U. Glaeser

Conclusion
This chapter section has introduced the reader to four effective heuristics that belong to the class of general
approximation iterative algorithms, namely SA, GA, tabu search, and SimE. From the immense literature
that is available it is evident that for a large variety of applications, in certain settings, these heuristics
produce excellent results. All five algorithms are general iterative metaheuristics. A value of the objective
function is used to compare results of consecutive iterations and a solution is selected based on its value.
All algorithms incorporate domain specific knowledge to dictate the search strategy. They also tolerate
some element of nondeterminism that helps the search escape out of local minima. They all rely on
the use of a suitable cost function, which provides feedback to the algorithm as the search progresses. The
principle difference among these heuristics is how and where domain specific knowledge is used. For
example, in SA such knowledge is mainly included in the cost function. Elements involved in a perturbation
are selected randomly, and perturbations are accepted or rejected according to the Metropolis criterion,
which is a function of the cost. The cooling schedule has also a major impact on the algorithm performance
and must be carefully crafted to the problem domain as well as the particular problem instance.
For the two evolutionary algorithms discussed in the chapter, GA and SimE, domain specific
knowledge is exploited in all phases. In the case of GA, the fitness of individual solutions incorporates
domain specific knowledge. Selection for reproduction, the genetic operations, as well as generation
of the new population also incorporate a great deal of heuristic knowledge about the problem domain.
In SimE, each individual element of a solution is characterized by a goodness measure that is highly
correlated with the objective function. The perturbation step (selection followed by allocation) affects
mostly low goodness elements. Therefore, domain specific knowledge is included in every step of the
SimE algorithm.
Tabu search is different from the above heuristics in that it has an explicit memory component. At
each iteration the neighborhood of the current solution is partially explored, and a move is made to the
best nontabu solution in that neighborhood. The neighborhood function as well as tabu list size and
content are problem specific. The direction of the search is also influenced by the memory structures
(whether intensification or diversification is used).
A classification of meta-heuristics proposed by Glover and Laguna [130] is based on three basic
features: (1) the use of adaptive memory, where the letter A is used if the meta-heuristic employs adaptive
memory, and the letter M is used if it is memoryless; (2) the kind of neighborhood exploration, where
the letter N is used if the meta-heuristic performs a systematic neighborhood search, and the letter S is
used if stochastic sampling is followed; and (3) the number of current solutions carried from one iteration
to the next, where the digit 1 is used if the meta-heuristic maintains a single solution, and the letter P
is used if a parallel search is performed with a population of solutions of cardinality P. For example,
according to this classification, GA is M/S/P, tabu search is A/N/1, SA is M/S/1, and SimE is also M/S/1.
It is also possible to make hybrids of these algorithms. The basic idea of hybridization is to enhance
the strengths and compensate for the weaknesses of two or more complementary approaches. For the
details about the hybridization the readers are referred to [8].
In this chapter section, it has not been the authors’ intention to demonstrate the superiority of one
algorithm over the other. Actually it would be unwise to rank such algorithms. Each one of them has its
own merits. Recently, an interesting theoretical study has been reported by Wolpert and Macready in
which they proved a number of theorems stating that the average performance of any pair of iterative
(deterministic or nondeterministic) algorithms across all problems is identical. That is, if an algorithm
performs well on a certain class of problems then it necessarily pays for that with degraded performance
on the remaining set of problems [146]; however, it should be noted that the reported theorems assume
that the algorithms do not include domain specific knowledge of the problems being solved. Obviously,
it would be expected that a well-engineered algorithm would exhibit superior performance to that of a
poorly engineered one.
© 2002 by CRC Press LLC