1,094 research outputs found
Fast calculation of multiobjective probability of improvement and expected improvement criteria for Pareto optimization
The use of surrogate based optimization (SBO) is widely spread in engineering design to reduce the number of computational expensive simulations. However, "real-world" problems often consist of multiple, conflicting objectives leading to a set of competitive solutions (the Pareto front). The objectives are often aggregated into a single cost function to reduce the computational cost, though a better approach is to use multiobjective optimization methods to directly identify a set of Pareto-optimal solutions, which can be used by the designer to make more efficient design decisions (instead of weighting and aggregating the costs upfront). Most of the work in multiobjective optimization is focused on multiobjective evolutionary algorithms (MOEAs). While MOEAs are well-suited to handle large, intractable design spaces, they typically require thousands of expensive simulations, which is prohibitively expensive for the problems under study. Therefore, the use of surrogate models in multiobjective optimization, denoted as multiobjective surrogate-based optimization, may prove to be even more worthwhile than SBO methods to expedite the optimization of computational expensive systems. In this paper, the authors propose the efficient multiobjective optimization (EMO) algorithm which uses Kriging models and multiobjective versions of the probability of improvement and expected improvement criteria to identify the Pareto front with a minimal number of expensive simulations. The EMO algorithm is applied on multiple standard benchmark problems and compared against the well-known NSGA-II, SPEA2 and SMS-EMOA multiobjective optimization methods
Generating Interpretable Fuzzy Controllers using Particle Swarm Optimization and Genetic Programming
Autonomously training interpretable control strategies, called policies,
using pre-existing plant trajectory data is of great interest in industrial
applications. Fuzzy controllers have been used in industry for decades as
interpretable and efficient system controllers. In this study, we introduce a
fuzzy genetic programming (GP) approach called fuzzy GP reinforcement learning
(FGPRL) that can select the relevant state features, determine the size of the
required fuzzy rule set, and automatically adjust all the controller parameters
simultaneously. Each GP individual's fitness is computed using model-based
batch reinforcement learning (RL), which first trains a model using available
system samples and subsequently performs Monte Carlo rollouts to predict each
policy candidate's performance. We compare FGPRL to an extended version of a
related method called fuzzy particle swarm reinforcement learning (FPSRL),
which uses swarm intelligence to tune the fuzzy policy parameters. Experiments
using an industrial benchmark show that FGPRL is able to autonomously learn
interpretable fuzzy policies with high control performance.Comment: Accepted at Genetic and Evolutionary Computation Conference 2018
(GECCO '18
Diversifying Multi-Objective Gradient Techniques and their Role in Hybrid Multi-Objective Evolutionary Algorithms for Deformable Medical Image Registration
Gradient methods and their value in single-objective, real-valued
optimization are well-established. As such, they play
a key role in tackling real-world, hard optimization problems
such as deformable image registration (DIR). A key question
is to which extent gradient techniques can also play a role in
a multi-objective approach to DIR. We therefore aim to exploit
gradient information within an evolutionary-algorithm-based
multi-objective optimization framework for DIR. Although an
analytical description of the multi-objective gradient (the set
of all Pareto-optimal improving directions) is
available, it is nontrivial how to best choose the most
appropriate direction per solution because these directions are
not necessarily uniformly distributed in objective space. To
address this, we employ a Monte-Carlo method to obtain
a discrete, spatially-uniformly distributed approximation of
the set of Pareto-optimal improving directions. We then
apply a diversification technique in which each solution is
associated with a unique direction from this set based on its
multi- as well as single-objective rank. To assess its utility,
we compare a state-of-the-art multi-objective evolutionary
algorithm with three different hybrid versions thereof on
several benchmark problems and two medical DIR problems.
