Vector bin packing with heterogeneous bins: application to the machine reassignment problem

The two-dimensional heterogeneous vector bin packing problem (2DHet-VBPP) consists of packing the set of items into the set of various type bins, respecting their two resource limits. The problem is to minimize the total cost of all bins. The problem, known to be NP-hard, can be formulated as a pure integer linear program, but optimal solutions can be obtained by the CPLEX Optimizer engine only for small instances. This paper proposes a metaheuristic approach to the 2DHet-VBPP, based on Reduced variable neighborhood search (RVNS). All RVNS elements are adapted to the considered problem and many procedures are designed to improve efficiency of the method. As the Two-dimensional Homogeneous-VBPP (2DHom-VBPP) is more often treated, we considered also a special version of the RVNS algorithm to solve the 2DHom-VBPP. The results obtained and compared to both CPLEX results and results on benchmark instances from literature, justify the use of the RVNS algorithm to solve large instances of these optimization problems.

Approximation and online algorithms for multidimensional bin packing: A survey

We address the machine reassignment problem proposed in the context of the ROADEF/EURO challenge 2012 in partnership with Google. The problem consists in reassigning a set of processes to a set of multiple-resource machines so as to minimize a weighted function of the machines load, the resources balance, and the costs of moving processes while satisfying numerous constraints. We propose an optimization-based heuristic that requires decomposing the problem into a sequence of small-sized instances that are iteratively solved using a general MIP solver. To speed-up the solution process several algorithmic expedients are embedded. Extensive computational experiments provide evidence that the proposed approach exhibits a very good performance.

On data reduction for dynamic vector bin packing

Railway crew scheduling deals with generating driver duties for a given train timetable such that all work regulations are met and the resulting schedule has minimal cost. Typical problem instances in the freight railway industry require the generation of duties for thousands of drivers operating tens of thousands of trains per week. Due to short runtime requirements, common solution approaches decompose the optimization problem into smaller subproblems that are solved separately. Several studies have shown that the way of decomposing the problem significantly affects the solution quality. An overall best decomposition strategy for a freight railway crew scheduling problem, though, is not known. In this paper, we present general considerations on when to assign two scheduled train movements to separate subproblems (and when to rather assign them to the same subproblem) and deduct a graph partitioning based decomposition algorithm with several variations. Using a set of real-world problem instances from a major European railway freight carrier, we evaluate our strategy and benchmark the performance of the decomposition algorithm both against a common non-decomposition algorithm and a lower bound on the optimal solution schedule. The test runs show that our decomposition algorithm is capable of producing high-quality solution schedules while significantly cutting runtimes compared to the non-decomposition solution algorithm. We are following a "greenfield" approach, where no information on previous schedules is needed. Hence, our approach is applicable to any railway crew scheduling setting, including network enlargement, integration of new customers, etc.

A proposed approach is specialized for large scale vehicle routing problems(VRPs) and based on area segmentation and gradual area integration mechanisms so as to avoid combinatorial explosion. The purpose of the proposed approach is to deconstruct large scale problem into small size sub-problems and gradually restore these to original state. Firstly, an original large scale problem is divided into some small sub-areas and optimal solutions in each sub-area are derived. When a best incumbent solution remains unchanged for a certain period, subareas are gradually integrated and new optimal solutions in a new integrated sub-area are newly searched through use of the obtained solutions in previous sub area. This gradual integration and optimization are iterated until every sub-area are integrated into the one (the original problem), and the optimal solution of original problem can be obtained at this time. The proposed approach aims to deconstruct large scale problem into small size sub-problems and perform more efficient search. Through some typical test problems, it was demonstrated that our approach could derive better results more effectively than conventional approach.

In this article, we present a QR updating procedure as a solution approach for linear least squares problem with equality constraints. We reduce the constrained problem to unconstrained linear least squares and partition it into a small subproblem. The QR factorization of the subproblem is calculated and then we apply updating techniques to its upper triangular factor R to obtain its solution. We carry out the error analysis of the proposed algorithm to show that it is backward stable. We also illustrate the implementation and accuracy of the proposed algorithm by providing some numerical experiments with particular emphasis on dense problems.

Linguistic Geometry for autonomous navigation

The application of a parallelized multilevel fast multipole method (MLFMM) is described and illustrated through examples for the solution of large scale and complex EMC problems. Furthermore, to reduce the modeling complexity of such EMC problems, we propose a combination of field with network theory to split large problems into smaller sub-problems which can be analyzed individually and then again assembled together by means of network theory.

Optimization problems are very complex to be solved, as they can present multiple optimal solutions and, in certain cases, only a globally optimal solution. The mathematical formulation of these problems is composed of continuous and discrete variables with linear and nonlinear functions. The solution of these problems by mathematical modeling through solvers may not converge to a feasible solution or may demand much computational time, when many variables are considered. Thus, using metaheuristics to solve these problems is desirable according to the literature. The scatter search (SS) metaheuristic algorithm has been highlighted in the literature as an excellent combinatorial optimization algorithm for dealing with quality and diversity solutions. This work aims to present two methods using the SS algorithm to solve problems with continuous and discrete variables. Therefore, the SS algorithm is implemented to solve the traveling salesperson problem (TSP), which is a problem that contains only discrete variables, and also, another version of SS is implemented to solve the optimal power flow (OPF) problem, which has continuous and discrete variables. Two instances of the TSP and three instances of the OPF problem were used. The results show that the SS solves both problems efficiently and presents better results in some cases than the solutions of the same problems using classical mathematical models through solvers. It is concluded that implementing the SS algorithm does not require much effort and that good results can be achieved for solving optimization problems with variables of any nature.

