Ordered branch searches

Example 14.6. Use the ordered branch search method to determine the optimal sequence for the problem of Example 14.2. 

The following cost data, which include operating cost and depreciation of capital investment, pertain to Problem 14.1. Determine by the ordered branch search technique ... 

Annual cost data for all the possible splits are given below. Use the ordered branch search technique to determine ... 

In the context of liquid-vapor coexistence the particle number N (or equivalently the number density p = N/V) plays the role of an order parameter. Estimates of the distribution Po N p, T) are available from the simulation for all the points chosen to define the path. One may then identify the free energy difference from the integrated areas of the branches of this distribution associated with each phase and proceed to search for coexistence using the criterion that these integrated areas should be equal ((8) et seq.). Figure 2 show some explicit results [41] for a Lennard-Jones fluid. 

In order to derive precursor compounds, SYNLMA must search the reaction rule data base and match the goal compound with the product side of a reaction rule. This process begins at the top layer, which builds the problem solving tree. It calls the middle layer to add a new branch to the tree. 

Within a search tree, the computational time for detecting the largest MCSS candidates depends on the order of its branches. Appropriate rearrangement of the... 

Heuristic searches usually guarantee neither a global optimal solution nor a bound on the error when computation stops because they make preemptive moves—moves for which there are viable alternatives that are not explored. In order to carry out a more exhaustive search, such moves must be taken as provisional. That is, a record must be retained of the alternatives not yet pursued, and search must backtrack to those alternatives, pursuing them until they prove incapable of producing an satisfactory solution. As the search encouters a particular partiM solution, it either terminates that solution, that is, finds it to admit no improving move, or branches it, that is, extends it by one applicable move. The best feasible solution encountered is recorded as the incumbent solution. Thus, if the search exhausts all open alternatives, the incumbent solution is a global optimum. 

Figure 20 The backtracking trees presented here represent the interaction of four amino acid residues. In (a) the top of the tree is the first residue side chain that possess two possible rotameric states, thus two branches. Residue 2 is on the next level and has three rotamers. The third residue has five possible rotamers, and Residue 4 has two possible rotamer states. The tree in (a) is not efficient because of the number of rotamer options for Residue 3. The same set of residues are evaluated in (b), but the order in which they are examined is changed. Residue 1 is still first, but that is now followed by Residue 4, then Residue 2, and finally Residue 3. Residues having the fewest possible rotamers are evaluated first, thus increasing the speed of the search for the GMEC. A total of 60 possible side-chain interactions exist in this example with the most favorable denoted with a circle [1, 2, 5, 1]. The arrows denote the path of the most favorable rotamer combination. This image was adapted from Canutescu et al. ...

On a fundamental level, these parallel implementations exploit the inherent branch-and-bound stmcture of the aBB algorithm. A major characteristic of a branch and bound framework is that as the size of the domain decreases, the quality of the representation improves, which implies that finer initial domains result in better approximations. This is equivalent to simultaneously exploring multiple domains in order to perform a more efficient search, which is the rationale behind advocating the development of a parallel algorithm. 

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