Jonathan E. Rowe

Parallel Problem Solving from Nature - PPSN VIII

Two ideas taken from Bayesian optimization and classifier systems are presented for personnel scheduling based on choosing a suitable scheduling rule from a set for each person’s assignment. Unlike our previous work of using genetic algorithms whose learning is implicit, the learning in both approaches is explicit, i.e. we are able to identify building blocks directly. To achieve this target, the Bayesian optimization algorithm builds a Bayesian network of the joint probability distribution of the rules used to construct solutions, while the adapted classifier system assigns each rule a strength value that is constantly updated according to its usefulness in the current situation. Computational results from 52 real data instances of nurse scheduling demonstrate the success of both approaches. It is also suggested that the learning mechanism in the proposed approaches might be suitable for other scheduling problems.

Molecular circuits for associative learning in single-celled organisms

We demonstrate how a single-celled organism could undertake associative learning. Although to date only one previous study has found experimental evidence for such learning, there is no reason in principle why it should not occur. We propose a gene regulatory network that is capable of associative learning between any pre-specified set of chemical signals, in a Hebbian manner, within a single cell. A mathematical model is developed, and simulations show a clear learned response. A preliminary design for implementing this model using plasmids within Escherichia coli is presented, along with an alternative approach, based on double-phosphorylated protein kinases.

Particle swarm optimization and fitness sharing to solve multi-objective optimization problems

The particle swarm optimization algorithm has been shown to be a competitive heuristic to solve multi-objective optimization problems. Also, fitness sharing concepts have shown to be significant when used by multi-objective optimization methods. In this paper we introduce an algorithm that makes use of these two main concepts, particle swarm optimization and fitness sharing to tackle multi-objective optimization problems.

Exact Schema Theory and Markov Chain Models for Genetic Programming and Variable-length Genetic Algorithms with Homologous Crossover

Genetic Programming (GP) homologous crossovers are a group of operators, including GP one-point crossover and GP uniform crossover, where the offspring are created preserving the position of the genetic material taken from the parents. In this paper we present an exact schema theory for GP and variable-length Genetic Algorithms (GAs) which is applicable to this class of operators. The theory is based on the concepts of GP crossover masks and GP recombination distributions that are generalisations of the corresponding notions used in GA theory and in population genetics, as well as the notions of hyperschema and node reference systems, which are specifically required when dealing with variable size representations.In this paper we also present a Markov chain model for GP and variable-length GAs with homologous crossover. We obtain this result by using the core of Voses model for GAs in conjunction with the GP schema theory just described. The model is then specialised for the case of GP operating on 0/1 trees: a tree-like generalisation of the concept of binary string. For these, symmetries exist that can be exploited to obtain further simplifications.In the absence of mutation, the Markov chain model presented here generalises Voses GA model to GP and variable-length GAs. Likewise, our schema theory generalises and refines a variety of previous results in GP and GA theory.

Group properties of crossover and mutation

It is supposed that the finite search space has certain symmetries that can be described in terms of a group of permutations acting upon it. If crossover and mutation respect these symmetries, then these operators can be described in terms of a mixing matrix and a group of permutation matrices. Conditions under which certain subsets of are invariant under crossover are investigated, leading to a generalization of the term schema. Finally, it is sometimes possible for the group acting on to induce a group structure on itself.

Properties of Gray and Binary Representations

Representations are formalized as encodings that map the search space to the vertex set of a graph. We define the notion of bit equivalent encodings and show that for such encodings the corresponding Walsh coefficients are also conserved. We focus on Gray codes as particular types of encoding and present a review of properties related to the use of Gray codes. Gray codes are widely used in conjunction with genetic algorithms and bit-climbing algorithms for parameter optimization problems. We present new convergence proofs for a special class of unimodal functions; the proofs show that a steepest ascent bit climber using any reflected Gray code representation reaches the global optimum in a number of steps that is linear with respect to the encoding size. There are in fact many different Gray codes.Shifting is defined as a mechanism for dynamically switching from one Gray code representation to another in order to escape local optima. Theoretical results that substantially improve our understanding of the Gray codes and the shifting mechanism are presented. New proofs also shed light on the number of unique Gray code neighborhoods accessible via shifting and on how neighborhood structure changes during shifting. We show that shifting can improve the performance of both a local search algorithm as well as one of the best genetic algorithms currently available.

Theoretical analysis of local search strategies to optimize network communication subject to preserving the total number of links

Purpose – A variety of phenomena such as world wide web, social or business networks, interactions are modelled by various kinds of networks (such as the scale free or preferential attachment networks). However, due to the model‐specific requirements one may want to rewire the network to optimize the communication among the various nodes while not overloading the number of channels (i.e. preserving the number of edges). The purpose of this paper is to present a formal framework for this problem and to examine a family of local search strategies to cope with it.Design/methodology/approach – This is mostly theoretical work. The authors use rigorous mathematical framework to set‐up the model and then we prove some interesting theorems about it which pertain to various local search algorithms that work by rerouting the network.Findings – This paper proves that in cases when every pair of nodes is sampled with non‐zero probability then the algorithm is ergodic in the sense that it samples every possible networ...

The origin of autonomous agents by natural selection.

We propose conditions in which an autonomous agent could arise, and increase in complexity. It is assumed that on the primitive Earth there arose a recycling flow-reactor containing spontaneously formed oil droplets or lipid aggregates. These droplets grew at a basal rate by simple incorporation of lipid phase material, and divided by external agitation. This type of system was able to implement a natural selection algorithm once heredity was added. Macroevolution became possible by selection for rarely occurring chemical reactions that produced holistic autocatalytic molecular replicators (contained within the aggregate) capable of doubling at least as fast as the lipid aggregate, and which were also capable of benefiting the growth of its lipid aggregate container. No nucleotides or monomers capable of modular heredity were required at the outset. To explicitly state this hypothesis, a computer model was developed that employed an artificial chemistry, exhibiting conservation of mass and energy, incorporated within each individual of a population of lipid aggregates. This model evolved increasingly complex self-sustaining processes of constitution, a result that is also expected in real chemistry.

An Evolution Strategy Using a Continuous Version of the Gray-Code Neighbourhood Distribution

We derive a continuous probability distribution which generates neig- hbours of a point in an interval in a similar way to the bitwise mutation of a Gray code binary string. This distribution has some interesting scale-free properties which are analogues of properties of the Gray code neighbourhood structure. A simple (1+1)-ES using the new distribution is proposed and evaluated on a set of benchmark problems, on which it performs remarkably well. The critical parame- ter is theprecision of the distribution, which corresponds to the string length in the discrete case. The algorithm is also tested on a difficult real-world problem from medical imaging, on which it also performs well. Some observations concerning the scale-free properties of the distribution are made, although further analysis is required to understand why this simple algorithm works so well.

Unbiased black box search algorithms

We formalize the concept of an unbiased black box algorithm, which generalises the idea previously introduced by Lehre and Witt. Our formalization of bias relates to the symmetry group of the problem class under consideration, establishing a connection with previous work on No Free Lunch. Our definition is motivated and justified by a series of results, including the outcome that given a biased algorithm, there exists a corresponding unbiased algorithm with the same expected behaviour (over the problem class) and equal or better worst-case performance. For the case of evolutionary algorithms, it is already known how to construct unbiased mutation and crossover operators, and we summarise those results.