We study the problem of virtual machine (VM) placement and migration in a data center. In the current approaches, VMs are assigned to physical servers using on-demand provisioning. Such an approach is simple but it often results in a poor performance due to resource fragmentation. Additionally, sub-optimal VM placement usually generates unneeded VM migration and unnecessary cross network traffic. The efficiency of a datacenter therefore significantly depends on how VMs are provisioned and where they are placed. A good placement scheme will not only improve the quality of service but also reduce the operation cost of the data center. In this paper, we study the problem of optimal VM placement and migration to minimize resource usage and power consumption in a data center. We formulate the optimization problem as a joint multiple objective function and solve it by leveraging the framework of convex optimization. Due to the intractable nature of the combinatorial optimization, we then propose Multi-level Join VM Placement and Migration (MJPM) algorithms based on the relaxed convex optimization framework to approximate the optimal solution. The theoretical analysis demonstrates the effectiveness of our proposed algorithms that substantially increases data center efficiency. In addition, our extensive simulation results on different practical topologies show significant performance improvement over the existing approaches.

Objectives: Hardware virtualization is an evolving technology, because it has the potential to facilitate the consolidation of multiple workloads on a single physical host directly through cloud. We introduce the First-Last algorithm to minimize energy consumption and migration. Methods: The problem is treated as an instance of bin packing algorithm which focuses on saving energy. However the overloading of active hosts and the resultant migration are the drawbacks of this approach. This algorithm was tested on a set of heterogeneous virtual machines which have demands in both single and multi-dimension and came either statically or dynamically to the server. Findings: The virtual machine placement problem can be treated as a bin packing problem, wherein the physical machines/hosts are the bins and the virtual machines are the objects. It can then be solved through various approaches such as first fit, best fit, next fit et cetera. Using the first fit algorithm, the virtual machine is placed into the first active host which can accommodate it. If none of the active hosts satisfy the VM’s demand, then a new host is made active. In the best fit method, all the active hosts are checked first and then the host which would suffer minimum resource wastage upon VM placement is chosen. Next fit algorithm places the VM in the last /most recently activated host. While first fit is best suited for optimal performance, best fit keeps the least number of hosts active, thereby saving energy but at the cost of performance since migration overhead increases. Next fit approach would fail unless the virtual machines have been arranged in the increasing order of their demands. The firstlast algorithm that we introduce balances on energy consumption as well as performance by reducing migration. It also reduces the time complexity to a certain extent. Applications: The algorithm has a comparatively lower time complexity than the existing virtual machine placement algorithms. It also reduces the energy consumption as well as migration to a certain extent.

[Purpose] Server virtualization technology is the basic form for the cloud data center to serve customers. While the cloud data center reduces the SLA violations in the early stage, the increase in the utilization of resources such as virtual machine servers and network equipment and decrease in energy consumption have become an important issue for reduction of operating costs. Therefore, on the background of the cloud data center network based on SDN technology, this paper studies a cloud data center resource utilization and energy consumption optimization strategy through virtual machine migration and integration. [Method] The technology based on SDN is firstly introduced, the approximate optimal solution FFD algorithm for the multidimensional vector bin packing problem is then presented, the Partheno-Genetic Algorithm (PGA) is then recommended, finally a Hybrid Partheno genetic Algorithm (HPGA) based on the both is established and a mathematic model is created. [Results] By combining the advantages of FFD and PGA, this paper improves the utilization of the resources of the entire cloud data center, reduces energy consumption, and prevents the occurrence of computing “hot spots”. [Conclusion] Experiments in CloudSim prove the effectiveness of the algorithm. Compared with FFD and PGA algorithms, it is able to enhance the efficiency of the Data Center effectively, and obtain the optimal solution more quickly, thereby balancing the physical resources of the server.

Energy efficiency is one of the important issues in green cloud data centers (DCs). In this context, a virtual machine (VM) placement is one of the important techniques which can be used to achieve energy efficiency in such environments. Bio-inspired optimization algorithms are widely used in the literature to solve the VM placement (VMP) problem and different types of them are benefited to achieve energy efficiency while meeting Quality of Service (QoS) and user-specified constraints such as deadlines and cost. This paper presents a comprehensive survey and taxonomy of the bio-inspired VMP schemes. For this purpose, we first provide the essential concepts regarding the VMP and describe various objectives and factors which can be considered in this process. Then, we provide a taxonomy of VMP schemes regarding their applied optimization algorithms and compare their employed factors in the VMP process as well as simulator environments and the metrics which have been utilized in the verification of the investigated VMP frameworks. Finally, the concluding remarks and future researches directions are provided.

Energy-efficient virtual machine placement in data centres via an accelerated Genetic Algorithm with improved fitness computation