Heuristic ordering search

Given a polarization operation clusto C, a heuristic ordering 

This procedure greedily constructs the ordering starting from the leaf element I of the polarization. The variable current keeps a pointer to the most recently ordered element, initialized to /. At each point in constructing the ordering, a set of possible candidates is identified, where the candidates correspond to the operations in the cluster that are compatible with the partial ordo induced by the polarization. For each candidate Vy, a slack value f vy) is defined as follows  

Intuitively, the slack is a measure of the length of the longest cycle that would be formed if Vy is selected and serialized as the next element in the ordering Ord. It must always be positive since otherwise the serialization is not valid. Among the possible candidates, the one with minimum slack is selected 

Candid = compatible(Ord) h select most constrained candidate / 

Add Vy to the ordering Ord and serialize graph Recompute all-pairs longest path  

---

Virtual screening applications based on superposition or docking usually contain difficult-to-solve optimization problems with a mixed combinatorial and numerical flavor. The combinatorial aspect results from discrete models of conformational flexibility and molecular interactions. The numerical aspect results from describing the relative orientation of two objects, either two superimposed molecules or a ligand with respect to a protein in docking calculations. Problems of this kind are in most cases hard to solve optimally with reasonable compute resources. Sometimes, the combinatorial and the numerical part of such a problem can be separated and independently solved. For example, several virtual screening tools enumerate the conformational space of a molecule in order to address a major combinatorial part of the problem independently (see for example [199]). Alternatively, heuristic search techniques are used to tackle the problem as a whole. Some of them will be covered in this section. 

In order to build an MTree model from more than two Feature Trees, the dynamic match-search algorithm can be applied in a hierarchical manner. We developed two efficient heuristics for this task ... 

Concerning tactics, in many cases, heuristic devices or rules of thumb are used. For the intramolecular dynamics problem, low-order (meaning usually first-order) perturbation theory is frequently used in the tactical search. Imagine that we begin with state )) in tier t. This state has the zero-order energy ) . We compute the first-order coupling strength to the candidate state fc) in tier t + 1 ... 

Simulated annealing as well as taboo search are often used in the following manner. First an attempt is made to find a reasonably good initial solution for a problem via a heuristic. After this has been done, either a simulated annealing or a taboo search procedure is used as a postprocessor in order to search for an even better solution. The postprocessor is then run for a given amount of time. 

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. 

In terms of coding method, it is necessary to depend on the situation of practice to set up the appropriate encoding and decoding scheme in order to overcome the shortcomings of the binary code. When variables are real vectors, we can directly use code by real number to inject heuristic information relevant to the field of problem in order to increase the search ability of GA. 

Once the objective functions are defined in previous paragraph then the optimal location of energy dissipation dampers needs be determined. Three types of heuristic search algorithms can be used in order to solve the nonlinear constrained optimization problem ... 

Heuristic synthesis from examples involves more or less heavy use of heuristics in order to prune the search space. 

---