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Multiple Criteria Decision Making (MCDM) is firmly rooted in an alternative concept of optimality where multiple (rather than single) criteria characterize the notion of “the best” (or optimal), as is prevalent in the areas of e...
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Multiple Criteria Decision Making (MCDM) is firmly rooted in an alternative concept of optimality where multiple (rather than single) criteria characterize the notion of “the best” (or optimal), as is prevalent in the areas of economics, engineering, management and business. These are often constrained problems where search for an optimal solution requires some form of evaluating criteria performance tradeoffs. Because there are no tradeoffs along a single criterion, optimality is an essentially multi-criteria concept. In this paper we extend and develop the notion of optimum as a balance among multiple criteria. We introduce eight different, separate and mutually irreducible optimality concepts in a classification scheme where the traditional single-objective optimality is only a special case. These eight optimality concepts provide a useful initiatory framework for the future MCDM research and applications.
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Many real-world optimization problems have to be treated as multi-objective optimization problems. An approach, well established in recent years, is to find Pareto optimal configurations of the trial variables by detecting nondomi...
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Many real-world optimization problems have to be treated as multi-objective optimization problems. An approach, well established in recent years, is to find Pareto optimal configurations of the trial variables by detecting nondominated solutions with the help of a suitable vector optimization method. Alternatively, relying on scalar optimization methods (both stochastic or deterministic), a suitable objective function taking all objectives into account simultaneously has to be defined. Depending on the number of trial variables, a scalar objective function of that type will exhibit a considerable number of feasible local solutions besides the global one. Therefore, a useful scalar optimization strategy should be able to end up (with a high probability) in the best of all possible solutions in the given search space and additionally detect as many local solutions as possible. Some population-based stochastic methods are implicitly suited for that task; others can be enhanced to fulfill these requirements. Higher order evolution strategies have successfully been tuned for that kind of problem by introducing cluster sensitive recombination [niching higher order evolution strategy (NES)]. The firefly algorithm (FFA) mimics the behavior of fireflies, which use a kind of flashing light to communicate with other members of their species. Since the intensity of the light of a single firefly diminishes with increasing distance, the FFA is implicitly able to detect local solutions on its way to the best solution for a given scalar objective function. The FFA will be applied to the well-known Rastrigin test function and to a shielding/shunting electromagnetic problem with two and three objectives, respectively, and its results will be compared with the ones obtained with an NES.
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We present optimization algorithms for the design of complex hierarchical systems, motivated by applications to the design of nanoporous materials. Nanoporous materials have a broad range of engineering applications, including gas...
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We present optimization algorithms for the design of complex hierarchical systems, motivated by applications to the design of nanoporous materials. Nanoporous materials have a broad range of engineering applications, including gas storage and filtration, electrical energy storage in batteries and capacitors, and catalysis. The design of such materials involves modeling of the material over many length scales, leading to a hierarchy of mathematical models. Our algorithms are also hierarchical in structure with the goal of exploiting the model hierarchy to obtain solutions more rapidly. We discuss the choice of optimization models, initialization schemes, the hierarchical optimization algorithm, software design, and computational results.
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Bayesian optimization has become a widely used tool in the optimization and machine learning communities. It is suitable to problems as simulation/optimization and/or with an objective function computationally expensive to evaluat...
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Bayesian optimization has become a widely used tool in the optimization and machine learning communities. It is suitable to problems as simulation/optimization and/or with an objective function computationally expensive to evaluate. Bayesian optimization is based on a surrogate probabilistic model of the objective whose mean and variance are sequentially updated using the observations and an “acquisition” function based on the model, which sets the next observation at the most “promising” point. The most used surrogate model is the Gaussian Process which is the basis of well-known Kriging algorithms. In this paper, the authors consider the pump scheduling optimization problem in a Water Distribution Network with both ON/OFF and variable speed pumps. In a global optimization model, accounting for time patterns of demand and energy price allows significant cost savings. Nonlinearities, and binary decisions in the case of ON/OFF pumps, make pump scheduling optimization computationally challenging, even for small Water Distribution Networks. The well-known EPANET simulator is used to compute the energy cost associated to a pump schedule and to verify that hydraulic constraints are not violated and demand is met. Two Bayesian Optimization approaches are proposed in this paper, where the surrogate model is based on a Gaussian Process and a Random Forest, respectively. Both approaches are tested with different acquisition functions on a set of test functions, a benchmark Water Distribution Network from the literature and a large-scale real-life Water Distribution Network in Milan, Italy.
