FUELGEN: effective evolutionary design of refuellings for pressurized water reactors

The paper describes the design of an efficient and robust genetic algorithm for the nuclear fuel loading problem (i.e., refuellings: the in-core fuel management problem) - a complex combinatorial, multimodal optimisation., Evolutionary computation as performed by FUELGEN replaces heuristic search of the kind performed by the FUELCON expert system (CAI 12/4), to solve the same problem. In contrast to the traditional genetic algorithm which makes strong requirements on the representation used and its parameter setting in order to be efficient, the results of recent research results on new, robust genetic algorithms show that representations unsuitable for the traditional genetic algorithm can still be used to good effect with little parameter adjustment. The representation presented here is a simple symbolic one with no linkage attributes, making the genetic algorithm particularly easy to apply to fuel loading problems with differing core structures and assembly inventories. A nonlinear fitness function has been constructed to direct the search efficiently in the presence of the many local optima that result from the constraint on solutions.

A generational scheme for partitioning graphs

Graph partitioning divides a graph into several pieces by cutting edges. Very effective heuristic partitioning algorithms have been developed which run in real-time, but it is unknown how good the partitions are since the problem is, in general, NP-complete. This paper reports an evolutionary search algorithm for finding benchmark partitions. Distinctive features are the transmission and modification of whole subdomains (the partitioned units) that act as genes, and the use of a multilevel heuristic algorithm to effect the crossover and mutations. Its effectiveness is demonstrated by improvements on previously established benchmarks.

Relations, residuals, regular interiors, and relative regular equivalence

Given a relation α (a binary sociogram) and an a priori equivalence relation π, both on the same set of individuals, it is interesting to look for the largest equivalence πo that is contained in and is regular with respect to α. The equivalence relation πo is called the regular interior of π with respect to α. The computation of πo involves the left and right residuals, a concept that generalized group inverses to the algebra of relations. A polynomial-time procedure is presented (Theorem 11) and illustrated with examples. In particular, the regular interior gives meet in the lattice of regular equivalences: the regular meet of regular equivalences is the regular interior of their intersection. Finally, the concept of relative regular equivalence is defined and compared with regular equivalence.