Andrew J Parkes - Profile on Academia.edu (original) (raw)

Papers by Andrew J Parkes

An ensemble based Genetic Programming system to predict English football premier league games

ABSTRACT Predicting the result of a football game is challenging due to the complexity and uncert... more ABSTRACT Predicting the result of a football game is challenging due to the complexity and uncertainties of many possible influencing factors involved. Genetic Programming (GP) has been shown to be very successful at evolving novel and unexpected ways of solving problems. In this work, we apply GP to the problem of predicting the outcomes of English Premier League games with the result being either win, lose or draw. We select 25 features from each game as the inputs to our GP system, which will then generate a function to predict the result. The experimental test on the prediction accuracy of a single GP-generated function is promising. One advantage of our GP system is, by implementing different runs or using different settings, it can generate as many high quality functions as we want. It has been showed that combining the decisions of a number of classifiers can provide better results than a single one. In this work, we combine 43 different GP-generated functions together and achieve significantly improved system performance.

Scaling Properties of Pure Random Walk on Random 3-SAT

Lecture Notes in Computer Science, 2002

Experimental results are given on the scaling of the Pure Random Walk version (PRWSAT) ofWalkSAT.... more Experimental results are given on the scaling of the Pure Random Walk version (PRWSAT) ofWalkSAT. PRWSAT is very simple because of the absence of heuristics: not only the clause is selected at random, but also the literal within that clause. The main result is that, despite the simplicity and absence of heuristics, it has non-trivial behavior on Random 3-SAT. There appears to be a threshold at a clause/variable ratio of about 2.65. Below the threshold, problems are solved in a tightly-distributed and linear number of flips. Above the threshold scaling appears to be non-polynomial. The simplicity and the nontrivial threshold make it a good candidate for theoretical analysis.

Progress in Multi-Genus Calculations for the Spinning String

Springer eBooks, 1990

We review progress in the calculation of multiloop amplitudes for the closed Neveu-Schwarz-Ramond... more We review progress in the calculation of multiloop amplitudes for the closed Neveu-Schwarz-Ramond string in a flat ten dimensional background. When the picture changing operators are placed at the zeroes of a holomorphic one-form then it turns out to be possible to do the sum over spin structures for genus g ≤ 9 for the vacuum amplitude. The result of this sum is zero point wise in moduli space and not just a total derivative as might be expected in a more general gauge. We look at the possibility that singularities could arise for certain values of the moduli and also discuss why this gauge choice is so powerful by showing the similarity to “light-cone” diagrams.

Satisfiability algorithms and finite quantification

Abstract This paper makes three observations with regard to the application of algorithms such as... more Abstract This paper makes three observations with regard to the application of algorithms such as wsat and relsat to problems of practical interest. First, we identify a speci c calculation (\ subsearch") that is performed at each inference step by any existing satis ...

Physics Letters B, Nov 1, 1984

European Journal of Operational Research, Jul 1, 2017

Nuclear Physics B, Aug 1, 1983

It is shown that there exists a class of finite four-dimensional field theories. This class is ge... more It is shown that there exists a class of finite four-dimensional field theories. This class is generated by adding specific combinations of mass terms as well as terms cubic in the scalar and pseudo-scalar fields to the N = 4 supersymmetric Yang-Mills theory.

N = 1 supersymmetric mass terms in the N = 4 supersymmetric Yang-Mills theory

Physics Letters B, Mar 1, 1983

Abstract It is argued that the addition of N = 1 supersymmetric mass terms to the N = 4 supersymm... more Abstract It is argued that the addition of N = 1 supersymmetric mass terms to the N = 4 supersymmetric Yang-Mills theory does not result in a change in the ultraviolet properties of the theory.

