The problem that this paper investigates, namely, optimization of overlay computing systems, follows naturally from growing need for effective processing and consequently, fast development of various distributed systems. We consider an overlay-based computing system, i.e., a virtual computing system is deployed on the top of an existing physical network (e.g., Internet) providing connectivity between computing nodes. The main motivation behind the overlay concept is simple provision of network functionalities (e.g., diversity, flexibility, manageability) in a relatively cost-effective way as well as regardless of physical and logical structure of underlying networks. The workflow of tasks processed in the computing system assumes that there are many sources of input data and many destinations of output data, i.e., many-to-many transmissions are used in the system. The addressed optimization problem is formulatedin the form of an ILP (Integer Linear Programing) model. Since the model is computationally demanding and NP-complete, besides the branch-and-bound algorithm included in the CPLEX solver, we propose additional cut inequalities. Moreover, we present and test two effective heuristic algorithms: tabu search and greedy. Both methods yield satisfactory results close to optimal.
We derive exact and approximate controllability conditions for the linear one-dimensional heat equation in an infinite and a semi-infinite domains. The control is carried out by means of the time-dependent intensity of a point heat source localized at an internal (finite) point of the domain. By the Green’s function approach and the method of heuristic determination of resolving controls, exact controllability analysis is reduced to an infinite system of linear algebraic equations, the regularity of which is sufficient for the existence of exactly resolvable controls. In the case of a semi-infinite domain, as the source approaches the boundary, a lack of L2-null-controllability occurs, which is observed earlier by Micu and Zuazua. On the other hand, in the case of infinite domain, sufficient conditions for the regularity of the reduced infinite system of equations are derived in terms of control time, initial and terminal temperatures. A sufficient condition on the control time, heat source concentration point and initial and terminal temperatures is derived for the existence of approximately resolving controls. In the particular case of a semi-infinite domain when the heat source approaches the boundary, a sufficient condition on the control time and initial temperature providing approximate controllability with required precision is derived.
In the paper, we present a coordinated production planning and scheduling problem for three major shops in a typical alloy casting foundry, i.e. a melting shop, molding shop with automatic line and a core shop. The castings, prepared from different metal, have different weight and different number of cores. Although core preparation does not required as strict coordination with molding plan as metal preparation in furnaces, some cores may have limited shelf life, depending on the material used, or at least it is usually not the best organizational practice to prepare them long in advance. Core shop have limited capacity, so the cores for castings that require multiple cores should be prepared earlier. We present a mixed integer programming model for the coordinated production planning and scheduling problem of the shops. Then we propose a simple Lagrangian relaxation heuristic and evolutionary based heuristic to solve the coordinated problem. The applicability of the proposed solution in industrial practice is verified on large instances of the problem with the data simulating actual production parameters in one of the medium size foundry.
The paper presents a novel Iterated Local Search (ILS) algorithm to solve multi-item multi-family capacitated lot-sizing problem with setup costs independent of the family sequence. The model has a direct application to real production planning in foundry industry, where the goal is to create the batches of manufactured castings and the sequence of the melted metal loads to prevent delays in delivery of goods to clients. We extended existing models by introducing minimal utilization of furnace capacity during preparing melted alloy. We developed simple and fast ILS algorithm with problem-specific operators that are responsible for the local search procedure. The computational experiments on ten instances of the problem showed that the presence of minimum furnace utilization constraint has great impact on economic and technological conditions of castings production. For all test instances the proposed heuristic is able to provide the results that are comparable to state-of-the art commercial solver.
The problem of sequencing jobs on a single machine to minimize total cost (earliness and tardiness) is nowadays not just important due to traditional concerns but also due to its importance in the context of Collaborative Networked Organizations and Virtual Enterprises, where precision about promptly responses to customers’ requests, along with other important requirements, assume a crucial role. In order to provide a contribution in this direction, in this paper the authors contribute with an applied constructive heuristics that tries to find appropriate solutions for single machine scheduling problems under different processing times and due dates, and without preemption allowed. In this paper, two different approaches for single-machine scheduling problems, based on external and internal performance measures are applied to the problem and a comparative analysis is performed. Computational results are presented for the problem under Just-in-Time and agile conditions on which each job has a due date, and the objective is to minimize the sum of holding costs for jobs completed before their due date and tardiness costs for jobs completed after their due date. Additional computational tests were developed based on different customer and enterprise oriented performance criteria, although preference is given to customer-oriented measures, namely the total number of tardy jobs and the maximum tardiness.
The results presented here are twofold. First, a heuristic algorithm is proposed which, through removing some unnecessary arcs from a digraph, tends to reduce it into an adjoint and thus simplifies the search for a Hamiltonian cycle. Second, a heuristic algorithm for DNA sequence assembly is proposed, which uses a graph model of the problem instance, and incorporates two independent procedures of reducing the set of arcs - one of them being the former algorithm. Finally, results of tests of the assembly algorithm on parts of chromosome arm 2R of Drosophila melanogaster are presented.