiblity (HSF); where NCV and WM factors are combined with giving dominance to NCV over WM. In current research three constrained versions of TLBO are formulated by the name NCVSF-TLBO, WMSF-TLBO, and HSF-TLBO; while implanting NCVSF, WMSF, and HSF in the framework of TLBO, respectively. These constrained versions of TLBO are evaluated on CEC-2006 with the remarks that HSF-TLBO got prominent and flourishing status among these.


Processes ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1778
Author(s):  
Tae-Hee Lee ◽  
Jin-Hwan Lee ◽  
Kyung-Pyo Yi ◽  
Dong-Kuk Lim

The topology algorithm (TA) can effectively find an optimal solution by changing the material and shape of the design target without the limitation of design variables. In this paper, a genetic topology algorithm (GTA) is proposed for the design optimization of a synchronous reluctance motor (SynRM). By applying the stochastic algorithm (genetic algorithm (GA)) and the deterministic algorithm (ON-OFF method) to the design, the optimal shape can be found quickly and effectively. The GTA, which improves manufacturability by removing the aliasing that occurs in TA, was applied to the design of SynRM to search for the optimal model. After dividing the rotor into a reverse mesh grid, the optimal topology was searched for by GA and ON-OFF methods. Then, mechanical stability was verified through stress analysis, and additional performance improvement was obtained through the skew technique. The final design, which satisfies the minimum efficiency, required torque, and torque ripple was derived by applying the step-by-step design using GTA to the SynRM optimization.


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