A new approach to data clustering is proposed, in which two or more measures of cluster quality a... more A new approach to data clustering is proposed, in which two or more measures of cluster quality are simultaneously optimized using a multiobjective evolutionary algorithm (EA). For this purpose, the PESA-II EA is adapted for the clustering problem by the incorporation of specialized mutation and initialization procedures, described herein.
Abstract The probabilistic traveling salesman problem concerns the best way to visit a set of cus... more Abstract The probabilistic traveling salesman problem concerns the best way to visit a set of customers located in some metric space, where each customer requires a visit only with some known probability. A solution to this problem is an a priori tour which visits all customers, and the objective is to minimize the expected length of the a priori tour over all customer subsets, assuming that customers in any given subset must be visited in the same order as they appear in the a priori tour.
In engineering and other 'real-world'applications, multiobjective optimization problems must freq... more In engineering and other 'real-world'applications, multiobjective optimization problems must frequently be tackled on a tight evaluation budget—tens or hundreds of function evaluations, rather than thousands. In this paper, we investigate two algorithms that use advanced initialization and search strategies to operate better under these conditions. The first algorithm, Bin_MSOPS, uses a binary search tree to divide up the decision space, and tries to sample from the largest empty regions near 'fit'solutions.
Abstract The probabilistic traveling salesman problem concerns the best way to visit a set of cus... more Abstract The probabilistic traveling salesman problem concerns the best way to visit a set of customers located in some metric space, where each customer requires a visit only with some known probability. A solution to this problem is an a priori tour which visits all customers, and the objective is to minimize the expected length of the a priori tour over all customer subsets, assuming that customers in any given subset must be visited in the same order as they appear in the a priori tour.
Predicting stochastic search algorithm performance using landscape state machines
Abstract A landscape state machine (LSM) is a Markov model describing the transition probabilitie... more Abstract A landscape state machine (LSM) is a Markov model describing the transition probabilities between the fitness' levels' of an optimization problem, when a given neighbourhood (or mutation) operator is applied.
Assessing the performance of the pareto archived evolution strategy
Abstract Proper comparison of the performance of two or more multiobjective optimisers is a compl... more Abstract Proper comparison of the performance of two or more multiobjective optimisers is a complex problem of prime importance to the multiobjective evolutionary eld. In this workshop paper we report on the use of sound statistical techniques and new test functions to assess the performance of a novel evolutionary optimiser, the Pareto Archived Evolutionary Strategy, and to compare its performance with two well known MOGAs.
Here,” small” corresponds to a prespecified threshold of the DM. Uncertainty (especially noise) i... more Here,” small” corresponds to a prespecified threshold of the DM. Uncertainty (especially noise) in the constraints gives rise to the issue of reliability. We explain reliability in the last section, where we will also propose to solve uncertainty in the constraints by chance-constrained optimization.
The number of instrumental parameters controlling modern analytical apparatus can be substantial,... more The number of instrumental parameters controlling modern analytical apparatus can be substantial, and varying them systematically to optimize a particular chromatographic separation, for example, is out of the question because of the astronomical number of combinations that are possible (ie, the “search space” is very large). However, heuristic methods, such as those based on evolutionary computing, can be used to explore such search spaces efficiently.
This chapter is concerned with unsupervised classification, that is, the analysis of data sets fo... more This chapter is concerned with unsupervised classification, that is, the analysis of data sets for which no (or very little) training data is available. The main goals in this data-driven type of analysis are the discovery of a data set's underlying structure, and the identification of groups (or clusters) of homogeneous data items—a process commonly referred to as cluster analysis.
In this paper we assess the performance of three modern multiobjective evolutionary algorithms on... more In this paper we assess the performance of three modern multiobjective evolutionary algorithms on a real-world optimization problem related to the management of distributed databases. The algorithms assessed are the Strength Pareto Evolutionary Algorithm (SPEA), the Pareto Archived Evolution Strategy (PAES), and M-PAES, which is a Memetic Algorithm based variant of PAES.
Abstract The large majority of existing clustering algorithms are centered around the notion of a... more Abstract The large majority of existing clustering algorithms are centered around the notion of a feature, that is, individual data items are represented by their intrinsic properties, which are summarized by (usually numeric) feature vectors. However, certain applications require the clustering of data items that are defined by exclusively extrinsic properties: only the relationships between individual data items are known (that is, their similarities or dissimilarities).
