2020 IEEE Symposium Series on Computational Intelligence (SSCI), 2020
The Pareto dominance relation is a special case of a cone order. Cone orders and the Pareto order... more The Pareto dominance relation is a special case of a cone order. Cone orders and the Pareto order are translation invariant and also multiplication invariant by any positive real. Employment of more general cone orders instead of the Pareto order gives rise to interesting exploration opportunities for algorithm design. In this paper, the standard Pareto dominance relation has been extended to cone dominance with a pointed convex obtuse cone, a superset of the Pareto dominance cone, i.e., the non-negative orthant, by rotating the edges of the Pareto order cone. The basic idea is in line with earlier work on cone-orders in multicriteria decision making and here, in particular, the cone-order is used (1) to increase solutions’ dominance area and hence improve the convergence speed of the algorithm and (2) to formulate trade-off constraints. The minima of the obtuse cone order are also Pareto optimal. However, not all minima of the Pareto order are also minima of the obtuse cone order. Therefore we use the edge-rotated cone in an alternating manner with the standard Pareto cone to guarantee coverage of the entire Pareto front. The edge-rotated cones have been integrated in several state-of-the-art multi-objective evolutionary algorithms (MOEAs) and proven to be able to improve the performance of MOEAs on multi-objective optimization problems with the linear, concave, convex and disconnected Pareto front. Furthermore, when the edges of the cone are rotated by different angles, the algorithm obtains solution sets located in different areas of the Pareto front. This behavior can be used to take the preference of the targeted region on the Pareto front into the algorithm. In particular, by using obtuse cones, regions where trade-off is very unbalanced can be discarded. This is quantified by showing a relationship between the angle and the trade-off rate corresponding to this angle.
As more and more people worldwide make use of services provided through the Internet, the damage ... more As more and more people worldwide make use of services provided through the Internet, the damage caused by attacks aiming to disrupt these services keeps increasing. One such type of attack is the DoS (Denial of Service) attack, in which an attacker attempts to keep the victim’s resources such as bandwidth, memory, CPU cycles or number of connections occupied and degrade the experience of legitimate users communicating with the victim. In this work, we develop a system to detect such attacks by creating forecast models of network traffic features using timeseries algorithms, and detecting anomalies by tracking outlying values.
2016 12th International Conference on Natural Computation, Fuzzy Systems and Knowledge Discovery (ICNC-FSKD), 2016
The ultimate goal of multi-objective optimization is to provide potential solutions to a decision... more The ultimate goal of multi-objective optimization is to provide potential solutions to a decision maker. Usually, what they are concerned with is a Pareto front in an interesting/preferred region, instead of the whole Pareto front. In this paper, a method for effectively approximating a preferred Pareto front, based on multiobjective efficient global optimization (EGO), is introduced. EGO uses Gaussian processes (or Kriging) to build a model of the objective function. Our variant of EGO uses truncated expected hypervolume improvement (TEHVI) as an infill criterion, which takes predictive mean, variance and preference region in the objective space into consideration. Compared to expected hypervolume improvement (EHVI), the probability density function in TEHVI follows a truncated normal distribution. This paper proposes a TEHVI method that makes it possible to set a region of interest on the Pareto front and focus search effectively on this preferred region. An expression for the exact and efficient computation of the TEHVI for truncation over a two dimensional range is derived, and benchmark results on standard bi-objective problems for small budget of evaluations are computed, confirming the effectiveness of the new approach.
We continue recent work on the definition of multimodality in multiobjective optimization (MO) an... more We continue recent work on the definition of multimodality in multiobjective optimization (MO) and the introduction of a test bed for multimodal MO problems. This goes beyond well-known diversity maintenance approaches but instead focuses on the landscape topology induced by the objective functions. More general multimodal MO problems are considered by allowing ellipsoid contours for single-objective subproblems. An experimental analysis compares two MO algorithms, one that explicitly relies on hypervolume gradient approximation, and one that is based on local search, both on a selection of generated example problems. We do not focus on performance but on the interaction induced by the problems and algorithms, which can be described by means of specific characteristics explicitly designed for the multimodal MO setting. Furthermore, we widen the scope of our analysis by additionally applying visualization techniques in the decision space. This strengthens and extends the foundations ...
