The geometrical problem of finding a possible disassembly sequence for an object is considered for a limited class of objects: those whose parts can be made from collections of unit cubes. For such objects, we consider motions of their component parts which are translations in one of three orthogonal directions.A working program has been implemented in POP-11, which finds a disassembly sequence for an object defined by a 3D cube map. Each disassembly step may consist of either one or two linear motions of single parts. Removal of subassemblies consisting of more than one part is not considered.To ensure properly the validity of a disassembly motion, both local and global geometric information must be considered. The local geometric feasibility of a motion relates to whether an infinitesimal motion can be made, and it is determined by the surface contacts (mates) between a part and other parts. The global geometric feasibility of a motion relates to whether a finite (or infinite) motion can be made in a particular direction. It depends not only on the relationship between the part to be moved and those that it touches, but also on its relationship with, potentially, all the other parts in the assembly. To determine the global geometric feasibility of a motion, the idea of coupling between two faces is introduced. Coupling is a directional quantity which gives the finite limit on the relative motion between two faces. By considering the coupling information for all the faces of a part, it is easy to determine the finite motions that are possible in any direction.

This paper describes a new technique for tackling highly epistatic combinatorial optimization problems. Rather than having a simple representation, simple operators, a simple fitness function, but a highly epistatic search space, this technique is intended to spread the problem’s complexity more evenly. Using our new technique, known as expansive coding, the representation, operators and fitness function become more complicated, but the search space becomes less epistatic, and therefore easier for a GA to tackle. In effect, the combinatorial task is changed to a function optimization one. We demonstrate how this technique can be applied in the field of arithmetic algorithm design/electronic circuit simplification. In the design of a multiplier for quaternion numbers, consistently good results are obtained.

The traditional GA as described in Part of this article uses point crossover where the two mating chromosomes are each cut once at corresponding points and the sections after the cuts exchanged However many di erent crossover algorithms have been devised often involving more than one cut point DeJong DeJ investigated the e ectiveness of multiple point crossover and concluded as reported in Gol a p that point crossover gives an improvement but that adding further crossover points reduces the performance of the GA The problem with adding additional crossover points is that building blocks are more likely to be disrupted However an advantage of having more crossover points is that the problem space may be searched more thoroughly

Genetic Algorithms (GAs) are adaptive methods which may be used to solve search and optimisation problems. They are based on the genetic processes of biological organisms. Over many generations, natural populations evolve according to the principles of natural selection and \survival of the ttest, rst clearly stated by Charles Darwin in The Origin of Species. By mimicking this process, genetic algorithms are able to \evolve solutions to real world problems, if they have been suitably encoded. For example, GAs can be used to design bridge structures, for maximum strength/weight ratio, or to determine the least wasteful layout for cutting shapes from cloth. They can also be used for online process control, such as in a chemical plant, or load balancing on a multi-processor computer system. The basic principles of GAs were rst laid down rigourously by Holland [Hol75], and are well described in many texts (e.g. [Dav87, Dav91, Gre86, Gre90, Gol89a, Mic92]). GAs simulate those processes in natural populations which are essential to evolution. Exactly which biological processes are essential for evolution, and which processes have little or no role to play is still a matter for research; but the foundations are clear. In nature, individuals in a population compete with each other for resources such as food, water and shelter. Also, members of the same species often compete to attract a mate. Those individuals which are most successful in surviving and attracting mates will have relatively larger numbers of o spring. Poorly performing individuals will produce few of even no o spring at all. This means that the genes from the highly adapted, or individuals will spread to an increasing number of individuals in each successive generation. The combination of good characteristics from di erent ancestors can sometimes produce \super o spring, whose tness is greater than that of either parent. In this way, species evolve to become more and more well suited to their environment. GAs use a direct analogy of natural behaviour. They work with a population of \individuals, each representing a possible solution to a given problem. Each individual is assigned a tness according to how good a solution to the problem it is. For example, the tness score might be the strength/weight ratio for a given bridge design. (In nature this is equivalent to assessing how e ective an organism is at competing for resources.) The highly t individuals are given opportunities to \reproduce, by \cross breeding with other