Exact algorithms

The preferable theoretical tools for the description of dynamical processes in systems of a few atoms are certainly quantum mechanical calculations. There is a large arsenal of powerful, well established methods for quantum mechanical computations of processes such as photoexcitation, photodissociation, inelastic scattering and reactive collisions for systems having, in the present state-of-the-art, up to three or four atoms, typically. " Both time-dependent and time-independent numerically exact algorithms are available for many of the processes, so in cases where potential surfaces of good accuracy are available, excellent quantitative agreement with experiment is generally obtained. In addition to the full quantum-mechanical methods, sophisticated semiclassical approximations have been developed that for many cases are essentially of near-quantitative accuracy and certainly at a level sufficient for the interpretation of most experiments.These methods also are com-... 

Before a new stage decomposition based hybrid evolutionary algorithm is proposed in Section 9.4, we briefly review the algorithm for general 2S-MILPs of Caroe and Schultz [11] which is regarded as the state-of-the-art exact algorithm for 2S-MILPs... 

Puchinger, J. and Raidl, G. (2005) Combining Metaheuristics and Exact Algorithms in Combinatorial Optimization ... 

Variations of two exact algorithms (algorithms that will always find the optimal solution) are commonly used. The first is to search exhaustively through all possible tree topologies for the best solution(s). This method is computationally simple for 9 or fewer taxa (for which there are 135,135 labeled, unrooted, bifurcating trees) and is only moderately time-consuming for 10 or 11 taxa (2,027,025 and 34,459,425 trees, respectively).2 For 12 taxa, the evaluation becomes laborious (654,729,075 trees), and for 13 or more taxa (a 13,749,310,575 trees) the calculations are usually impractical. The chief advantages of exhaustive searches are (1) the optimal tree(s) is always found and (2) all other possibilities can be ranked with respect to the optimal solution(s). 

If the exact algorithms described above are not feasible for a given data set (the limitation is usually number of taxa), then various heuristic approaches can be tried. The heuristics used should be described in sufficient detail that they can be replicated, and so that alternative searches can be attempted. It is also worthwhile to discuss the number of alternative solutions examined, to give a sense of the thoroughness of the search. 

Carraghan R, Pardalos PM. Exact algorithm for the maximum clique problem. Oper Res Lett 1990 9 375-382. 

Existing exact algorithms for the VRPTW have been reported to solve problems with up to 100 stops. However, the problems encountered in parcel dehvery are often substantially larger than this. Moreover, these problems need to be solved quickly because of the short-term planning horizon. For these reasons, much of the work in this area has focused on the development of heuristic algorithms— algorithms that attempt to find good solutions instead of optimal solutions. 

Logistics network configuration Simulation, heuristics, exact algorithms... 

Evolutionary computation, see Genetic algorithms E-work, 606 Exact algorithms, 2014 Exchange rates, 2401 Excite, 266, 272 Exclusive distribution, 2129 Execution, gulf of, 1018 Executive decision support systems, see Group decision support systems Executive information systems (EIS), 84 Executive sponsorship (of ISE), 22-23 Expansion flexibility, 499 Expectation, principle of (decision theory), 2377-2378... 

Zhang and Li (2007) presented an article that analyzes multi-periodic vehicle fleet size and routing problem, and dynamic vehicle fleet size. The authors decompose the model with Dantzig-Wolf decomposition method, and derive an exact algorithm for the model based on simplex method, dynamic programming method, and branch and bound method. 

Zhang Y, Li J (2007) Dynamic optimal model of vehicle fleet size and exact algorithm. Syst Eng Theory Pract 27(02) 83-91... 

Golhar and Sarker (1992) and Jamal and Sarker (1993) consider the basic model under policy (a) with the assumption that the conversion rate from raw material to final product is one to one. Two cases are considered (i) Imperfect matching - production uptime and cycle time are not exact integer multiples of finished product delivery cycle (ii) Perfect matching the above numbers are integers. An iterative heuristic is used to solve the problem. Sarker and Parija (1994) consider exactly the same problem except that the conversion rate from raw material to final product is not assumed to be one to one. An exact algorithm is proposed. 

From these equations Keller [7] suggests an exact algorithm for the solution of (4.4). It consists of successive steps for the solution of the Schur complement equation and finally a backward solution to determine Ax. Chan [5] further develops this algorithm using specific approximations of the vector p and the matrix C. To get an impression of his method we want to present his suggestion on the computation of p. Since... 

VRP is considered an VP-hard problem that requires long computational time to solve by the exact algorithm if the problem size is large. As an alternative, metaheuristic approaches can provide good quality solution to VP-hard problem with a reasonable solution time and many metaheuristic approaches have been applied to deal with the variants of VRPs. 

HIS uses a modified global data-flow analysis based loosely on du-chaining (definition-use) [2]. Since most high-level synthesis literature does not address this step in detail and often restricts it to so called basic blocks (e.g., [38]), and since data-flow analysis can be computationally expensive, we include the exact algorithm used below. It first computes the reachability for each value assigned and then its lifetime. HIS performs global data-flow analysis not restricted to basic blocks. In this case the control flow (conditional execution and iteration) must be taken into account ... 

---