2016 IEEE Congress on Evolutionary Computation (CEC), 2016
In optimization with expensive black box evaluations, the expected improvement algorithm (also ca... more In optimization with expensive black box evaluations, the expected improvement algorithm (also called efficient global optimization) is a commonly applied method. It uses Gaussian Processes (or Kriging) to build a model of the objective function and uses the expected improvement as an infill criterion, taking into account both - predictive mean and variance. It has been generalized to multi-objective optimization using the expected hypervolume improvement, which measures the expected gain in the hypervolume indicator of a Pareto front approximation. However, this criterion assumes an unbounded objective space even if it is often known a-priori that the objective function values are within a prescribed range, e.g., lower bounded by zero. To take advantage of such a-priori knowledge, this paper introduces the truncated expected hypervolume improvement and a multiobjective efficient global optimization method that is based on it. In this paper it is shown how to compute the truncated expected hypervolume improvement exactly and efficiently. Then it is tested as an infill criterion in efficient global optimization. It is shown that it can effectively make use of a-priori knowledge and achieve better results in cases where such knowledge is given. The usefulness of the new approach is demonstrated in benchmark examples and applications from robust PID (proportional-integral-derivative) controller optimization. The empirical studies in this paper are confined to the bi-objective case.
ABSTRACT In this paper we discuss cone-based hypervolume indicators (CHI) that generalize the cla... more ABSTRACT In this paper we discuss cone-based hypervolume indicators (CHI) that generalize the classical hypervolume indicator (HI) in Pareto optimization. A family of polyhedral cones with scalable opening angle γ is studied. These γ-cones can be efficiently constructed and have a number of favorable properties. It is shown that for γ-cones dominance can be checked efficiently and the CHI computation can be reduced to the computation of the HI in linear time with respect to the number of points μ in an approximation set. Besides, individual contributions to these can be computed using a similar transformation to the case of Pareto dominance cones. Furthermore, we present first results on theoretical properties of optimal μ-distributions of this indicator. It is shown that in two dimensions and for linear Pareto fronts the optimal μ-distribution has uniform gap. For general Pareto curves and γ approaching zero, it is proven that the optimal μ-distribution becomes equidistant in the Manhattan distance. An important implication of this theoretical result is that by replacing the classical hypervolume indicator by CHI with γ-cones in hypervolume-based algorithms, such as the SMS-EMOA, the distribution can be shifted from a distribution that is focussed more on the knee point region to a distribution that is uniformly distributed. This is illustrated by numerical examples in 2-D. Moreover, in 3-D a similar dependency on γ is observed.
2020 IEEE Symposium Series on Computational Intelligence (SSCI), 2020
The Pareto dominance relation is a special case of a cone order. Cone orders and the Pareto order... more The Pareto dominance relation is a special case of a cone order. Cone orders and the Pareto order are translation invariant and also multiplication invariant by any positive real. Employment of more general cone orders instead of the Pareto order gives rise to interesting exploration opportunities for algorithm design. In this paper, the standard Pareto dominance relation has been extended to cone dominance with a pointed convex obtuse cone, a superset of the Pareto dominance cone, i.e., the non-negative orthant, by rotating the edges of the Pareto order cone. The basic idea is in line with earlier work on cone-orders in multicriteria decision making and here, in particular, the cone-order is used (1) to increase solutions’ dominance area and hence improve the convergence speed of the algorithm and (2) to formulate trade-off constraints. The minima of the obtuse cone order are also Pareto optimal. However, not all minima of the Pareto order are also minima of the obtuse cone order. Therefore we use the edge-rotated cone in an alternating manner with the standard Pareto cone to guarantee coverage of the entire Pareto front. The edge-rotated cones have been integrated in several state-of-the-art multi-objective evolutionary algorithms (MOEAs) and proven to be able to improve the performance of MOEAs on multi-objective optimization problems with the linear, concave, convex and disconnected Pareto front. Furthermore, when the edges of the cone are rotated by different angles, the algorithm obtains solution sets located in different areas of the Pareto front. This behavior can be used to take the preference of the targeted region on the Pareto front into the algorithm. In particular, by using obtuse cones, regions where trade-off is very unbalanced can be discarded. This is quantified by showing a relationship between the angle and the trade-off rate corresponding to this angle.
As more and more people worldwide make use of services provided through the Internet, the damage ... more As more and more people worldwide make use of services provided through the Internet, the damage caused by attacks aiming to disrupt these services keeps increasing. One such type of attack is the DoS (Denial of Service) attack, in which an attacker attempts to keep the victim’s resources such as bandwidth, memory, CPU cycles or number of connections occupied and degrade the experience of legitimate users communicating with the victim. In this work, we develop a system to detect such attacks by creating forecast models of network traffic features using timeseries algorithms, and detecting anomalies by tracking outlying values.