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In the research projects and industrial projects severe optimization problems can be met,where the number of variables is high,there are a lot of constraints,and they are highly nonlinear and mostly discrete issues,where the runni...
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In the research projects and industrial projects severe optimization problems can be met,where the number of variables is high,there are a lot of constraints,and they are highly nonlinear and mostly discrete issues,where the running time can be calculated sometimes in weeks with the usual optimization methods on an average computer.In most cases in the logistics industry,the most robust constraint is the time.The optimizations are running on a typical office configuration,and the company accepts the suboptimal solution what the optimization method gives within the appropriate time limit.That is,why adaptivity is needed.The adaptivity of the optimization technique includes parameters of fine-tuning.On this way,the most sensitive setting can be found.In this article,some additional adaptive methods for logistic problems have been investigated to increase the effectivity,improve the solution in a strict time condition.
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We present three new copositivity tests based upon difference-of-convex (d.c.) decompositions, and combine them to a branch-and-bound algorithm of ω-subdivision type. The tests employ LP or convex QP techniques, but also can be u...
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We present three new copositivity tests based upon difference-of-convex (d.c.) decompositions, and combine them to a branch-and-bound algorithm of ω-subdivision type. The tests employ LP or convex QP techniques, but also can be used heuristically using appropriate test points. We also discuss the selection of efficient d.c. decompositions and propose some preprocessing ideas based on the spectral d.c. decomposition. We report on first numerical experience with this procedure which are very promising.
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In this paper, plasma generation optimization (PGO) as a newly developed physics-based metaheuristic algorithm is applied to perform the size, layout, and topology optimization problems of skeletal structures. PGO is a population-...
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In this paper, plasma generation optimization (PGO) as a newly developed physics-based metaheuristic algorithm is applied to perform the size, layout, and topology optimization problems of skeletal structures. PGO is a population-based optimizer inspired by the process of plasma generation. In this optimization method, each agent is modeled as an electron. The movement of electrons and changing their energy level are performed based on simulating the process of excitation, de-excitation, and ionization. These processes occur iteratively through the plasma generation. Evaluating the robustness and performance of the PGO is illustrated through six design examples for different types of structural optimization. The results reveal that the PGO algorithm outperforms other state-of-the-art optimization techniques considered from the literature.
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In earlier proposals, the robust counterpart of conic optimization problems exhibits a lateral increase in complexity, i.e., robust linear programming problems (LPs) become second order cone problems (SOCPs), robust SOCPs become s...
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In earlier proposals, the robust counterpart of conic optimization problems exhibits a lateral increase in complexity, i.e., robust linear programming problems (LPs) become second order cone problems (SOCPs), robust SOCPs become semidefinite programming problems (SDPs), and robust SDPs become NP-hard. We propose a relaxed robust counterpart for general conic optimization problems that (a) preserves the computational tractability of the nominal problem; specifically the robust conic optimization problem retains its original structure, i.e., robust LPs remain LPs, robust SOCPs remain SOCPs and robust SDPs remain SDPs, and (b) allows us to provide a guarantee on the probability that the robust solution is feasible when the uncertain coefficients obey independent and identically distributed normal distributions.
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We propose a randomized search method called Stochastic Model Reference Adaptive Search (SMRAS) for solving stochastic optimization problems in situations where the objective functions cannot be evaluated exactly, but can be estim...
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We propose a randomized search method called Stochastic Model Reference Adaptive Search (SMRAS) for solving stochastic optimization problems in situations where the objective functions cannot be evaluated exactly, but can be estimated with some noise (or uncertainty), e.g., via simulation. The method generalizes the recently proposed Model Reference Adaptive Search (MRAS) for deterministic optimization, which is motivated by the well-known Cross-Entropy (CE) method. We prove global convergence of SMRAS in a general stochastic setting, and carry out numerical studies to illustrate its performance. An emphasis of this paper is on the application of SMRAS for solving static stochastic optimization problems; its various applications for solving dynamic decision making problems can be found in [7].
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In this paper we propose anew approach for constructing efficient schemes for non-smooth convex optimization. It is based on a special smoothing technique, which can be applied to functions with explicit max-structure. Our approac...
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In this paper we propose anew approach for constructing efficient schemes for non-smooth convex optimization. It is based on a special smoothing technique, which can be applied to functions with explicit max-structure. Our approach can be considered as an alternative to black-box minimization. From the viewpoint of efficiency estimates, we manage to improve the traditional bounds on the number of iterations of the gradient schemes from O (1/is an element of(2)) to O (1/is an element of), keeping basically the complexity of each iteration unchanged.
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