Evolution and Optimum Seeking

Tabu Search and Other Hybrid Concepts 163
Aggressive exploration using a short-term memory forms the core of the TS. From
a candidate list of (non-exhaustive) moves the best admissible one is chosen. The decision
is based on tabu restrictions on the one hand and on aspiration criteria on the
other. Whereas aspiration criteria aim at perpetuating former successful operations, tabu
restrictions help to avoid stepping back to inferior solutions and repeating already investigated
trial moves. Although the best admissible step does not necessarily lead to
an improvement, only better solutions are stored as real moves. Successes and failures
are used to update the tabu list and the aspiration memory. If no further improvements
can be found, or after a speci ed number of iterations, one transfers the results to the
longer-term memories and switches to either an intensi cation or a diversi cation mode.
Intensi cation combined with the medium-term memory refers to procedures for reinforcing
movecombinations historically found good, whereas diversi cation combined with
the long-term memory refers to exploring new regions of the search space. The rst articles
of Glover (1986, 1989) present many ideas to decide upon switching back and forth
between the three modes. Many morehave been conceived and published together with
application results. In some cases complete procedures from other optimization paradigms
have been used within the di erent phases of the TS, e.g., line search orgradient-liketechniques
during intensi cation, and GAs during diversi cation.
Instead of going into further details here, it seems appropriate to give some hints that
point to rather similar hybrid methods, more or less centered around either GAs, ESs, or
SA as the main strategy.
One could start again with Powell's rule to look for further restart points in the
vicinity of the nal solutions of his conjugate direction method (Chap. 3, Sect. 3.2.2.1)
or with the restart rule of the simplex method according to Nelder and Mead (Chap. 3,
Sect. 3.2.1.5), in order to interpret them in terms of some kind of diversi cation phase. But
in general, both approaches cannot be classi ed as better ideas than starting a speci c
optimum seeking method from di erent initial solutions and simply comparing all the
(maybe di erent) outcomes, and choosing the best one as the nal solution. It might
even be more promising to use di erent strategies from the same starting point and to
select the overall best outcome again as a new start condition. On MIMD (multiple
instructions, multiple data) parallel computers or nets of workstations the competition of
di erent search methods could even be used to set up a knowledge base that adapts to
a speci c situation (e.g., Peters, 1989, 1991). Only individual conclusions for one or the
other special application can be drawn from this kind of metastrategic approach, however.
At the close of this general survey, only a few further hints will be given regarding the
vast number of recent proposals.
Ablay (1987), for example, uses a basic search routine similar to Rechenberg's (1+1)
ES and interrupts it more or less frequently by a pure random search in order to avoid
premature stagnation as well as convergence to a non-global local optimum.
The replicator algorithm of Voigt (1989) also refers to organic evolution as a metaphor
(see also Voigt, Muhlenbein, and Schwefel, 1990). Its modelling technique may be called
descriptive, according to earlier work of Feistel and Ebeling (1989). Ebeling (1992) even
proposes to incorporate ontogenetic learning features (so-called Haeckel strategy).
Muhlenbein and Schlierkamp-Voosen (1993a,b) proposed a so-called breeder GA, which