Scheduling the maintenances of nuclear power plants is a complex optimization problem, formulated in 2-stage stochastic programming for the EURO ROADEF 2010 challenge. The first level optimizes the maintenance dates and refueling decisions. The second level optimizes the production to fulfill the power demands and to ensure feasibility and costs of the first stage decisions. This paper solves a deterministic version of the problem, studying Mixed Integer Programming (MIP) formulations and matheuristics. Relaxing only two sets of constraints of the ROADEF challenge, a MIP formulation can be written using only binary variables for the maintenance dates. The MIP formulations are used to design constructive matheuristics and a Variable Neighborhood Descent (VND) local search. These matheuristics produce very high quality solutions. Some intermediate results explains results of the Challenge: the relaxation of constraints CT6 are justified and neighborhood analyses with MIP-VND justifies the choice of neighborhoods to implement for the problem. Lastly, an extension with stability costs for monthly reoptimization is considered, with efficient bi-objective matheuristics.
(2013) considered an exact formulation of CT6 constraints, in a CG approach dualizing coupling constraints among units @cite_6 , i.e. CT1 demands and CT14 to CT21 scheduling constraints. The MIP considered a unique scenario, the average one, with production time steps aggregated weekly. The CG approach is deployed to compute a LP relaxation relaxing scheduling constraints CT14-CT21, with subproblems solved by dynamic programming. The further CG heuristic incorporate these scheduling constraints in the integer resolution with the columns generated. The solution of this MIP gives the outage dates and week where the CT6 constraints are activated, the final cost and feasibility issues for the whole problem are given computing the production by Linear Programming (LP). This approach was one of the most effective for the challenge, up to $2
@cite_6
1605513453 2015462215 2074208271 2048441570
Consideration is given to the problem of nonpreemptively scheduling a set of N independent tasks to a system of M identical processors, with the objective to minimize the overall finish time. Since this problem is known to be NP-Hard, and hence unlikely to permit an efficient solution procedure, heuristic algorithms are studied in an effort to provide near-optimal results. Worst-case analysis is used to gauge the worth of a scheduling procedure. For a particular algorithm, an upper bound is sought for the length of its schedule expressed relative to an optimal assignment of tasks to processors. Departing from more traditional schemes of only determining an algorithm's worst-case performance bound, the work contained herein focuses on modifying a scheduling heuristic for "bad" regions of the input space, thereby improving its worst-case bound. It is shown that rather simple alterations, having little effect on the run-time of an algorithm, may guarantee a significantly better behavior. The O 1-INTERCHANGE heuristic is improved so that, while its time complexity is still O(NlogM), its worst-case performance bound is reduced from 2 to 4 3 times optimal. The familiar LPT algorithm is altered so that, while its time complexity is still O(NlogN), its worst-case bound is reduced from 4 3 to 5 4 times optimal. The major effort of this research is devoted to proving that the MULTIFIT heuristic can be modified, without increasing its time complexity from O(NlogN), so that its worst-case performance bound is reduced from some value in the range 13 11, 6 5 to 72 61 times optimal, a better bound as of this writing than that yielded by any other known polynomial-time algorithm. Abstract The problem of locating hub facilities and allocating non-hub nodes to those hubs arises frequently in the design of communication networks, airline passenger flow and parcel delivery networks. In this paper we consider uncapacitated multiple and single allocation p -hub median problems. We develop new mixed 0 1 linear formulations with tight linear programming relaxations. The approach is tested on a well known and heavily used benchmark data set of real-world problems with resulting LP relaxations ranging from 10010 to 391 250 variables and from 2 101 to 31 901 constraints, which proved to be difficult linear programs. Yet, this approach proved to be very effective: in almost all instances the linear programming solution was integer. In cases with fractional solutions, the integrality was achieved by adding a small partial set of integrality constraints. Therefore, we extended the range of optimally solvable instances of these NP-hard hub location problems, which have defied researchers for the last ten years. As an additional result for the single allocation case we were able to establish optimality of all heuristic solutions obtained via tabu search algorithm from a previous study. For the more difficult single allocation p -hub median problem we also used the best known heuristic solution as a guidance in adding integrality constraints. This novel linkage between optimal and heuristic solutions has a potential impact in a number of other problem settings, where efficient heuristic solutions exist and are probably, but not provably optimal. We present a framework for robustly estimating registration between a 3D volume image and a 2D projection image and evaluate its precision and robustness in spine interventions for vertebral localization in the presence of anatomical deformation. The framework employs a normalized gradient information similarity metric and multi-start covariance matrix adaptation evolution strategy optimization with local-restarts, which provided improved robustness against deformation and content mismatch. The parallelized implementation allowed orders-of-magnitude acceleration in computation time and improved the robustness of registration via multi-start global optimization. Experiments involved a cadaver specimen and two CT datasets (supine and prone) and 36 C-arm fluoroscopy images acquired with the specimen in four positions (supine, prone, supine with lordosis, prone with kyphosis), three regions (thoracic, abdominal, and lumbar), and three levels of geometric magnification (1.7, 2.0, 2.4). Registration accuracy was evaluated in terms of projection distance error (PDE) between the estimated and true target points in the projection image, including 14 400 random trials (200 trials on the 72 registration scenarios) with initialization error up to ±200 mm and ±10°. The resulting median PDE was better than 0.1 mm in all cases, depending somewhat on the resolution of input CT and fluoroscopy images. The cadaver experiments illustrated the tradeoff between robustness and computation time, yielding a success rate of 99.993 in vertebral labeling (with 'success' defined as PDE <5 mm) using 1,718 664 ± 96 582 function evaluations computed in 54.0 ± 3.5 s on a mid-range GPU (nVidia, GeForce GTX690). Parameters yielding a faster search (e.g., fewer multi-starts) reduced robustness under conditions of large deformation and poor initialization (99.535 success for the same data registered in 13.1 s), but given good initialization (e.g., ±5 mm, assuming a robust initial run) the same registration could be solved with 99.993 success in 6.3 s. The ability to register CT to fluoroscopy in a manner robust to patient deformation could be valuable in applications such as radiation therapy, interventional radiology, and an assistant to target localization (e.g., vertebral labeling) in image-guided spine surgery. General-purpose graphics processing units (GPGPUs) are at their best in accelerating computation by exploiting abundant thread-level parallelism (TLP) offered by many classes of HPC applications. To facilitate such high TLP, emerging programming models like CUDA and OpenCL allow programmers to create work abstractions in terms of smaller work units, called cooperative thread arrays (CTAs). CTAs are groups of threads and can be executed in any order, thereby providing ample opportunities for TLP. The state-of-the-art GPGPU schedulers allocate maximum possible CTAs per-core (limited by available on-chip resources) to enhance performance by exploiting TLP. However, we demonstrate in this paper that executing the maximum possible number of CTAs on a core is not always the optimal choice from the performance perspective. High number of concurrently executing threads might cause more memory requests to be issued, and create contention in the caches, network and memory, leading to long stalls at the cores. To reduce resource contention, we propose a dynamic CTA scheduling mechanism, called DYNCTA, which modulates the TLP by allocating optimal number of CTAs, based on application characteristics. To minimize resource contention, DYNCTA allocates fewer CTAs for applications suffering from high contention in the memory sub-system, compared to applications demonstrating high throughput. Simulation results on a 30-core GPGPU platform with 31 applications show that the proposed CTA scheduler provides 28 average improvement in performance compared to the existing CTA scheduler.