Journal of Artificial Intelligence Research, Feb 1, 2004

Physics Letters B, Oct 1, 1985

National Conference on Artificial Intelligence, Aug 4, 1996

National Conference on Artificial Intelligence, Jul 1, 1998

When search techniques are used to solve a practical problem, the solution produced is often brit... more When search techniques are used to solve a practical problem, the solution produced is often brittle in the sense that small execution difficulties can have an arbitrarily large effect on the viability of the solution. The AI community has responded to this difficulty by investigating the development of "robust problem solvers" that are intended to be proof against this difficulty. We argue that robustness is best cast not as a property of the problem solver, but as a property of the solution. We introduce a new class of models for a logical theory, called supermodels, that captures this idea. Supermodels guarantee that the model in question is robust, and allow us to quantify the degree to which it is so. We investigate the theoretical properties of supermodels, showing that finding supermodels is typically of the same theoretical complexity as finding models. We provide a general way to modify a logical theory so that a model of the modified theory is a supermodel of the original. Experimentally, we show that the supermodel problem exhibits phase transition behavior similar to that found in other satisfiability work.

Physics Letters B, Jun 1, 1985

We consider the one-loop finite N = 1 Yang-Mills theories and by a mixture of direct calculation ... more We consider the one-loop finite N = 1 Yang-Mills theories and by a mixture of direct calculation and deductions from the all-orders finiteness of some N = 2 theories we find an expression h)r the three-loop divergence in the matter field self-energy. We also discuss the effect of explicit supersymmetry breaking terms at the two-loop level.

Physics Letters B, Apr 1, 1984

The two4oop ~ function for an arbitrary rigid supersymmetric theory is given. The necessary and s... more The two4oop ~ function for an arbitrary rigid supersymmetric theory is given. The necessary and sufficient conditions for a rigid supersymmetric theory to be finite at one loop are derived. It is shown that these conditions also imply two4oop f'miteness.

Portfolio optimization is one of the most important problems in the finance field. The traditiona... more Portfolio optimization is one of the most important problems in the finance field. The traditional mean-variance model has its drawbacks since it fails to take the market uncertainty into account. In this work, we investigate a two-stage stochastic portfolio optimization model with a comprehensive set of real world trading constraints in order to capture the market uncertainties in terms of future asset prices. A hybrid approach, which integrates genetic algorithm (GA) and a linear programming (LP) solver is proposed in order to solve the model, where GA is used to search for the assets selection heuristically and the LP solver solves the corresponding sub-problems of weight allocation optimally. Scenarios are generated to capture uncertain prices of assets for five benchmark market instances. The computational results indicate that the proposed hybrid algorithm can obtain very promising solutions. Possible future research directions are also discussed.

Annals of Operations Research, Sep 9, 2015

Commercial airports are under increasing pressure to comply with the Eurocontrol Collaborative De... more Commercial airports are under increasing pressure to comply with the Eurocontrol Collaborative Decision Making (CDM) initiative, to ensure that information is passed between stakeholders, integrate automated decision support or make predictions. These systems can also aid effective operations beyond the airport by communicating scheduling decisions to other relevant parties, such as Eurocontrol, for passing on to downstream airports and enabling overall airspace improvements. One of the major CDM components is aimed at producing the target take-off times and target startup-approval times, i.e. scheduling when the aircraft should push back from the gates and start their engines and when they will take off. For medium-sized airports, a common choice for this is a "Pre-Departure Sequencer" (PDS). In this paper, we describe the design and requirements challenges which arose during our development of a PDS system for medium sized international airports. Firstly, the scheduling problem is highly dynamic and event driven. Secondly, it is important to end-users that the system be predictable and, as far as possible, transparent in its operation, with decisions that can be explained. Thirdly, users can override decisions, and this information has to be taken into account. Finally, it is important that the system is as fair as possible for all users This work was supported in part by an EPSRC 'Research Development Fund' and also by EPSRC grant EP/F033613/1

Nuclear Physics B, Jun 1, 1992

Yang-Mills (SDYM) and also that, in perturbation theory, it has has a vanishing four particle sca... more Yang-Mills (SDYM) and also that, in perturbation theory, it has has a vanishing four particle scattering amplitude. We discuss how the dynamics of the three particle scattering implies that on shell states can only scatter if their momenta lie in the same self-dual plane and then investigate classical SDYM with the aim of comparing exact solutions with the tree level perturbation theory predictions. In particular for the gauge group SL(2,C) with a plane wave Hirota ansatz SDYM reduces to a complicated set of algebraic relations due to de Vega. Here we solve these conditions and the solutions are shown to correspond to collisions of plane wave kinks. The main result is that for a class of kinks the resulting phase shifts are non-zero, the solution as a whole is not pure gauge and so the scattering seems nontrivial. However the stress energy and Lagrangian density are confined to string like regions in the space time and in particular are zero for the incoming/outgoing kinks so the solution does not correspond to physical four point scattering.

