Abstract—This paper addresses the multistage expansion
problem for multistate series-parallel systems. The study period is
divided into several stages. At each stage the demand distribution
is predicted in the form of a cumulative demand curve. The
additional elements chosen from a list of available products can
be included into any system-component at any stage to increase
the total system capacity and/or reliability. Each element is
characterized by its capacity (productivity), availability, and cost.
The objective is to minimize the sum of costs of the investments
over the study period while satisfying reliability constraints at
each stage.
To solve the problem, a genetic algorithm is used as an optimization
tool. The solution encoding technique allows the genetic algorithm
to manipulate integer strings representing multistage expansion
planes. A solution quality index comprises both reliability
& cost estimations. The procedure based on the universal generating
function is used for evaluating the availability of multistate
series-parallel systems. An example illustrates finding the optimal
expansion plan for a coal-transportation system of a power station.
Index Terms—Expansion planning, genetic algorithm, redundancy
optimization, universal generating function.
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