In this paper we present a family of multi-objective hypergraph partitioning algorithms based on the multilevel paradigm, which are capable of producing solutions in which both the cut and the maximum subdomain degree are simultaneously minimized. This type of partitionings are critical for existing and emerging applications in VLSI CAD as they allow to both minimize and evenly distribute the i...

Understanding finite-size effects is one of the key open questions in solving planar AdS/CFT. In this paper we discuss these effects in the AdS5×S string theory at one-loop in the world-sheet coupling. First we provide a very general, efficient way to compute the fluctuation frequencies, which allows to determine the energy shift for very general multi-cut solutions. Then we apply this to two-c...

In this paper, a new approach for solving the second order fuzzy differential equations (FDE) with fuzzy initial value, under strongly generalized H-differentiability is presented. Solving first order fuzzy differential equations by extending 1-cut solution of the original problem and solving fuzzy integro-differential equations has been investigated by some authors (see for example cite{darabi...

a significant portion of gross domestic production (gdp) in any country belongs to the transportation system. transportation equipment, in the other hand, is supposed to be great consumer of oil products. many attempts have been assigned to the vehicles to cut down greenhouse gas (ghg). in this paper a novel heuristic algorithm based on clark and wright algorithm called green clark and wright (...

Graph processing has become an integral part of big data analytics. With the ever increasing size of the graphs, one needs to partition them into smaller clusters, which can be managed and processed more easily on multiple machines in a distributed fashion. While there exist numerous solutions for edge-cut partitioning of graphs, very little effort has been made for vertex-cut partitioning. Thi...

The Split Delivery Vehicle Routing Problem with Time Windows (SDVRPTW) is a notoriously hard combinatorial optimization problem. First, it is hard to find a useful compact Mixed-Integer Programming (MIP) formulation for the SDVRPTW. Standard modeling approach either suffer from inherent symmetries (MIPs with a vehicle index) or cannot exactly capture all aspects of feasibility. Due to the possi...

In graph clustering methods, MinMax Cut tends to provide more balanced clusters as compared to Ratio Cut and Normalized Cut. The traditional approach used spectral relaxation to solve the graph cut problem. The main disadvantage of this approach is that the obtained spectral solution has mixed signs, which could severely deviate from the true solution and have to resort to other clustering meth...

In a domain with cut static boundary-value problems of piezoelectricity are investigated. The existence and uniqueness of solutions of the considered boundary value problems are proved and an asymptotic expansion of solutions near the edges of the cut are obtained. Let Ω and Ω1 (Ω1 ⊂ Ω) be a bounded domains in the three-dimensional Euclidean space R with infinitely smooth boundaries ∂Ω and ∂Ω1,...

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...