National Conference on Artificial Intelligence, Jul 27, 1997

Many problem ensembles exhibit a phase transition that is associated with a large peak in the ave... more Many problem ensembles exhibit a phase transition that is associated with a large peak in the average cost of solving the problem instances. However, this peak is not necessarily due to a lack of solutions: indeed the average number of solutions is typically exponentially large. Here, we study this situation within the context of the satisfiability transition in Random SSAT. We find that a significant subclass of instances emerges as we cross the phase transition. These instances are characterized by having about 85-95% of their variables occurring in unary prime implicates (UPIs), with their remaining variables being subject to few constraints. In such instances the models are not randomly distributed but all lie in a cluster that is exponentially large, but still admits a simple description. Studying the effect of UPIs on the local search algorithm WSAT shows that these "single-cluster" instances are harder to solve, and we relate their appearance at the phase transition to the peak in search cost.

An ensemble based Genetic Programming system to predict English football premier league games

ABSTRACT Predicting the result of a football game is challenging due to the complexity and uncert... more ABSTRACT Predicting the result of a football game is challenging due to the complexity and uncertainties of many possible influencing factors involved. Genetic Programming (GP) has been shown to be very successful at evolving novel and unexpected ways of solving problems. In this work, we apply GP to the problem of predicting the outcomes of English Premier League games with the result being either win, lose or draw. We select 25 features from each game as the inputs to our GP system, which will then generate a function to predict the result. The experimental test on the prediction accuracy of a single GP-generated function is promising. One advantage of our GP system is, by implementing different runs or using different settings, it can generate as many high quality functions as we want. It has been showed that combining the decisions of a number of classifiers can provide better results than a single one. In this work, we combine 43 different GP-generated functions together and achieve significantly improved system performance.

Scaling Properties of Pure Random Walk on Random 3-SAT

Lecture Notes in Computer Science, 2002

Experimental results are given on the scaling of the Pure Random Walk version (PRWSAT) ofWalkSAT.... more Experimental results are given on the scaling of the Pure Random Walk version (PRWSAT) ofWalkSAT. PRWSAT is very simple because of the absence of heuristics: not only the clause is selected at random, but also the literal within that clause. The main result is that, despite the simplicity and absence of heuristics, it has non-trivial behavior on Random 3-SAT. There appears to be a threshold at a clause/variable ratio of about 2.65. Below the threshold, problems are solved in a tightly-distributed and linear number of flips. Above the threshold scaling appears to be non-polynomial. The simplicity and the nontrivial threshold make it a good candidate for theoretical analysis.

Progress in Multi-Genus Calculations for the Spinning String

Springer eBooks, 1990

We review progress in the calculation of multiloop amplitudes for the closed Neveu-Schwarz-Ramond... more We review progress in the calculation of multiloop amplitudes for the closed Neveu-Schwarz-Ramond string in a flat ten dimensional background. When the picture changing operators are placed at the zeroes of a holomorphic one-form then it turns out to be possible to do the sum over spin structures for genus g ≤ 9 for the vacuum amplitude. The result of this sum is zero point wise in moduli space and not just a total derivative as might be expected in a more general gauge. We look at the possibility that singularities could arise for certain values of the moduli and also discuss why this gauge choice is so powerful by showing the similarity to “light-cone” diagrams.

Satisfiability algorithms and finite quantification

Abstract This paper makes three observations with regard to the application of algorithms such as... more Abstract This paper makes three observations with regard to the application of algorithms such as wsat and relsat to problems of practical interest. First, we identify a speci c calculation (\ subsearch") that is performed at each inference step by any existing satis ...

