Branch and bound technique

You can now see why for line A a branch-and-bound technique is not required to solve the design problem. Because of the way the objective function is formulated, if the ratio (pd ps) = 1, the term involving compressor i vanishes from the first summation in the objective function. This outcome is equivalent to the deletion of compressor i in the execution of a branch-and-bound strategy. (Of course the pipeline segments joined at node i may be of different diameters.) But when... 

Branch and bound techniques, discrete optimization via, 26 1023 Branched aliphatic solvents, 23 104 Branched alkylbenzene (BAB), 77 725 Branched copolymers, 7 610t Branched epoxies, 70 364 Branched olefins, 77 724, 726 Branched polycarbonates, 79 805 Branched polymers, 20 391 Branched primary alcohols, synthetic processes for, 2 2 7t Branching... 

The basic idea of the branch-and-bound technique is to divide and conquer. If the original problem is very... 

In the scheduling field, the branch and bound technique appears to be more widely used than dynamic programming. The technique is basically an enumeration process that attempts to eliminate, through a bounding process, as many sequences as possible from consideration. The bounding process is very problem specific. Here the technique is applied to the Fm C problem (see Ignall and Schrage 1965). 

Ignall, E., and Schrage, L. E. (1965), Application of the Branch and Bound Technique to Some Flow-Shop Problems, Operations Research, Vol. 13, pp. 400-412. 

Deutsch, D.F., 1971. A Branch and Bound Technique for Mixed-Product Assembly Line Balancing, PhD dissertation, Arizona State University. 

Observe that in the case that all gates have only a single candidate assignment (or, equivalently, that a single candidate has been chosen for each movable gate). Generalized STA reduces to traditional STA. It should also be noted that our branch-and-bound technique is an anytime algorithm, and may be interrupted prior to completion to obtain a suboptimal solution (e.g., based on a timeout limit, maximal number of nodes, etc.). 

InfraAlyzer 400 data, having a maximum of 19 data points/spectrum, are restricted in the variety of mathematical manipulations available for the purpose of generating a predictive equation. Even so, many methods were tried [23]. Eventually, the branch and bound technique of Furnival and Wilson [24] was found both satisfactory in performance and easy to apply, being part of the BMDP statistical software package [25]. With careful choice of the limiting parameters stable equations were consistently produced. 

The flowshop problem has been widely studied in the fields of both operations research (Lagweg et al., 1978 Baker, 1975) and chemical engineering (Rajagopalan and Karimi, 1989 Wiede and Reklaitis, 1987). Since the purpose of this chapter is to illustrate a novel technique to synthesize new control knowledge for branch-and-bound algorithms, we... 

In general, branch-and-bound [5] is an enumerative search space exploration technique that successively constructs a decision tree. In each node, the feasible region is divided into two or more disjoint subsets which are then assigned to child nodes. During the search space exploration for minimization problems, a lower bound of the objective function is computed in each node and compared against the lowest upper bound found so far. If the lower bound is greater than the upper bound, the corresponding branch is said to be fathomed and not explored anymore. The exploration terminates when a certain gap between the upper and the lower bound is reached or when the all possible subsets have been enumerated. 

Computation of lower bounds of costs to the final state. This technique is common in branch-and-bound algorithms, lower bounds can be obtained by heuristics [21] or by linear programming [22-25]. 

Westerberg, A.W. and Stephanopoulos, G., "Studies in Process Synthesis—I. Branch and Bound Strategy with List Techniques for the Synthesis of Separation Schemes," Chemical Engineering Science, Vol. 30, pp 963-972, 1975. 

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