Combining Genetic Algorithms and Simulated Annealing for Constructing Lotto Designs

An \(LD(n,k,p,t:b)\) Lotto design is a set of \(b\) \(k\)-sets (blocks) of an \(n\)-set such that any \(p\)-set intersects at least one block in \(t\) or more elements. Let \({L}(n,k,p,t)\) denote the minimum number of blocks for any \(LD(n,k,p,t:b)\) Lotto design. This paper describes an algorithm used to construct Lotto designs by combining genetic algorithms and simulated annealing and provides some experimental results.