4,821 research outputs found

    A hybrid constraint programming and semidefinite programming approach for the stable set problem

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    This work presents a hybrid approach to solve the maximum stable set problem, using constraint and semidefinite programming. The approach consists of two steps: subproblem generation and subproblem solution. First we rank the variable domain values, based on the solution of a semidefinite relaxation. Using this ranking, we generate the most promising subproblems first, by exploring a search tree using a limited discrepancy strategy. Then the subproblems are being solved using a constraint programming solver. To strengthen the semidefinite relaxation, we propose to infer additional constraints from the discrepancy structure. Computational results show that the semidefinite relaxation is very informative, since solutions of good quality are found in the first subproblems, or optimality is proven immediately.Comment: 14 page

    An Efficient Algorithm for Fuzzy Linear Fractional Programming Problems via Ranking Function

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    في العديد من التطبيقات مثل الإنتاج ، يعد التخطيط لصانع القرار أمرًا مهمًا في تحسين دالة الهدف الضبابية للمسالة  حيث تحتوي على نسبة دالتين ضبابيتين ، والتي يمكن ان تسلم باستخدام تقنية مسالة البرمجة الكسرية الضبابية  . يتم النظر في فئة خاصة من تقنية التحسين تسمى مسالة البرمجة الكسرية الضبابية في هذا العمل عندما تكون معاملات دالة الهدف للمسالة ضبابية. تم اقتراح دالة الترتيب الجديدة واستخدامها لتحويل بيانات مسالة البرمجة الكسرية الضبابية من رقم غامض إلى رقم واضح بحيث يمكن تجنب العيب عند معالجة المسالة الضبابية الأصلية. هنا يتم اعتماد نهج وظيفة الترتيب الجديدة للأرقام الضبابية العادية لترتيب الأرقام الضبابية المثلثية مع حسابات أبسط وأسهل بالإضافة إلى تقصيرها في الإجراءات. يتم تقليل مشكلة البرمجة الكسرية الضبابية أولاً إلى مشكلة البرمجة الكسرية ثم حلها باستخدام التقنية للحصول على الحل الأمثل. لديها القدرة على إعطاء أفضل حل لدعم نظرية الحل المقترحة في هذا العمل ، يتم تضمين بعض مسائل البرمجة الكسرية الضبابية لضمان ميزة وكفاءة ودقة الخوارزمية المقترحة. بالإضافة إلى ذلك ، تصف هذه الورقة البحثية مقارنة بين حلولنا المثالية مع الحلول الأخرى القائمة لعدم المساواة للقيود في مسائل البرمجة الكسرية الضبابية.In many applications such as production, planning, the decision maker is important in optimizing an objective function that has fuzzy ratio two functions which can be handed using fuzzy fractional programming problem technique. A special class of optimization technique named fuzzy fractional programming problem is considered in this work when the coefficients of objective function are fuzzy. New ranking function is proposed and used to convert the data of the fuzzy fractional programming problem from fuzzy number to crisp number so that the shortcoming when treating the original fuzzy problem can be avoided. Here a novel ranking function approach of ordinary fuzzy numbers is adopted for ranking of triangular fuzzy numbers with simpler and easier calculations as well as shortening in the procedures. The fuzzy fractional programming problem is the first reduced to a fractional programming problem and then solved with the technique to obtain the optimal solution. It has a power to give a best solution for supporting the solution theory proposed in this work, some numerical fuzzy fractional programming problem are included to ensure the advantage, efficiency and accuracy of the suggested algorithm. In addition, this research paper describes a comparison between our optimal solutions with other existing solutions for inequalities constrains fuzzy fractional program

    Chromatic PAC-Bayes Bounds for Non-IID Data: Applications to Ranking and Stationary β\beta-Mixing Processes

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    Pac-Bayes bounds are among the most accurate generalization bounds for classifiers learned from independently and identically distributed (IID) data, and it is particularly so for margin classifiers: there have been recent contributions showing how practical these bounds can be either to perform model selection (Ambroladze et al., 2007) or even to directly guide the learning of linear classifiers (Germain et al., 2009). However, there are many practical situations where the training data show some dependencies and where the traditional IID assumption does not hold. Stating generalization bounds for such frameworks is therefore of the utmost interest, both from theoretical and practical standpoints. In this work, we propose the first - to the best of our knowledge - Pac-Bayes generalization bounds for classifiers trained on data exhibiting interdependencies. The approach undertaken to establish our results is based on the decomposition of a so-called dependency graph that encodes the dependencies within the data, in sets of independent data, thanks to graph fractional covers. Our bounds are very general, since being able to find an upper bound on the fractional chromatic number of the dependency graph is sufficient to get new Pac-Bayes bounds for specific settings. We show how our results can be used to derive bounds for ranking statistics (such as Auc) and classifiers trained on data distributed according to a stationary {\ss}-mixing process. In the way, we show how our approach seemlessly allows us to deal with U-processes. As a side note, we also provide a Pac-Bayes generalization bound for classifiers learned on data from stationary φ\varphi-mixing distributions.Comment: Long version of the AISTATS 09 paper: http://jmlr.csail.mit.edu/proceedings/papers/v5/ralaivola09a/ralaivola09a.pd
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