In this paper, a modified Pascoletti-Serafini scalarization approach, called MOP_MPS, is proposed to generate approximations of a Pareto front of bounded multi-objective optimizationproblems (MOPs). The objective is ...
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In this paper, a modified Pascoletti-Serafini scalarization approach, called MOP_MPS, is proposed to generate approximations of a Pareto front of bounded multi-objective optimizationproblems (MOPs). The objective is obtaining some points with an almost even distribution overall Pareto front. This algorithm is applied to six test problems with convex, non-convex, connected, and dis-connected Pareto fronts, and its results are compared with results of some famous algorithms. The results emphasize that MOP_MPS is effective and competitive in comparing with the other considered algorithms. In addition, it is shown that an optimal solution of a multiplicative programming problem is a properly Pareto optimal solution of an MOP. By considering this relation between MOPs and multiplicative programming problems (MPPs), another algorithm based on MOP_MPS, called MPP_MPS, is suggested for approximately solving non-linear MPPs in which functions multiplied are continuous and bounded from below. The computational results on seven problems of convex MPPs demonstrate that the algorithm is much better than a cut and bound algorithm presented by Shao and Ehrgott in terms of CPU time.
In this work, a differentiable multiobjective optimization problem with generalized cone constraints is considered, and the equivalence of weak Pareto solutions for the problem and for its eta-approximated problem is ...
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In this work, a differentiable multiobjective optimization problem with generalized cone constraints is considered, and the equivalence of weak Pareto solutions for the problem and for its eta-approximated problem is established under suitable conditions. Two existence theorems for weak Pareto solutions for this kind of multiobjective optimization problem are proved by using a Karush-Kuhn-Tucker type optimality condition and the F-KKM theorem. (C) 2007 Elsevier Ltd. All rights reserved.
The majority of real-world problems encountered by engineers involve simultaneous optimization of competing objectives. In this case instead of single optima, there is a set of alternative trade-offs, generally known ...
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The majority of real-world problems encountered by engineers involve simultaneous optimization of competing objectives. In this case instead of single optima, there is a set of alternative trade-offs, generally known as Pareto-optimal solutions. The use of evolutionary algorithms Pareto GA, which was first introduced by Goldberg in 1989, has now become a sort of standard in solving multiobjective optimization problems (MOPs). Though this approach was further developed leading to numerous applications, these applications are based on Pareto ranking and employ the use of the fitness sharing function to maintain diversity. Another scheme for solving MOPs has been presented by J. Nash to solve MOPs originated from Game Theory and Economics. Sefrioui introduced the Nash Genetic Algorithm in 1998. This approach combines genetic algorithms with Nash's idea. Another central achievement of Game Theory is the introduction of an Evolutionary Stable Strategy, introduced by Maynard Smith in 1982. In this paper, we will try to find ESS as a solution of MOPs using our game model based co-evolutionary algorithm. First, we will investigate the validity of our co-evolutionary approach to solve MOPs. That is, we will demonstrate how the evolutionary game can be embodied using co-evolutionary algorithms and also confirm whether it can reach the optimal equilibrium point of a MOP. Second, we will evaluate the effectiveness of our approach, comparing it with other methods through rigorous experiments on several mops.
This study presents the modeling of the multiobjective optimization problem in an intuitionistic fuzzy environment. The uncertain parameters are depicted as intuitionistic fuzzy numbers, and the crisp version is obtai...
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This study presents the modeling of the multiobjective optimization problem in an intuitionistic fuzzy environment. The uncertain parameters are depicted as intuitionistic fuzzy numbers, and the crisp version is obtained using the ranking function method. Also, we have developed a novel interactive neutrosophic programming approach to solve multiobjective optimization problems. The proposed method involves neutral thoughts while making decisions. Furthermore, various sorts of membership functions are also depicted for the marginal evaluation of each objective simultaneously. The different numerical examples are presented to show the performances of the proposed solution approach. A case study of the cloud computing pricing problem is also addressed to reveal the real-life applications. The practical implication of the current study is also discussed efficiently. Finally, conclusions and future research scope are suggested based on the proposed work.
In this paper, a differentiable multiobjective optimization problem with generalized cone constrains is considered, and the equivalence of weak Pareto solutions for the problem and for its (eta)-approximated problem i...
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ISBN:
(纸本)9780819493057
In this paper, a differentiable multiobjective optimization problem with generalized cone constrains is considered, and the equivalence of weak Pareto solutions for the problem and for its (eta)-approximated problem is established under suitable conditions.
In this paper, we develop Newton's method for robust counterpart of an uncertain multiobjective optimization problem under an arbitrary finite uncertainty nonempty set. Here the robust counterpart of an uncertain ...