Some multiobjective optimizers are better than others
Abstract The No-Free-Lunch (NFL) theorems hold for general multiobjective fitness spaces, in the ... more Abstract The No-Free-Lunch (NFL) theorems hold for general multiobjective fitness spaces, in the sense that, over a space of problems which is closed under permutation, any two algorithms will produce the same set of multiobjective samples. However, there are salient ways in which NFL does not generally hold in multiobjective optimization. Previously we have shown that a'free lunch'can arise when comparative metrics (rather than absolute metrics) are used for performance measurement.
The term 'multiobjectivization'refers to the casting of a single-objec-tive optimization problem ... more The term 'multiobjectivization'refers to the casting of a single-objec-tive optimization problem as a multiobjective one, a transformation that can be achieved by the addition of supplementary objectives or by the decomposition of the original objective function. In this paper, we analyze how multiobjectivization by decomposition changes the fitness landscape of a given problem and affects search. We find that decomposition has only one possible effect: to introduce plateaus of incomparable solutions.
The dual role of fragments in fragment‐assembly methods for de novo protein structure prediction
Abstract In fragment-assembly techniques for protein structure prediction, models of protein stru... more Abstract In fragment-assembly techniques for protein structure prediction, models of protein structure are assembled from fragments of known protein structures. This process is typically guided by a knowledge-based energy function and employs a heuristic optimisation method. The fragments play two important roles in this process: they define the set of structural parameters available, and they also assume the role of the main variation operators that are utilised by the optimiser.
DNA sequences that can bind selectively and specifically to target molecules are known as aptamer... more DNA sequences that can bind selectively and specifically to target molecules are known as aptamers. Normally such binding analyses are performed using soluble aptamers. However, there is much to be gained by using an on-chip or microarray format, where a large number of aptameric DNA sequences can be interrogated simultaneously.
Towards landscape analyses to inform the design of a hybrid local search for the multiobjective quadratic assignment problem
Abstract The quadratic assignment problem (QAP) is a very difficult and practically relevant comb... more Abstract The quadratic assignment problem (QAP) is a very difficult and practically relevant combinatorial optimization problem which has attracted much research effort Local search (LS) moves can be quickly evaluated on the QAP, and hence favoured methods tend to be hybrids of global optimization schemes and LS.
Abstract. Ant-based clustering and sorting is a nature-inspired heuristic for general clustering ... more Abstract. Ant-based clustering and sorting is a nature-inspired heuristic for general clustering tasks. It has been applied variously, from problems arising in commerce, to circuit design, to text-mining, all with some promise. However, although early results were broadly encouraging, there has been very limited analytical evaluation of antbased clustering.
We introduce a new multiobjective evolutionary algorithm called PESA (the Pareto Envelope-based S... more We introduce a new multiobjective evolutionary algorithm called PESA (the Pareto Envelope-based Selection Algorithm), in which selection and diversity maintenance are controlled via a simple hyper-grid based scheme. PESA's selection method is relatively unusual in comparison with current well known multiobjective evolutionary algorithms, which tend to use counts based on the degree to which solutions dominate others in the population. The diversity maintenance method is similar to that used by certain other methods.
Abstract Evolutionary multiobjective optimization (EMO) boasts a proliferation of algorithms and ... more Abstract Evolutionary multiobjective optimization (EMO) boasts a proliferation of algorithms and benchmark problems. We need principled ways to compare the performance of different EMO algorithms, but this is complicated by the fact that the result of an EMO run is not a single scalar value, but a collection of vectors forming a nondominated set. Various metrics for nondominated sets have been suggested. We compare several, using the framework of'outperformance relations'(Hansen and Jaszkiewicz, 1998).
Abstract: In this paper, the problem of unsupervised feature selection and its formulation as a m... more Abstract: In this paper, the problem of unsupervised feature selection and its formulation as a multiobjective optimization problem are investigated. Two existing multiobjective methods from the literature are revisited and used as the basis for an algorithmic framework, encompassing both wrapper and filter methods of feature selection.
