1,771 research outputs found
Rank-Based Learning and Local Model Based Evolutionary Algorithm for High-Dimensional Expensive Multi-Objective Problems
Surrogate-assisted evolutionary algorithms have been widely developed to
solve complex and computationally expensive multi-objective optimization
problems in recent years. However, when dealing with high-dimensional
optimization problems, the performance of these surrogate-assisted
multi-objective evolutionary algorithms deteriorate drastically. In this work,
a novel Classifier-assisted rank-based learning and Local Model based
multi-objective Evolutionary Algorithm (CLMEA) is proposed for high-dimensional
expensive multi-objective optimization problems. The proposed algorithm
consists of three parts: classifier-assisted rank-based learning,
hypervolume-based non-dominated search, and local search in the relatively
sparse objective space. Specifically, a probabilistic neural network is built
as classifier to divide the offspring into a number of ranks. The offspring in
different ranks uses rank-based learning strategy to generate more promising
and informative candidates for real function evaluations. Then, radial basis
function networks are built as surrogates to approximate the objective
functions. After searching non-dominated solutions assisted by the surrogate
model, the candidates with higher hypervolume improvement are selected for real
evaluations. Subsequently, in order to maintain the diversity of solutions, the
most uncertain sample point from the non-dominated solutions measured by the
crowding distance is selected as the guided parent to further infill in the
uncertain region of the front. The experimental results of benchmark problems
and a real-world application on geothermal reservoir heat extraction
optimization demonstrate that the proposed algorithm shows superior performance
compared with the state-of-the-art surrogate-assisted multi-objective
evolutionary algorithms. The source code for this work is available at
https://github.com/JellyChen7/CLMEA
Hybridization of multi-objective deterministic particle swarm with derivative-free local searches
The paper presents a multi-objective derivative-free and deterministic global/local hybrid algorithm for the efficient and effective solution of simulation-based design optimization (SBDO) problems. The objective is to show how the hybridization of two multi-objective derivative-free global and local algorithms achieves better performance than the separate use of the two algorithms in solving specific SBDO problems for hull-form design. The proposed method belongs to the class of memetic algorithms, where the global exploration capability of multi-objective deterministic particle swarm optimization is enriched by exploiting the local search accuracy of a derivative-free multi-objective line-search method. To the authors best knowledge, studies are still limited on memetic, multi-objective, deterministic, derivative-free, and evolutionary algorithms for an effective and efficient solution of SBDO for hull-form design. The proposed formulation manages global and local searches based on the hypervolume metric. The hybridization scheme uses two parameters to control the local search activation and the number of function calls used by the local algorithm. The most promising values of these parameters were identified using forty analytical tests representative of the SBDO problem of interest. The resulting hybrid algorithm was finally applied to two SBDO problems for hull-form design. For both analytical tests and SBDO problems, the hybrid method achieves better performance than its global and local counterparts
Hypervolume-based multi-objective local search
This paper presents a multi-objective local search, where the selection is realized according to the hypervolume contribution of solutions. The HBMOLS algorithm proposed is inspired from the IBEA algorithm, an indicator-based multi-objective evolutionary algorithm proposed by Zitzler and Künzli in 2004, where the optimization goal is defined in terms of a binary indicator defining the selection operator. In this paper, we use the indicator optimization principle, and we apply it to an iterated local search algorithm, using hypervolume contribution indicator as selection mechanism. The methodology proposed here has been defined in order to be easily adaptable and to be as parameter-independent as possible. We carry out a range of experiments on the multi-objective flow shop problem and the multi-objective quadratic assignment problem, using the hypervolume contribution selection as well as two different binary indicators which were initially proposed in the IBEA algorithm. Experimental results indicate that the HBMOLS algorithm is highly effective in comparison with the algorithms based on binary indicators
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)
PasMoQAP: A Parallel Asynchronous Memetic Algorithm for solving the Multi-Objective Quadratic Assignment Problem
Multi-Objective Optimization Problems (MOPs) have attracted growing attention
during the last decades. Multi-Objective Evolutionary Algorithms (MOEAs) have
been extensively used to address MOPs because are able to approximate a set of
non-dominated high-quality solutions. The Multi-Objective Quadratic Assignment
Problem (mQAP) is a MOP. The mQAP is a generalization of the classical QAP
which has been extensively studied, and used in several real-life applications.
The mQAP is defined as having as input several flows between the facilities
which generate multiple cost functions that must be optimized simultaneously.
In this study, we propose PasMoQAP, a parallel asynchronous memetic algorithm
to solve the Multi-Objective Quadratic Assignment Problem. PasMoQAP is based on
an island model that structures the population by creating sub-populations. The
memetic algorithm on each island individually evolve a reduced population of
solutions, and they asynchronously cooperate by sending selected solutions to
the neighboring islands. The experimental results show that our approach
significatively outperforms all the island-based variants of the
multi-objective evolutionary algorithm NSGA-II. We show that PasMoQAP is a
suitable alternative to solve the Multi-Objective Quadratic Assignment Problem.Comment: 8 pages, 3 figures, 2 tables. Accepted at Conference on Evolutionary
Computation 2017 (CEC 2017
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
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