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In this paper, we develop Newton's method for robust counterpart of an uncertain multiobjective optimization problem under an arbitrary finite uncertainty nonempty set. Here the robust counterpart of an uncertain multiobjective optimization problem is the minimum of objective wise worst case, which is the nonsmooth deterministic multiobjective optimization problem. To solve this robust counterpart with the help of Newton's method, a suproblem is constructed and solved to find a descent direction for robust counterpart. An Armijo type inexact line search technique is developed to find a suitable step length. With the help of the descent direction and step length, we present the Newton's algorithm for the robust counterpart. The convergence of the Newton's algorithm for the robust counterpart is obtained under some usual assumptions. We also prove that the algorithm converges with super linear and quadratic rate under different assumptions. Finally, we verify the algorithm and compare with the weighted sum method via some numerical problems.
In this paper, the exact analytical solution for the environmental/economic dispatch (EED) optimizationproblem is presented for the first time. The EED, which simultaneously satisfies multiple contradictory criteria,...
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In this paper, the exact analytical solution for the environmental/economic dispatch (EED) optimizationproblem is presented for the first time. The EED, which simultaneously satisfies multiple contradictory criteria, is stated as a multiobjective optimization problem (MOP). Our paper has improved several aspects of a previous analytical approach. First, we take into account the unit capacity constraints in the exact formulae. Second, we obtain the set of compromise solutions known as Pareto optimal solutions and, third, our treatment of transmission losses satisfies the power balance constraint. In contrast with the known heuristic methods used in the literature, which only provide a reasonable solution (suboptimal, nearly global optimal), our method provides the global solution. Moreover, our method can obtain the Pareto optimal set under different loading conditions. The performance of the proposed technique is validated using a standard test system.
In this paper, we study necessary optimality conditions for local Pareto and weak Pareto solutions of multiobjectiveproblems involving inequality and equality constraints in terms of convexificators. We develop the e...
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In this paper, we study necessary optimality conditions for local Pareto and weak Pareto solutions of multiobjectiveproblems involving inequality and equality constraints in terms of convexificators. We develop the enhanced Karush-Kuhn-Tucker conditions and introduce the associated pseudonormality and quasinormality conditions. We also introduce several other new constraint qualifications which entirely depend on the feasible set. Then a connecting link between these constraint qualifications is presented. Moreover, we provide several examples that clarify the interrelations between the different results that we have established.
The rapidly evolving industry standards and transformative advances in the field of Internet of Things are expected to create a tsunami of Big Data shortly. This, in turn, will demand real-time data analysis and proce...
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The rapidly evolving industry standards and transformative advances in the field of Internet of Things are expected to create a tsunami of Big Data shortly. This, in turn, will demand real-time data analysis and processing from cloud computing platforms. A substantial part of the computing infrastructure is supported by large-scale and geographically distributed data centers (DCs). Nevertheless, these DCs impose a substantial cost in terms of rapidly growing energy consumption, which in turn adversely affects the environment. In this context, efficient resource utilization is seen as a potential candidate to enhance energy efficiency and minimize the load on the power sector. Nevertheless, in the majority of the public clouds, the resources are idle most of the time (i.e., under-utilized) as the load of the servers is unpredictable;thereby leading to a lofty increase in the energy utilization index and wastage of resources. Thus, it is highly essential to devise a precise and efficient resource management technique. Therefore, in this article, we leverage the advantages of software defined data centers (SDDCs) to minimize energy utilization levels. Precisely, SDDC refers to the process of programmatically abstracting the logical computing, network, and storage resources;and configuring them in real-time based on workload demands. In detail, we demonstrate the possibility of 1) designing a consolidated SDDC-based model to jointly optimize the process of virtual machine (VM) deployment and network bandwidth allocation for reduced energy consumption and guaranteed quality of service (QoS), particularly for heterogeneous computing infrastructures;2) formulating a multiobjective optimization problem to deduce the optimal allocation of resources for both critical and noncritical applications;and 3) designing an efficient scheme based on heuristics to provide suboptimal results for the formulated multiobjective optimization problem. The proposed article presents a suboptim
This paper applies the Bayesian optimization Algorithm with Tabu Search (Tabu-BOA) to electric equipment configuration problems in a power plant. Tabu-BOA is a hybrid evolutionary computation algorithm with competent ...
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This paper applies the Bayesian optimization Algorithm with Tabu Search (Tabu-BOA) to electric equipment configuration problems in a power plant. Tabu-BOA is a hybrid evolutionary computation algorithm with competent genetic algorithms and meta-heuristics. The configuration problems we consider have complex combinatorial properties, and therefore are hard to formulate and solve via conventional mathematical programming techniques. Using the proposed method, we have solved the following problems (in order of increasing complexity): (I) cost minimization of electric equipment configuration and the corresponding cabling, (2) plus choice of the power plant operation patterns, (3) plus parallel operation of multiple transformers, (4) plus change of the supply voltages (high voltage or low voltage) to the electric power load, and (5) with addition of another objective, that is, both minimization of the cost and maximization of the surplus power supply. (C) 2005 Wiley Periodicals, Inc.
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