A new approach to data clustering is proposed, in which two or more measures of cluster quality a... more A new approach to data clustering is proposed, in which two or more measures of cluster quality are simultaneously optimized using a multiobjective evolutionary algorithm (EA). For this purpose, the PESA-II EA is adapted for the clustering problem by the incorporation of specialized mutation and initialization procedures, described herein.
Abstract The probabilistic traveling salesman problem concerns the best way to visit a set of cus... more Abstract The probabilistic traveling salesman problem concerns the best way to visit a set of customers located in some metric space, where each customer requires a visit only with some known probability. A solution to this problem is an a priori tour which visits all customers, and the objective is to minimize the expected length of the a priori tour over all customer subsets, assuming that customers in any given subset must be visited in the same order as they appear in the a priori tour.
In engineering and other 'real-world'applications, multiobjective optimization problems must freq... more In engineering and other 'real-world'applications, multiobjective optimization problems must frequently be tackled on a tight evaluation budget—tens or hundreds of function evaluations, rather than thousands. In this paper, we investigate two algorithms that use advanced initialization and search strategies to operate better under these conditions. The first algorithm, Bin_MSOPS, uses a binary search tree to divide up the decision space, and tries to sample from the largest empty regions near 'fit'solutions.
Abstract The probabilistic traveling salesman problem concerns the best way to visit a set of cus... more Abstract The probabilistic traveling salesman problem concerns the best way to visit a set of customers located in some metric space, where each customer requires a visit only with some known probability. A solution to this problem is an a priori tour which visits all customers, and the objective is to minimize the expected length of the a priori tour over all customer subsets, assuming that customers in any given subset must be visited in the same order as they appear in the a priori tour.
Predicting stochastic search algorithm performance using landscape state machines
Abstract A landscape state machine (LSM) is a Markov model describing the transition probabilitie... more Abstract A landscape state machine (LSM) is a Markov model describing the transition probabilities between the fitness' levels' of an optimization problem, when a given neighbourhood (or mutation) operator is applied.
Assessing the performance of the pareto archived evolution strategy
Abstract Proper comparison of the performance of two or more multiobjective optimisers is a compl... more Abstract Proper comparison of the performance of two or more multiobjective optimisers is a complex problem of prime importance to the multiobjective evolutionary eld. In this workshop paper we report on the use of sound statistical techniques and new test functions to assess the performance of a novel evolutionary optimiser, the Pareto Archived Evolutionary Strategy, and to compare its performance with two well known MOGAs.
Here,” small” corresponds to a prespecified threshold of the DM. Uncertainty (especially noise) i... more Here,” small” corresponds to a prespecified threshold of the DM. Uncertainty (especially noise) in the constraints gives rise to the issue of reliability. We explain reliability in the last section, where we will also propose to solve uncertainty in the constraints by chance-constrained optimization.
The number of instrumental parameters controlling modern analytical apparatus can be substantial,... more The number of instrumental parameters controlling modern analytical apparatus can be substantial, and varying them systematically to optimize a particular chromatographic separation, for example, is out of the question because of the astronomical number of combinations that are possible (ie, the “search space” is very large). However, heuristic methods, such as those based on evolutionary computing, can be used to explore such search spaces efficiently.
This chapter is concerned with unsupervised classification, that is, the analysis of data sets fo... more This chapter is concerned with unsupervised classification, that is, the analysis of data sets for which no (or very little) training data is available. The main goals in this data-driven type of analysis are the discovery of a data set's underlying structure, and the identification of groups (or clusters) of homogeneous data items—a process commonly referred to as cluster analysis.
In this paper we assess the performance of three modern multiobjective evolutionary algorithms on... more In this paper we assess the performance of three modern multiobjective evolutionary algorithms on a real-world optimization problem related to the management of distributed databases. The algorithms assessed are the Strength Pareto Evolutionary Algorithm (SPEA), the Pareto Archived Evolution Strategy (PAES), and M-PAES, which is a Memetic Algorithm based variant of PAES.
Abstract The large majority of existing clustering algorithms are centered around the notion of a... more Abstract The large majority of existing clustering algorithms are centered around the notion of a feature, that is, individual data items are represented by their intrinsic properties, which are summarized by (usually numeric) feature vectors. However, certain applications require the clustering of data items that are defined by exclusively extrinsic properties: only the relationships between individual data items are known (that is, their similarities or dissimilarities).