Results show that the diversification strategy successfully
leads to unbiased improvement, helping an adaptive hybrid
scheme solve all problems, but the evolutionary algorithm
remains the most powerful optimization method, providing
the best balance between proximity and diversity
A survey on handling computationally expensive multiobjective optimization problems with evolutionary algorithms
This is the author accepted manuscript. The final version is available from Springer Verlag via the DOI in this record.Evolutionary algorithms are widely used for solving multiobjective optimization problems but are often criticized because of a large number of function evaluations needed. Approximations, especially function approximations, also referred to as surrogates or metamodels are commonly used in the literature to reduce the computation time. This paper presents a survey of 45 different recent algorithms proposed in the literature between 2008 and 2016 to handle computationally expensive multiobjective optimization problems. Several algorithms are discussed based on what kind of an approximation such as problem, function or fitness approximation they use. Most emphasis is given to function approximation-based algorithms. We also compare these algorithms based on different criteria such as metamodeling technique and evolutionary algorithm used, type and dimensions of the problem solved, handling constraints, training time and the type of evolution control. Furthermore, we identify and discuss some promising elements and major issues among algorithms in the literature related to using an approximation and numerical settings used. In addition, we discuss selecting an algorithm to solve a given computationally expensive multiobjective optimization problem based on the dimensions in both objective and decision spaces and the computation budget available.The research of Tinkle Chugh was funded by the COMAS Doctoral Program (at the University of Jyväskylä) and FiDiPro Project DeCoMo (funded by Tekes, the Finnish Funding Agency for Innovation), and the research of Dr. Karthik Sindhya was funded by SIMPRO project funded by Tekes as well as DeCoMo
One PLOT to Show Them All: Visualization of Efficient Sets in Multi-Objective Landscapes
Visualization techniques for the decision space of continuous multi-objective
optimization problems (MOPs) are rather scarce in research. For long, all
techniques focused on global optimality and even for the few available
landscape visualizations, e.g., cost landscapes, globality is the main
criterion. In contrast, the recently proposed gradient field heatmaps (GFHs)
emphasize the location and attraction basins of local efficient sets, but
ignore the relation of sets in terms of solution quality.
In this paper, we propose a new and hybrid visualization technique, which
combines the advantages of both approaches in order to represent local and
global optimality together within a single visualization. Therefore, we build
on the GFH approach but apply a new technique for approximating the location of
locally efficient points and using the divergence of the multi-objective
gradient vector field as a robust second-order condition. Then, the relative
dominance relationship of the determined locally efficient points is used to
visualize the complete landscape of the MOP. Augmented by information on the
basins of attraction, this Plot of Landscapes with Optimal Trade-offs (PLOT)
becomes one of the most informative multi-objective landscape visualization
techniques available.Comment: This version has been accepted for publication at the 16th
International Conference on Parallel Problem Solving from Nature (PPSN XVI
A Multi-Objective Deep Reinforcement Learning Framework
This paper introduces a new scalable multi-objective deep reinforcement
learning (MODRL) framework based on deep Q-networks. We develop a
high-performance MODRL framework that supports both single-policy and
multi-policy strategies, as well as both linear and non-linear approaches to
action selection. The experimental results on two benchmark problems
(two-objective deep sea treasure environment and three-objective Mountain Car
problem) indicate that the proposed framework is able to find the
Pareto-optimal solutions effectively. The proposed framework is generic and
highly modularized, which allows the integration of different deep
reinforcement learning algorithms in different complex problem domains. This
therefore overcomes many disadvantages involved with standard multi-objective
reinforcement learning methods in the current literature. The proposed
framework acts as a testbed platform that accelerates the development of MODRL
for solving increasingly complicated multi-objective problems.Comment: 21 page
Efficient Computation of Expected Hypervolume Improvement Using Box Decomposition Algorithms
In the field of multi-objective optimization algorithms, multi-objective
Bayesian Global Optimization (MOBGO) is an important branch, in addition to
evolutionary multi-objective optimization algorithms (EMOAs). MOBGO utilizes
Gaussian Process models learned from previous objective function evaluations to
decide the next evaluation site by maximizing or minimizing an infill
criterion. A common criterion in MOBGO is the Expected Hypervolume Improvement
(EHVI), which shows a good performance on a wide range of problems, with
respect to exploration and exploitation. However, so far it has been a
challenge to calculate exact EHVI values efficiently. In this paper, an
efficient algorithm for the computation of the exact EHVI for a generic case is
proposed. This efficient algorithm is based on partitioning the integration
volume into a set of axis-parallel slices. Theoretically, the upper bound time
complexities are improved from previously and , for two- and
three-objective problems respectively, to , which is
asymptotically optimal. This article generalizes the scheme in higher
dimensional case by utilizing a new hyperbox decomposition technique, which was
proposed by D{\"a}chert et al, EJOR, 2017. It also utilizes a generalization of
the multilayered integration scheme that scales linearly in the number of
hyperboxes of the decomposition. The speed comparison shows that the proposed
algorithm in this paper significantly reduces computation time. Finally, this
decomposition technique is applied in the calculation of the Probability of
Improvement (PoI)
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