Optimum Design of Steel Skeleton Structures - Music-Inspired Harmony Search Algorithm: Theory and Applications - page 86

review of discrete structural optimization methods is given by Arora [6]. The algo-
rithms that are based on mathematical programming techniques are deterministic.
They need an initial design point to initiate a search for the optimum solution and re-
quire gradient computations in the exploration process.
Another group of optimization techniques that have emerged recently are non-
deterministic approaches. These techniques do not require gradient information of the
objective function and constraints, and use probabilistic transition rules not determinis-
tic ones. They employ random number call, and incorporate a set of parameters that re-
quire to be adjusted prior to their use. These novel and innovative metaheuristic search
algorithms make use of ideas inspired from the nature. The basic idea behind these
techniques is to simulate natural phenomena, such as survival of the fittest, immune
system, swarm intelligence and the cooling process of molten metals through annealing
into a numerical algorithm [7-14]. The optimum structural design algorithms that are
based on these techniques are robust and quite effective in finding solutions to discrete
programming problems. A detailed review of these algorithms as well as their applica-
tions in optimum structural design is carried out by Saka [15]. One recent addition to
these techniques is the harmony search algorithm [16-21]. This approach is based on
the musical performance process that takes place when a musician searches for a better
state of harmony. Jazz improvisation seeks to find musically pleasing harmony similar
to the optimum design process which seeks to find optimum solution. The pitch of
each musical instrument determines the aesthetic quality, just as the objective function
value is determined by the set of values assigned to each decision variable. In this
chapter optimum design algorithm based on harmony search method is presented for
moment resisting steel frames, grillage systems and geodesic domes.
2 Harmony Search Method Based Optimum Design Algorithm
Consider a structural design problem where the total number of design variables is rep-
resented by nv . Let there be a design pool for each design variable that contains possi-
ble discrete values for that particular design variable. During the design process the
optimum design algorithm is required to carry out a selection for a design variable
among the values specified in the design pool of that particular design variable. In
some design problems there may be only one design pool for all the design variables
from which the selection is carried out, while in some other there can be more than one
design pool depending on the type of design variables. Hence the total number of dis-
crete values in design pools may vary depending on whether there is only one design
pool for all the variables or not. Let us consider at this stage for simplicity that there is
only one design pool from which the possible values of each design variable are to be
selected. Let there be ns discrete values in this pool. Each of these values can be a pos-
sible candidate for the design variable during the design process. In the design prob-
lems considered in this chapter the sequence number in the design pool corresponding
to each value is taken as design variable instead of the value itself. For example if a de-
sign pool has 64 discrete values for a design variable, an integer number between 1 to
64, say 24, specifies the particular value that can be adopted for the design variable un-
der consideration. This provides ease and flexibility in the implementation of computer
programming. Finding out the appropriate combination of these values such that the
objective function holds its minimum value while design constraints are satisfied is a