Some multiobjective optimizers are better than others
Abstract The No-Free-Lunch (NFL) theorems hold for general multiobjective fitness spaces, in the ... more Abstract The No-Free-Lunch (NFL) theorems hold for general multiobjective fitness spaces, in the sense that, over a space of problems which is closed under permutation, any two algorithms will produce the same set of multiobjective samples. However, there are salient ways in which NFL does not generally hold in multiobjective optimization. Previously we have shown that a'free lunch'can arise when comparative metrics (rather than absolute metrics) are used for performance measurement.
The term 'multiobjectivization'refers to the casting of a single-objec-tive optimization problem ... more The term 'multiobjectivization'refers to the casting of a single-objec-tive optimization problem as a multiobjective one, a transformation that can be achieved by the addition of supplementary objectives or by the decomposition of the original objective function. In this paper, we analyze how multiobjectivization by decomposition changes the fitness landscape of a given problem and affects search. We find that decomposition has only one possible effect: to introduce plateaus of incomparable solutions.
The dual role of fragments in fragment‐assembly methods for de novo protein structure prediction
Abstract In fragment-assembly techniques for protein structure prediction, models of protein stru... more Abstract In fragment-assembly techniques for protein structure prediction, models of protein structure are assembled from fragments of known protein structures. This process is typically guided by a knowledge-based energy function and employs a heuristic optimisation method. The fragments play two important roles in this process: they define the set of structural parameters available, and they also assume the role of the main variation operators that are utilised by the optimiser.
DNA sequences that can bind selectively and specifically to target molecules are known as aptamer... more DNA sequences that can bind selectively and specifically to target molecules are known as aptamers. Normally such binding analyses are performed using soluble aptamers. However, there is much to be gained by using an on-chip or microarray format, where a large number of aptameric DNA sequences can be interrogated simultaneously.
Towards landscape analyses to inform the design of a hybrid local search for the multiobjective quadratic assignment problem
Abstract The quadratic assignment problem (QAP) is a very difficult and practically relevant comb... more Abstract The quadratic assignment problem (QAP) is a very difficult and practically relevant combinatorial optimization problem which has attracted much research effort Local search (LS) moves can be quickly evaluated on the QAP, and hence favoured methods tend to be hybrids of global optimization schemes and LS.
Abstract. Ant-based clustering and sorting is a nature-inspired heuristic for general clustering ... more Abstract. Ant-based clustering and sorting is a nature-inspired heuristic for general clustering tasks. It has been applied variously, from problems arising in commerce, to circuit design, to text-mining, all with some promise. However, although early results were broadly encouraging, there has been very limited analytical evaluation of antbased clustering.
We introduce a new multiobjective evolutionary algorithm called PESA (the Pareto Envelope-based S... more We introduce a new multiobjective evolutionary algorithm called PESA (the Pareto Envelope-based Selection Algorithm), in which selection and diversity maintenance are controlled via a simple hyper-grid based scheme. PESA's selection method is relatively unusual in comparison with current well known multiobjective evolutionary algorithms, which tend to use counts based on the degree to which solutions dominate others in the population. The diversity maintenance method is similar to that used by certain other methods.
Abstract Evolutionary multiobjective optimization (EMO) boasts a proliferation of algorithms and ... more Abstract Evolutionary multiobjective optimization (EMO) boasts a proliferation of algorithms and benchmark problems. We need principled ways to compare the performance of different EMO algorithms, but this is complicated by the fact that the result of an EMO run is not a single scalar value, but a collection of vectors forming a nondominated set. Various metrics for nondominated sets have been suggested. We compare several, using the framework of'outperformance relations'(Hansen and Jaszkiewicz, 1998).
Abstract: In this paper, the problem of unsupervised feature selection and its formulation as a m... more Abstract: In this paper, the problem of unsupervised feature selection and its formulation as a multiobjective optimization problem are investigated. Two existing multiobjective methods from the literature are revisited and used as the basis for an algorithmic framework, encompassing both wrapper and filter methods of feature selection.
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Papers by Joshua Knowles