Search space pruning and global optimization of multiple gravity assist trajectories with deep space manoeuvres

This paper deals with the design of optimal multiple gravity assist trajectories with deep space manoeuvres. A pruning method which considers the sequential nature of the problem is presented. The method locates feasible vectors using local optimization and applies a clustering algorithm to find reduced bounding boxes which can be used in a subsequent optimization step. Since multiple local minima remain within the pruned search space, the use of a global optimization method, such as Differential Evolution, is suggested for finding solutions which are likely to be close to the global optimum. Two case studies are presented.

Search space pruning and global optimisation of Multiple Gravity Assist spacecraft trajectories

We introduce and describe the Multiple Gravity Assist problem, a global optimisation problem that is of great interest in the design of spacecraft and their trajectories. We discuss its formalization and we show, in one particular problem instance, the performance of selected state of the art heuristic global optimisation algorithms. A deterministic search space pruning algorithm is then developed and its polynomial time and space complexity derived. The algorithm is shown to achieve search space reductions of greater than six orders of magnitude, thus reducing significantly the complexity of the subsequent optimisation.

Stabilizing swarm intelligence search via positive feedback resource allocation

A novel Swarm Intelligence method for best-fit search, Stochastic Diffusion Search, is presented capable of rapid location of the optimal solution in the search space. Population based search mechanisms employed by Swarm Intelligence methods can suffer lack of convergence resulting in ill defined stopping criteria and loss of the best solution. Conversely, as a result of its resource allocation mechanism, the solutions SDS discovers enjoy excellent stability.

Minimum stable convergence criteria for stochastic diffusion search

An analysis of Stochastic Diffusion Search (SDS), a novel and efficient optimisation and search algorithm, is presented, resulting in a derivation of the minimum acceptable match resulting in a stable convergence within a noisy search space. The applicability of SDS can therefore be assessed for a given problem.

Resource allocation analysis of the stochastic diffusion search

The Stochastic Diffusion Search (SDS) was developed as a solution to the best-fit search problem. Thus, as a special case it is capable of solving the transform invariant pattern recognition problem. SDS is efficient and, although inherently probabilistic, produces very reliable solutions in widely ranging search conditions. However, to date a systematic formal investigation of its properties has not been carried out. This thesis addresses this problem. The thesis reports results pertaining to the global convergence of SDS as well as characterising its time complexity. However, the main emphasis of the work, reports on the resource allocation aspect of the Stochastic Diffusion Search operations. The thesis introduces a novel model of the algorithm, generalising an Ehrenfest Urn Model from statistical physics. This approach makes it possible to obtain a thorough characterisation of the response of the algorithm in terms of the parameters describing the search conditions in case of a unique best-fit pattern in the search space. This model is further generalised in order to account for different search conditions: two solutions in the search space and search for a unique solution in a noisy search space. Also an approximate solution in the case of two alternative solutions is proposed and compared with predictions of the extended Ehrenfest Urn model. The analysis performed enabled a quantitative characterisation of the Stochastic Diffusion Search in terms of exploration and exploitation of the search space. It appeared that SDS is biased towards the latter mode of operation. This novel perspective on the Stochastic Diffusion Search lead to an investigation of extensions of the standard SDS, which would strike a different balance between these two modes of search space processing. Thus, two novel algorithms were derived from the standard Stochastic Diffusion Search, ‘context-free’ and ‘context-sensitive’ SDS, and their properties were analysed with respect to resource allocation. It appeared that they shared some of the desired features of their predecessor but also possessed some properties not present in the classic SDS. The theory developed in the thesis was illustrated throughout with carefully chosen simulations of a best-fit search for a string pattern, a simple but representative domain, enabling careful control of search conditions.

Convergence analysis of stochastic diffusion search

In this paper we present a connectionist searching technique - the Stochastic Diffusion Search (SDS), capable of rapidly locating a specified pattern in a noisy search space. In operation SDS finds the position of the pre-specified pattern or if it does not exist - its best instantiation in the search space. This is achieved via parallel exploration of the whole search space by an ensemble of agents searching in a competitive cooperative manner. We prove mathematically the convergence of stochastic diffusion search. SDS converges to a statistical equilibrium when it locates the best instantiation of the object in the search space. Experiments presented in this paper indicate the high robustness of SDS and show good scalability with problem size. The convergence characteristic of SDS makes it a fully adaptive algorithm and suggests applications in dynamically changing environments.

Dynamic load balancing for the distributed mining of molecular structures

In molecular biology, it is often desirable to find common properties in large numbers of drug candidates. One family of methods stems from the data mining community, where algorithms to find frequent graphs have received increasing attention over the past years. However, the computational complexity of the underlying problem and the large amount of data to be explored essentially render sequential algorithms useless. In this paper, we present a distributed approach to the frequent subgraph mining problem to discover interesting patterns in molecular compounds. This problem is characterized by a highly irregular search tree, whereby no reliable workload prediction is available. We describe the three main aspects of the proposed distributed algorithm, namely, a dynamic partitioning of the search space, a distribution process based on a peer-to-peer communication framework, and a novel receiverinitiated load balancing algorithm. The effectiveness of the distributed method has been evaluated on the well-known National Cancer Institute’s HIV-screening data set, where we were able to show close-to linear speedup in a network of workstations. The proposed approach also allows for dynamic resource aggregation in a non dedicated computational environment. These features make it suitable for large-scale, multi-domain, heterogeneous environments, such as computational grids.

