{"title":"Complexity results on k-independence in some graph products","authors":"Márcia Cappelle, Erika Coelho, Otavio Mortosa, Julliano Nascimento","doi":"10.1051/ro/2024098","DOIUrl":"https://doi.org/10.1051/ro/2024098","url":null,"abstract":"For a positive integer k, a subset S of vertices of a graph G=(V,E) is k-independent if each vertex in S has at most k - 1 neighbors in S. We consider k-independent sets in two graph products: Cartesian and complementary prism. We show that k-independence remains NP-complete even for Cartesian products and complementary prisms. Furthermore, we present results on k-independence in grid graphs, which is a Cartesian product of two paths.","PeriodicalId":506995,"journal":{"name":"RAIRO - Operations Research","volume":"106 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141002305","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Reza Lotfi, Pedram MohajerAnsari, Mohammad Mehdi Sharifi Nevisi, Seyed Mahdi Sharifmousavi, Mohamad Afshar, Mojtaba Sadreddini Mehrjardi
{"title":"A robust, resilience and risk-aware solar energy farm location by bi-level programming approach","authors":"Reza Lotfi, Pedram MohajerAnsari, Mohammad Mehdi Sharifi Nevisi, Seyed Mahdi Sharifmousavi, Mohamad Afshar, Mojtaba Sadreddini Mehrjardi","doi":"10.1051/ro/2024100","DOIUrl":"https://doi.org/10.1051/ro/2024100","url":null,"abstract":"In challenging circumstances such as war, governments are shifting their focus towards Solar Energy (SE) as a Renewable Energy (RE) option through photovoltaic panels due to the rising costs associated with fossil fuel extraction and exploration. This model recommends a SE Location (SEL) that prioritizes Robustness, Resilience, and Risk awareness (3R) which is called 3RSEL. As a result, a Bi-Level Programming (BLP) is proposed to solve this problem for the first time. A heuristic approach is defined for a BLP mathematical model. This research generates a lower and upper bound to solve the model quickly. The results show that Yazd and Kerman are the optimal location for SEL. The main problem is compared to a situation where risk and robustness are not considered. It can be observed that the supplier's profit and energy production are lower than without risk and robustness, with a gap of -4.4%. The variability of the conservatism coefficient, discount rate, confidence level of Conditional Value at Risk (CVaR), and problem scale are considered. Increasing the conservatism coefficient decreases the supplier's profit function and energy output. Alternatively, increasing the discount rate decreases the supplier's profit function without affecting the energy output. Conversely, boosting the confidence level does not alter suppliers' profit function but results in declining energy output. Finally, as stated, it can be observed that the computation time increases with an increase in the scale of the problem.","PeriodicalId":506995,"journal":{"name":"RAIRO - Operations Research","volume":"5 18","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141004386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Successive upper approximation methods for generalized fractional programs\u0000\u0000 ","authors":"K. Boufi, Abdessamad Fadil, A. Roubi","doi":"10.1051/ro/2024097","DOIUrl":"https://doi.org/10.1051/ro/2024097","url":null,"abstract":"The majorization approximation procedure consists in replacing the resolution of a nonlinear optimization problem by solving a sequence of simpler ones, whose objective and constraint functions upper estimate those of the original problem. For generalized fractional programming, i.e., constrained minimization programs whose objective functions are maximums of finite ratios of functions, we propose an adapted scheme that simultaneously upper approximates parametric functions formed by the objective and constraint functions. For directionally convex functions, that is, functions whose directional derivatives are convex with respect to directions, we will establish that every cluster point of the generated sequence satisfies Karush-Kuhn-Tucker type conditions expressed in terms of directional derivatives. The proposed procedure unifies several existing methods and gives rise to new ones. Numerical problems are solved to test the efficiency of our methods, and comparisons with different approaches are given.","PeriodicalId":506995,"journal":{"name":"RAIRO - Operations Research","volume":"35 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141047373","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}