Physics Letters B, Nov 1, 1984

European Journal of Operational Research, Jul 1, 2017

Nuclear Physics B, Aug 1, 1983

It is shown that there exists a class of finite four-dimensional field theories. This class is ge... more It is shown that there exists a class of finite four-dimensional field theories. This class is generated by adding specific combinations of mass terms as well as terms cubic in the scalar and pseudo-scalar fields to the N = 4 supersymmetric Yang-Mills theory.

N = 1 supersymmetric mass terms in the N = 4 supersymmetric Yang-Mills theory

Physics Letters B, Mar 1, 1983

Abstract It is argued that the addition of N = 1 supersymmetric mass terms to the N = 4 supersymm... more Abstract It is argued that the addition of N = 1 supersymmetric mass terms to the N = 4 supersymmetric Yang-Mills theory does not result in a change in the ultraviolet properties of the theory.

Journal of Artificial Intelligence Research, Feb 1, 2004

Physics Letters B, Oct 1, 1985

National Conference on Artificial Intelligence, Aug 4, 1996

National Conference on Artificial Intelligence, Jul 1, 1998

When search techniques are used to solve a practical problem, the solution produced is often brit... more When search techniques are used to solve a practical problem, the solution produced is often brittle in the sense that small execution difficulties can have an arbitrarily large effect on the viability of the solution. The AI community has responded to this difficulty by investigating the development of "robust problem solvers" that are intended to be proof against this difficulty. We argue that robustness is best cast not as a property of the problem solver, but as a property of the solution. We introduce a new class of models for a logical theory, called supermodels, that captures this idea. Supermodels guarantee that the model in question is robust, and allow us to quantify the degree to which it is so. We investigate the theoretical properties of supermodels, showing that finding supermodels is typically of the same theoretical complexity as finding models. We provide a general way to modify a logical theory so that a model of the modified theory is a supermodel of the original. Experimentally, we show that the supermodel problem exhibits phase transition behavior similar to that found in other satisfiability work.

Physics Letters B, Jun 1, 1985

We consider the one-loop finite N = 1 Yang-Mills theories and by a mixture of direct calculation ... more We consider the one-loop finite N = 1 Yang-Mills theories and by a mixture of direct calculation and deductions from the all-orders finiteness of some N = 2 theories we find an expression h)r the three-loop divergence in the matter field self-energy. We also discuss the effect of explicit supersymmetry breaking terms at the two-loop level.

Physics Letters B, Apr 1, 1984

The two4oop ~ function for an arbitrary rigid supersymmetric theory is given. The necessary and s... more The two4oop ~ function for an arbitrary rigid supersymmetric theory is given. The necessary and sufficient conditions for a rigid supersymmetric theory to be finite at one loop are derived. It is shown that these conditions also imply two4oop f'miteness.

Portfolio optimization is one of the most important problems in the finance field. The traditiona... more Portfolio optimization is one of the most important problems in the finance field. The traditional mean-variance model has its drawbacks since it fails to take the market uncertainty into account. In this work, we investigate a two-stage stochastic portfolio optimization model with a comprehensive set of real world trading constraints in order to capture the market uncertainties in terms of future asset prices. A hybrid approach, which integrates genetic algorithm (GA) and a linear programming (LP) solver is proposed in order to solve the model, where GA is used to search for the assets selection heuristically and the LP solver solves the corresponding sub-problems of weight allocation optimally. Scenarios are generated to capture uncertain prices of assets for five benchmark market instances. The computational results indicate that the proposed hybrid algorithm can obtain very promising solutions. Possible future research directions are also discussed.

Annals of Operations Research, Sep 9, 2015

Commercial airports are under increasing pressure to comply with the Eurocontrol Collaborative De... more Commercial airports are under increasing pressure to comply with the Eurocontrol Collaborative Decision Making (CDM) initiative, to ensure that information is passed between stakeholders, integrate automated decision support or make predictions. These systems can also aid effective operations beyond the airport by communicating scheduling decisions to other relevant parties, such as Eurocontrol, for passing on to downstream airports and enabling overall airspace improvements. One of the major CDM components is aimed at producing the target take-off times and target startup-approval times, i.e. scheduling when the aircraft should push back from the gates and start their engines and when they will take off. For medium-sized airports, a common choice for this is a "Pre-Departure Sequencer" (PDS). In this paper, we describe the design and requirements challenges which arose during our development of a PDS system for medium sized international airports. Firstly, the scheduling problem is highly dynamic and event driven. Secondly, it is important to end-users that the system be predictable and, as far as possible, transparent in its operation, with decisions that can be explained. Thirdly, users can override decisions, and this information has to be taken into account. Finally, it is important that the system is as fair as possible for all users This work was supported in part by an EPSRC 'Research Development Fund' and also by EPSRC grant EP/F033613/1

