This paper proposes a novel surrogate-model-based multiobjective evolutionary algorithm called Differential Evolution for Multiobjective Optimization based on Gaussian Process models (GP-DEMO). The algorithm is based ...
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This paper proposes a novel surrogate-model-based multiobjective evolutionary algorithm called Differential Evolution for Multiobjective Optimization based on Gaussian Process models (GP-DEMO). The algorithm is based on the newly defined relations for comparing solutions under uncertainty. These relations minimize the possibility of wrongly performed comparisons of solutions due to inaccurate surrogate model approximations. The GP-DEMO algorithm was tested on several benchmark problems and two computationally expensive real-world problems. To be able to assess the results we compared them with another surrogate-model-based algorithm called Generational Evolution Control (GEC) and with the Differential Evolution for Multiobjective Optimization (DEMO). The quality of the results obtained with GP-DEMO was similar to the results obtained with DEMO, but with significantly fewer exactly evaluated solutions during the optimization process. The quality of the results obtained with GEC was lower compared to the quality gained with GP-DEMO and DEMO, mainly due to wrongly performed comparisons of the inaccurately approximated solutions. (C) 2014 Elsevier B.V. All rights reserved.
A central goal for multi-objective optimization problems is to compute their nondominated sets. In most cases these sets consist of infinitely many points and it is not a practical approach to compute them exactly. On...
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A central goal for multi-objective optimization problems is to compute their nondominated sets. In most cases these sets consist of infinitely many points and it is not a practical approach to compute them exactly. One solution to overcome this problem is to compute an enclosure, a special kind of coverage, of the nondominated set. For that computation one often makes use of so-called local upper bounds. In this paper we present a generalization of this concept. For the first time, this allows to apply a warm start strategy to the computation of an enclosure. We also show how this generalized concept allows to remove empty areas of an enclosure by deleting certain parts of the lower and upper bound sets which has not been possible in the past. We demonstrate how to apply our ideas to the box approximation algorithm, a general framework to compute an enclosure, as recently used in the solver called BAMOP. We show how that framework can be simplified and improved significantly, especially concerning its practical numerical use. In fact, we show for selected numerical instances that our new approach is up to eight times faster than the original one. Hence, our new framework is not only of theoretical but also of practical use, for instance for continuous convex or mixed-integer quadratic optimization problems.(c) 2023 Elsevier B.V. All rights reserved.
This paper presents a new two-phase algorithm for the bi-objective minimum spanning tree (BMST) problem. In the first phase, it computes the extreme supported efficient solutions resorting to both mathematical program...
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This paper presents a new two-phase algorithm for the bi-objective minimum spanning tree (BMST) problem. In the first phase, it computes the extreme supported efficient solutions resorting to both mathematical programming and algorithmic approaches, while the second phase is devoted to obtaining the remaining efficient solutions (non-extreme supported and non-supported). This latter phase is based on a new recursive procedure capable of generating all the spanning trees of a connected graph through edge interchanges based on increasing evaluation of non-zero reduced costs of associated weighted linear programs. Such a procedure exploits a common property of a wider class of problems to which the minimum spanning tree (MST) problem belongs, that is the spanning tree structure of its basic feasible solutions. Computational experiments are conducted on different families of graphs and with different types of cost. These results show that this new two-phase algorithm is correct, very easy to implement and it allows one to extract conclusions on the difficulty of finding the entire set of Pareto solutions of the BMST problem depending on the graph topology and the possible correlation of the edge costs.
In this paper, we extend the concept of quasidifferential to a new notion called semi-quasidifferential. This generalization is motivated by the convexificator notion. Some important properties of semiquasidifferentia...
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In this paper, we extend the concept of quasidifferential to a new notion called semi-quasidifferential. This generalization is motivated by the convexificator notion. Some important properties of semiquasidifferentials are established. The relationship between semi-quasidifferentials and the Clarke sub differential is studied, and a mean value theorem in terms of semi-quasidifferentials is proved. It is shown that this notion is helpful to investigate nonsmooth optimization problems even when the objective and/or constraint functions are discontinuous. Considering a multiobjective optimization problem, a characterization of some cones related to the feasible set is provided. They are used for deriving necessary and sufficient optimality conditions. We close the paper by obtaining optimality conditions in multi objective optimization in terms of semi-quasidifferentials. Some outcomes of the current work generalize the related results existing in the literature. (c) 2021 Elsevier B.V. All rights reserved.
Today's modern industries have found a wide array of applications for optimization methods based on modeling with Robust Parameter Designs (RPD). Methods of carrying out RPD have thus multiplied. However, little a...
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Today's modern industries have found a wide array of applications for optimization methods based on modeling with Robust Parameter Designs (RPD). Methods of carrying out RPD have thus multiplied. However, little attention has been given to the multiobjective optimization of correlated multiple responses using response surface with combined arrays. Considering this gap, this paper presents a multiobjective hybrid approach combining response surface methodology (RSM) with Principal Component Analysis (PCA) to study a multi-response dataset with an embedded noise factor, using a DOE combined array. How this approach differs from the most common approaches to RPD is that it derives the mean and variance equations using the propagation of error principle (POE). This comes from a control-noise response surface equation written with the most significant principal component scores that can be used to replace the original correlated dataset. Besides the dimensional reduction, this multiobjectiveprogramming approach has the benefit of considering the correlation among the multiple responses while generating convex Pareto frontiers to mean square error (MSE) functions. To demonstrate the procedure of the proposed approach, we used a bivariate case of AISI 52100 hardened steel turning employing wiper mixed ceramic tools. Theoretical and experimental results are convergent and confirm the effectiveness of the proposed approach. (C) 2014 Elsevier Ltd. All rights reserved.
