{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,11]],"date-time":"2026-04-11T18:25:28Z","timestamp":1775931928694,"version":"3.50.1"},"reference-count":28,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["11961001"],"award-info":[{"award-number":["11961001"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Construction Project of first-class subjects in Ningxia higher Education","award":["NXYLXK2017B09"],"award-info":[{"award-number":["NXYLXK2017B09"]}]},{"name":"Major proprietary funded project of North Minzu University","award":["ZDZX201901"],"award-info":[{"award-number":["ZDZX201901"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Asia Pac. J. Oper. Res."],"published-print":{"date-parts":[[2023,4]]},"abstract":"<jats:p> Founded on the idea of subdividing the [Formula: see text]-dimensional output space, a branch-and-bound algorithm for solving the sum-of-linear-ratios(SLR) problem is proposed. First, a two-stage equivalent transformation method is adopted to obtain an equivalent problem(EP) for the problem SLR. Second, by dealing with all nonlinear constraints and bilinear terms in EP and its sub-problems, a corresponding convex relaxation subproblem is obtained. Third, all redundant constraints in each convex relaxation subproblem are eliminated, which leads to a linear programming problem with smaller scale and fewer constraints. Finally, the theoretical convergence and computational complexity of the algorithm are demonstrated, and a series of numerical experiments illustrate the effectiveness and feasibility of the proposed algorithm. <\/jats:p>","DOI":"10.1142\/s0217595922500105","type":"journal-article","created":{"date-parts":[[2022,3,25]],"date-time":"2022-03-25T02:29:28Z","timestamp":1648175368000},"source":"Crossref","is-referenced-by-count":6,"title":["An Output-Space Based Branch-and-Bound Algorithm for Sum-of-Linear-Ratios Problem"],"prefix":"10.1142","volume":"40","author":[{"given":"Bo","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, P. R. 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