Optimization of Multiple-Rendezvous Low-Thrust Missions on General-Purpose Graphics Processing Units

A massively parallel method for the identification of optimal sequences of targets in multiple-rendezvous low-thrust missions is presented. Given a list of possible targets, a global search of sequences compatible with the mission requirements is performed. To estimate the feasibility of each transfer, a heuristic model based on Lambert's transfers is evaluated in parallel for each target, making use of commonly available general-purpose graphics processing units such as the Nvidia Tesla cards. The resulting sequences are ranked by user-specified criteria such as length or fuel consumption. The resulting preliminary sequences are then optimized to a full low-thrust trajectory using classical methods for each leg. The performance of the method is discussed as a function of various parameters of the algorithm. The efficiency of the general-purpose graphics processing unit implementation is demonstrated by comparing it with a traditional CPU-based branch-and-bound method. Finally, the algorithm is used to compute asteroid sequences used in a solution submitted to the seventh edition of the Global Trajectory Optimization Competition

Exact And Representative Algorithms For Multi Objective Optimization

In most real-life problems, the decision alternatives are evaluated with multiple conflicting criteria. The entire set of non-dominated solutions for practical problems is impossible to obtain with reasonable computational effort. Decision maker generally needs only a representative set of solutions from the actual Pareto front. First algorithm we present is for efficiently generating a well dispersed non-dominated solution set representative of the Pareto front which can be used for general multi objective optimization problem. The algorithm first partitions the criteria space into grids to generate reference points and then searches for non-dominated solutions in each grid. This grid-based search utilizes achievement scalarization function and guarantees Pareto optimality. The results of our experimental results demonstrate that the proposed method is very competitive with other algorithms in literature when representativeness quality is considered; and advantageous from the computational efficiency point of view. Although generating the whole Pareto front does not seem very practical for many real life cases, sometimes it is required for verification purposes or where DM wants to run his decision making structures on the full set of Pareto solutions. For this purpose we present another novel algorithm. This algorithm attempts to adapt the standard branch and bound approach to the multi objective context by proposing to branch on solution points on objective space. This algorithm is proposed for multi objective integer optimization type of problems. Various properties of branch and bound concept has been investigated and explained within the multi objective optimization context such as fathoming, node selection, heuristics, as well as some multi objective optimization specific concepts like filtering, non-domination probability, running in parallel. Potential of this approach for being used both as a full Pareto generation or an approximation approach has been shown with experimental studies

A parallel interval arithmetic-based reliable computing method on a GPU

Video cards have now outgrown their purpose of being only a simple tool for graphic display. With their high speed video memories, lots of maths units and parallelism, they can be very powerful accessories for general purpose computing tasks. Our selected platform for testing is the CUDA (Compute Unified Device Architecture), which offers us direct access to the virtual instruction set of the video card, and we are able to run our computations on dedicated computing kernels. The CUDA development kit comes with a useful toolbox and a wide range of GPU-based function libraries. In this parallel environment, we implemented a reliable method based on the Branch-and-Bound algorithm. This algorithm will give us the opportunity to use node level (also called low-level or type 1) parallelization, since we do not modify the searching trajectories; nor do we modify the dimensions of the Branch-and-Bound tree [5]. For testing, we chose the circle covering problem. We then scaled the problem up to three dimensions, and ran tests with sphere covering problems as well

B-LOG: A branch and bound methodology for the parallel execution of logic programs

We propose a computational methodology -"B-LOG"-, which offers the potential for an effective implementation of Logic Programming in a parallel computer. We also propose a weighting scheme to guide the search process through the graph and we apply the concepts of parallel "branch and bound" algorithms in order to perform a "best-first" search using an information theoretic bound. The concept of "session" is used to speed up the search process in a succession of similar queries. Within a session, we strongly modify the bounds in a local database, while bounds kept in a global database are weakly modified to provide a better initial condition for other sessions. We also propose an implementation scheme based on a database machine using "semantic paging", and the "B-LOG processor" based on a scoreboard driven controller