In this paper we propose a biobjective model for two-group classification via margin maximization, in which the margins in both classes are simultaneously maximized. The set of Pareto-optimal solutions is described, y...
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In this paper we propose a biobjective model for two-group classification via margin maximization, in which the margins in both classes are simultaneously maximized. The set of Pareto-optimal solutions is described, yielding a set of parallel hyperplanes, one of which is just the solution of the classical SVM approach. In order to take into account different misclassification costs or a priori probabilities, the ROC curve can be used to select one out of such hyperplanes by expressing the adequate tradeoff for sensitivity and specificity. Our result gives a theoretical motivation for using the ROC approach in case misclassification costs in the two groups are not necessarily equal. (c) 2005 Elsevier B.V. All rights reserved.
A mathematical programming technique developed recently that optimizes multiple correlated characteristics is the Multivariate Mean Square Error (MMSE). The MMSE approach has obtained noteworthy results, by avoiding t...
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A mathematical programming technique developed recently that optimizes multiple correlated characteristics is the Multivariate Mean Square Error (MMSE). The MMSE approach has obtained noteworthy results, by avoiding the production of inappropriate optimal points that can occur when a method fails to take into account a correlation structure. Where the MMSE approach is deficient, however, is in cases where the multiple correlated characteristics need to be optimized with varying degrees of importance. The MMSE approach, in treating all responses as having the same importance, is unable to attribute the desired weights. This paper thus introduces a strategy that weights the responses in the MMSE approach. The method, called the Weighted Multivariate Mean Square Error (WMMSE), utilizes a weighting procedure that integrates Principal Component Analysis (PCA) and Response Surface Methodology (RSM). In doing so, WMMSE obtains uncorrelated weighted objective functions from the original responses. After being mathematically programmed, these functions are optimized by employing optimization algorithms. We applied WMMSE to optimize a stainless steel cladding application executed via the flux-cored arc welding (FCAW) process. Four input parameters and eight response variables were considered. Stainless steel cladding, which carries potential benefits for a variety of industries, takes low cost materials and deposits over their surfaces materials having anti-corrosive properties. Optimal results were confirmed, which ensured the deposition of claddings with defect-free beads exhibiting the desired geometry and demonstrating good productivity indexes. (C) 2012 Elsevier B.V. All rights reserved.
Supply chain security is a major concern for logistics managers who have responsibility for inbound and outbound shipments to and from both domestic and international locations. We propose here that logistics decision...
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Supply chain security is a major concern for logistics managers who have responsibility for inbound and outbound shipments to and from both domestic and international locations. We propose here that logistics decisions concerning security in the supply chain will be made more effectively when made in concert with decisions in related supply chain processes, especially supplier and carrier selection. Indeed, managers may minimize cost, transit time, and security risk by integrating decision processes internally, as well as with their carrier's and supplier's operations. Thus, we account for both intra-firm collaboration between logistics and purchasing managers, as well as inter-firm collaboration among buyers, suppliers, and carriers in a supply chain. In this paper, we propose a decision process that features a set of security rules and a multi-objective optimization model to accomplish this aim. We then provide an illustration to demonstrate the potential usefulness of these concepts in practice.
Aquaculture development is considered as a viable sourer for providing high quality cheap protein, particularly, for developing countries where protein shortage already exists. However, complexities in such developmen...
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Aquaculture development is considered as a viable sourer for providing high quality cheap protein, particularly, for developing countries where protein shortage already exists. However, complexities in such development planning can be difficult without the aid of modern decision-aids such as multiple criteria decision making (MCDM) models. MCDM models are already in use in the business and manufacturing sectors. However, their use in agriculture is limited and their use in aquaculture is almost nonexistent. This paper presents a MCDM framework for the planning of regional aquaculture development. The MCDM model seeks a desirable allocation of resources and activity levels that strikes an acceptable balance among the various development goals under consideration subject to resource constraints, market constraints, and pollution constraints. To accommodate different decision situations, three different MCDM solution techniques are implemented, namely, multiple objective programming (MOP, compromise programming (CP), and weighted goal programming (WGP). The applicability of the framework is demonstrated through applying it to a case study from northern Egypt where aquaculture is a viable industry for supplying cheap and good quality protein, balancing the foreign exchange deficits, and creating employment opportunities. (C) 2001 Elsevier Science B.V. All rights reserved.
An efficient frontier in the typical portfolio selection problem provides an illustrative way to express the tradeoffs between return and risk. Following the basic ideas of modern portfolio theory as introduced by Mar...
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An efficient frontier in the typical portfolio selection problem provides an illustrative way to express the tradeoffs between return and risk. Following the basic ideas of modern portfolio theory as introduced by Markowitz, security returns are usually extracted from past data. Our purpose in this paper is to incorporate future returns scenarios in the investment decision process. For representative points on the efficient frontier, the minimax regret portfolio is calculated, on the basis of the aforementioned scenarios. These points correspond to specific weight combinations. In this way, the areas of the efficient frontier that are more robust than others are identified. The underlying key-contribution is related to the extension of the conventional minimax regret criterion formulation, in multiobjectiveprogramming problems. The validity of the approach is verified through an illustrative empirical testing application on the Eurostoxx 50. (C) 2017 Elsevier B.V. All rights reserved.
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