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By leveraging the geometric structures of optimal solutions and using gradient flows, we convert the path-planning problem into a system of finite dimensional ordinary differential equations, whose dimensions change dynamically. Then a stochastic differential equation based optimization method, called intermittent diffusion, is employed to obtain the global optimal solution. We demonstrate, via numerical examples, that the new algorithm can solve the problem efficiently. <\/jats:p>","DOI":"10.1177\/0278364917707252","type":"journal-article","created":{"date-parts":[[2017,5,17]],"date-time":"2017-05-17T06:08:16Z","timestamp":1495001296000},"page":"403-413","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":6,"title":["Method of evolving junctions: A new approach to optimal path-planning in 2D environments with moving obstacles"],"prefix":"10.1177","volume":"36","author":[{"given":"Wuchen","family":"Li","sequence":"first","affiliation":[{"name":"School of Mathematics, Georgia Institute of Technology, USA"}]},{"given":"Shui-Nee","family":"Chow","sequence":"additional","affiliation":[{"name":"School of Mathematics, Georgia Institute of Technology, USA"}]},{"given":"Magnus","family":"Egerstedt","sequence":"additional","affiliation":[{"name":"School of Electrical and Computer Engineering, 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