High performance subgraph mining in molecular compounds

Structured data represented in the form of graphs arises in several fields of the science and the growing amount of available data makes distributed graph mining techniques particularly relevant. In this paper, we present a distributed approach to the frequent subgraph mining problem to discover interesting patterns in molecular compounds. The problem is characterized by a highly irregular search tree, whereby no reliable workload prediction is available. We describe the three main aspects of the proposed distributed algorithm, namely a dynamic partitioning of the search space, a distribution process based on a peer-to-peer communication framework, and a novel receiver-initiated, load balancing algorithm. The effectiveness of the distributed method has been evaluated on the well-known National Cancer Institute’s HIV-screening dataset, where the approach attains close-to linear speedup in a network of workstations.

EOQ, JIT and fixed costs in the Ready-mixed concrete industry

The successful implementation of just-in-time (JIT) purchasing policy in many industries has prompted many companies that still use the economic order quantity (EOQ) purchasing policy to ponder if they should switch to the JIT purchasing policy. Despite existing studies that directly compare the costs between the EOQ and JIT purchasing systems, this decision is, however, still difficult to be made, especially when price discount has to be considered. JIT purchasing may not always be successful even though plants that adopted JIT operations have experienced or can take advantage of physical space reduction. Hence, the objective of this study is to expand on a classical EOQ with a price discount model to derive the EOQ–JIT cost indifference point. The objective was tested and achieved through a survey and case study conducted in the ready-mixed concrete industry in Singapore.

Investigating scaling of an abstracted LCS utilising ternary and S-Expression alphabets

Utilising the expressive power of S-Expressions in Learning Classifier Systems often prohibitively increases the search space due to increased flexibility of the endcoding. This work shows that selection of appropriate S-Expression functions through domain knowledge improves scaling in problems, as expected. It is also known that simple alphabets perform well on relatively small sized problems in a domain, e.g. ternary alphabet in the 6, 11 and 20 bit MUX domain. Once fit ternary rules have been formed it was investigated whether higher order learning was possible and whether this staged learning facilitated selection of appropriate functions in complex alphabets, e.g. selection of S-Expression functions. This novel methodology is shown to provide compact results (135-MUX) and exhibits potential for scaling well (1034-MUX), but is only a small step towards introducing abstraction to LCS.

Exploration vs exploitation in differential evolution

Differential Evolution (DE) is a tool for efficient optimisation, and it belongs to the class of evolutionary algorithms, which include Evolution Strategies and Genetic Algorithms. DE algorithms work well when the population covers the entire search space, and they have shown to be effective on a large range of classical optimisation problems. However, an undesirable behaviour was detected when all the members of the population are in a basin of attraction of a local optimum (local minimum or local maximum), because in this situation the population cannot escape from it. This paper proposes a modification of the standard mechanisms in DE algorithm in order to change the exploration vs. exploitation balance to improve its behaviour.

A grouped P2P network for scalable grid information services

Information services play a crucial role in grid environments in that the state information can be used to facilitate the discovery of resources and the services available to meet user requirements, and also to help tune the performance of a grid system. However, the large size and dynamic nature of the grid brings forth a number of challenges for information services. This paper presents PIndex, a grouped peer-to-peer network that can be used for scalable grid information services. PIndex builds on Globus MDS4, but introduces peer groups to dynamically split the large grid information search space into many small sections to enhance its scalability and resilience. PIndex is subsequently modeled with Colored Petri Nets for performance evaluation. The simulation results show that PIndex is scalable and resilient in dealing with a large number of peer nodes.

Advanced global optimisation for mission analysis and design

This report describes the analysis and development of novel tools for the global optimisation of relevant mission design problems. A taxonomy was created for mission design problems, and an empirical analysis of their optimisational complexity performed - it was demonstrated that the use of global optimisation was necessary on most classes and informed the selection of appropriate global algorithms. The selected algorithms were then applied to the di®erent problem classes: Di®erential Evolution was found to be the most e±cient. Considering the speci¯c problem of multiple gravity assist trajectory design, a search space pruning algorithm was developed that displays both polynomial time and space complexity. Empirically, this was shown to typically achieve search space reductions of greater than six orders of magnitude, thus reducing signi¯cantly the complexity of the subsequent optimisation. The algorithm was fully implemented in a software package that allows simple visualisation of high-dimensional search spaces, and e®ective optimisation over the reduced search bounds.

Attention through self-synchronisation in the spiking neuron stochastic diffusion network

The paper discusses ensemble behaviour in the Spiking Neuron Stochastic Diffusion Network, SNSDN, a novel network exploring biologically plausible information processing based on higher order temporal coding. SNSDN was proposed as an alternative solution to the binding problem [1]. SNSDN operation resembles Stochastic Diffusin on Search, SDS, a non-deterministic search algorithm able to rapidly locate the best instantiation of a target pattern within a noisy search space ([3], [5]). In SNSDN, relevant information is encoded in the length of interspike intervals. Although every neuron operates in its own time, ‘attention’ to a pattern in the search space results in self-synchronised activity of a large population of neurons. When multiple patterns are present in the search space, ‘switching of at- tention’ results in a change of the synchronous activity. The qualitative effect of attention on the synchronicity of spiking behaviour in both time and frequency domain will be discussed.

Software evolution: a graph based model

A model based on graph isomorphisms is used to formalize software evolution. Step by step we narrow the search space by an informed selection of the attributes based on the current state-of-the-art in software engineering and generate a seed solution. We then traverse the resulting space using graph isomorphisms and other set operations over the vertex sets. The new solutions will preserve the desired attributes. The goal of defining an isomorphism based search mechanism is to construct predictors of evolution that can facilitate the automation of ’software factory’ paradigm. The model allows for automation via software tools implementing the concepts.