Integer linear fractional programming problem with multiple objective MOILFP is an important field of research and has not received as much attention as did multiple objective linear fractional programming. In this work, we develop a branch and cut algorithm based on continuous fractional optimization, for generating the whole integer efficient solutions of the MOILFP problem. The basic idea of the computation phase of the algorithm is to optimize one of the fractional objective functions, then generate an integer feasible solution. Using the reduced gradients of the objective functions, an efficient cut is built and a part of the feasible domain not containing efficient solutions is truncated by adding this cut. A sample problem is solved using this algorithm, and the main practical advantages of the algorithm are indicated.
In this paper, a branch and bound multi-objective based method is proposed for reaching the non-dominated set. Two types of nodes are considered in the tree-search. The first type characterises the non-integer solutions found which are transformed to integer solutions by applying a branching procedure. The second type of nodes contains an integer solution and in this case efficient cuts are established in order either to remove dominated integer vectors or to fathom them. The method is compared advantageously with two exact methods of the literature tailored for the general case and also analysed computationally on benchmarks of MCDM library.Keywords: branch and bound; multi-objective programming; nondominated solution.Reference to this paper should be made as follows: Abbas, M., Chergui, M.E-A. and Mehdi, M.A. (2012) 'Efficient cuts for generating the non-dominated vectors for Multiple Objective Integer Linear Programming', Int.
Efficient cuts for generating the non-dominated vectors for MOILP
303of Mathematics and Laboratory LAID3, USTHB, his research interests include mathematical technics and tools for combinatorial optimisation problems. He works on modelling and solving real-world problems as an expert and develops exact and metaheuristic methods for multiobjective discrete optimisation problems. His recent works are focused on Multiobjective Combinatorial Optimisation (MOCO) in linear, hyperbolic and quadratic cases.Meriem Ait Mehdi received her Master's Degree in Operation Research from the
We investigate some results about mean-inequalities involving a large number of bivariate means. As application, we derive a lot of inequalities between four or more means among the standard means known in the literature.
Business process modeling notation (BPMN) is a widely used business model process. The importance of security is apparent, but traditionally, it is considered after the business processes definition. There is a need for integrated tools and a methodology that allows for specifying and enforcing compliance and security requirements for business process-driven enterprise systems. Therefore, it is very important to capture the security requirements at conceptual stage in order to identify the security needs. BPMN is lacking the ability to model and present security concepts. This will increase the vulnerability of the system and make the future development of security for the system more difficult. This article proposes a novel extension to BPMN notation based on cyber security ontologies. The authors incorporate visual constructs for modeling security requirements. In order to provide a commonly usable extension, these enhancements were implemented as BPMN metamodel extension. The authors illustrate capabilities and benefits of extension with a real-life example.
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