2016 12th International Conference on Natural Computation, Fuzzy Systems and Knowledge Discovery (ICNC-FSKD), 2016
The ultimate goal of multi-objective optimization is to provide potential solutions to a decision... more The ultimate goal of multi-objective optimization is to provide potential solutions to a decision maker. Usually, what they are concerned with is a Pareto front in an interesting/preferred region, instead of the whole Pareto front. In this paper, a method for effectively approximating a preferred Pareto front, based on multiobjective efficient global optimization (EGO), is introduced. EGO uses Gaussian processes (or Kriging) to build a model of the objective function. Our variant of EGO uses truncated expected hypervolume improvement (TEHVI) as an infill criterion, which takes predictive mean, variance and preference region in the objective space into consideration. Compared to expected hypervolume improvement (EHVI), the probability density function in TEHVI follows a truncated normal distribution. This paper proposes a TEHVI method that makes it possible to set a region of interest on the Pareto front and focus search effectively on this preferred region. An expression for the exact and efficient computation of the TEHVI for truncation over a two dimensional range is derived, and benchmark results on standard bi-objective problems for small budget of evaluations are computed, confirming the effectiveness of the new approach.
We continue recent work on the definition of multimodality in multiobjective optimization (MO) an... more We continue recent work on the definition of multimodality in multiobjective optimization (MO) and the introduction of a test bed for multimodal MO problems. This goes beyond well-known diversity maintenance approaches but instead focuses on the landscape topology induced by the objective functions. More general multimodal MO problems are considered by allowing ellipsoid contours for single-objective subproblems. An experimental analysis compares two MO algorithms, one that explicitly relies on hypervolume gradient approximation, and one that is based on local search, both on a selection of generated example problems. We do not focus on performance but on the interaction induced by the problems and algorithms, which can be described by means of specific characteristics explicitly designed for the multimodal MO setting. Furthermore, we widen the scope of our analysis by additionally applying visualization techniques in the decision space. This strengthens and extends the foundations ...
2016 IEEE Congress on Evolutionary Computation (CEC), 2016
In optimization with expensive black box evaluations, the expected improvement algorithm (also ca... more In optimization with expensive black box evaluations, the expected improvement algorithm (also called efficient global optimization) is a commonly applied method. It uses Gaussian Processes (or Kriging) to build a model of the objective function and uses the expected improvement as an infill criterion, taking into account both - predictive mean and variance. It has been generalized to multi-objective optimization using the expected hypervolume improvement, which measures the expected gain in the hypervolume indicator of a Pareto front approximation. However, this criterion assumes an unbounded objective space even if it is often known a-priori that the objective function values are within a prescribed range, e.g., lower bounded by zero. To take advantage of such a-priori knowledge, this paper introduces the truncated expected hypervolume improvement and a multiobjective efficient global optimization method that is based on it. In this paper it is shown how to compute the truncated expected hypervolume improvement exactly and efficiently. Then it is tested as an infill criterion in efficient global optimization. It is shown that it can effectively make use of a-priori knowledge and achieve better results in cases where such knowledge is given. The usefulness of the new approach is demonstrated in benchmark examples and applications from robust PID (proportional-integral-derivative) controller optimization. The empirical studies in this paper are confined to the bi-objective case.
ABSTRACT In this paper we discuss cone-based hypervolume indicators (CHI) that generalize the cla... more ABSTRACT In this paper we discuss cone-based hypervolume indicators (CHI) that generalize the classical hypervolume indicator (HI) in Pareto optimization. A family of polyhedral cones with scalable opening angle γ is studied. These γ-cones can be efficiently constructed and have a number of favorable properties. It is shown that for γ-cones dominance can be checked efficiently and the CHI computation can be reduced to the computation of the HI in linear time with respect to the number of points μ in an approximation set. Besides, individual contributions to these can be computed using a similar transformation to the case of Pareto dominance cones. Furthermore, we present first results on theoretical properties of optimal μ-distributions of this indicator. It is shown that in two dimensions and for linear Pareto fronts the optimal μ-distribution has uniform gap. For general Pareto curves and γ approaching zero, it is proven that the optimal μ-distribution becomes equidistant in the Manhattan distance. An important implication of this theoretical result is that by replacing the classical hypervolume indicator by CHI with γ-cones in hypervolume-based algorithms, such as the SMS-EMOA, the distribution can be shifted from a distribution that is focussed more on the knee point region to a distribution that is uniformly distributed. This is illustrated by numerical examples in 2-D. Moreover, in 3-D a similar dependency on γ is observed.
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