Nuclear Physics B, Jun 1, 1992

Yang-Mills (SDYM) and also that, in perturbation theory, it has has a vanishing four particle sca... more Yang-Mills (SDYM) and also that, in perturbation theory, it has has a vanishing four particle scattering amplitude. We discuss how the dynamics of the three particle scattering implies that on shell states can only scatter if their momenta lie in the same self-dual plane and then investigate classical SDYM with the aim of comparing exact solutions with the tree level perturbation theory predictions. In particular for the gauge group SL(2,C) with a plane wave Hirota ansatz SDYM reduces to a complicated set of algebraic relations due to de Vega. Here we solve these conditions and the solutions are shown to correspond to collisions of plane wave kinks. The main result is that for a class of kinks the resulting phase shifts are non-zero, the solution as a whole is not pure gauge and so the scattering seems nontrivial. However the stress energy and Lagrangian density are confined to string like regions in the space time and in particular are zero for the incoming/outgoing kinks so the solution does not correspond to physical four point scattering.

National Conference on Artificial Intelligence, Jul 27, 1997

Many problem ensembles exhibit a phase transition that is associated with a large peak in the ave... more Many problem ensembles exhibit a phase transition that is associated with a large peak in the average cost of solving the problem instances. However, this peak is not necessarily due to a lack of solutions: indeed the average number of solutions is typically exponentially large. Here, we study this situation within the context of the satisfiability transition in Random SSAT. We find that a significant subclass of instances emerges as we cross the phase transition. These instances are characterized by having about 85-95% of their variables occurring in unary prime implicates (UPIs), with their remaining variables being subject to few constraints. In such instances the models are not randomly distributed but all lie in a cluster that is exponentially large, but still admits a simple description. Studying the effect of UPIs on the local search algorithm WSAT shows that these "single-cluster" instances are harder to solve, and we relate their appearance at the phase transition to the peak in search cost.

A constraint satisfaction problem (CSP) is a combinatorial optimisation problem with many real wo... more A constraint satisfaction problem (CSP) is a combinatorial optimisation problem with many real world applications. One of the key aspects to consider when solving a CSP is the order in which the variables are selected to be instantiated. In this study, we describe a genetic programming hyper-heuristic approach to automatically produce heuristics for CSPs. Human-designed 'standard' heuristics are used as components enabling the construction of new variable ordering heuristics which is achieved through the proposed approach. We present empirical evidence that the heuristics produced by our approach are competitive considering the cost of the search when compared to the standard heuristics which are used to obtain the components for the new heuristics. The proposed approach is able to produce specialized heuristics for specific classes of instances that outperform the best standard heuristics for the same instances.

Variable ordering has been a recurrent topic of study in the field of constraint satisfaction bec... more Variable ordering has been a recurrent topic of study in the field of constraint satisfaction because of its impact in the cost of the search. Various variable ordering heuristics have been proposed to help guiding the search under different situations. One important direction of the study about variable ordering is the use of distinct heuristics as the search progresses to reduce the cost of the search. Even though the idea of combining heuristics goes back to the 60's, only a few works that study which heuristics to use and how they interact with each other have been described. In this investigation, we analyse the interactions of four important variable ordering heuristics by combining them through hyper-heuristics that decide the heuristic to apply based on the depth of the nodes in the search tree. The paper does not include any specific model for generating such hyper-heuristics; instead, it presents an analysis of the changes in the cost when different heuristics are applied during the search by using one simple hyper-heuristic representation. The results show that selectively applying distinct heuristics as the search progresses may lead to important reductions in the cost of the search with respect to the performance of the same heuristics used in isolation.