Search space

This virtual search space can be searched using a feature tree descriptor. 

Since the required search space is K 0-15, K/ 0-1, the following are examples of population membership... 

Optimization techniques can provide effective ways of sampling large search spaces, and hence several such methods have been applied to compound selec-... 

Constraint (3.8) reduces the search space by ensuring that the time at which a state s can be processed in unit j at time point p is at least after the sum of the durations of all previous tasks that have taken place in the unit. Constraint (3.9) ensures that the processing of state Sin into unit j can only take place after the previous batch has been processed. Constraint (3.10) stipulates that state sin can only be processed in unit j after it has been produced from unit j, where units j and / are consecutive stages in the recipe. 

At the start of a run, the random strings in the first population will correspond to points widely scattered across the search space, as illustrated in Figure 5.13. 

Give particles random positions and velocities in the search space. 

More generally, MILPs are solved with branch and bound algorithms, similar to the spatial branch and bound method of the previous section, that explore the search space. As seen in Fig. 3-61, binary variables are used to define the search tree, and a number of bounding properties can be noted from the structure of (3-110). 

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. 

A standard branch-and-bound algorithm is used to explore the first-stage search space while lower bounds are provided by the Lagrangian dual. Candidate solutions... 

The term evolutionary algorithm (EA) refers to a class of population based metaheuristic (probabilistic) optimization algorithms which imitate the Darwinian evolution ( survival ofthe fittest ). However, the biological terms are used as metaphors rather than in their exact meaning. The population of individuals denotes a set of solution candidates or points of the solution space. Each individual represents a point in the search space which is coded in the individual s representation (genome). The fitness of an individual is usually defined on the basis of the value of the objective function and determines its chances to stay in the population and to be used to generate new solution points. 

The ES used here is the mixed-integer ES for bounded search spaces [23]. It can operate on a general mixed-integer search space. The ES uses a population size of /i, with X offspring per generation. Self-adaptation is realized by extending... 

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