The paper discusses a new approach to solving computationally time-consuming multicriteria optimizationproblems in which some variable parameters can only take on discrete values. Under the proposed approach, the sol...
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ISBN:
(纸本)9783030816919;9783030816902
The paper discusses a new approach to solving computationally time-consuming multicriteria optimizationproblems in which some variable parameters can only take on discrete values. Under the proposed approach, the solution of mixed-integer optimization problems is reduced to solving a family of optimizationproblems where only continuous parameters are used. All problems of the family are solved simultaneously in time-shared mode, where the optimization problem for the next global search iteration is selected adaptively, taking into account the search information obtained in the course of the calculations. The suggested algorithms enable parallel computing on high-performance computing systems. The computational experiments confirm that the proposed approach can significantly reduce the computation volume and time required for solving complex multicriteria mixed-integer optimization problems.
This paper describes and assesses a parallel multimethod hyperheuristic for the solution of complex global optimizationproblems. In a multimethod hyperheuristic, different metaheuristics cooperate to outperform the r...
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This paper describes and assesses a parallel multimethod hyperheuristic for the solution of complex global optimizationproblems. In a multimethod hyperheuristic, different metaheuristics cooperate to outperform the results obtained by any of them isolated. The results obtained show that the cooperation of individual parallel searches modifies the systemic properties of the hyperheuristic, achieving significant performance improvements versus the sequential and the non-cooperative parallel solutions. Here we present and evaluate a hybrid parallel scheme of the multimethod, using both message-passing (MPI) and shared memory (OpenMP) models. The hybrid parallelization allows to achieve a better trade-off between performance and computational resources, through a compromise between diversity (number of islands) and intensity (number of threads per island). For the performance evaluation, we considered the general problem of reverse engineering nonlinear dynamic models in systems biology, which yields very large mixed-integer dynamic optimizationproblems. In particular, three very challenging problems from the domain of dynamic modeling of cell signaling were used as case studies. In addition, experiments have been carried out in a local cluster, a large supercomputer and a public cloud, to show the suitability of the proposed solution in different execution platforms.
We consider two-stage stochastic programming models with quantile criterion as well as models with a probabilistic constraint on the random values of the objective function of the second stage. These models allow us t...
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We consider two-stage stochastic programming models with quantile criterion as well as models with a probabilistic constraint on the random values of the objective function of the second stage. These models allow us to formalize the requirements for the reliability and safety of the system being optimized and to optimize system's performance under extreme conditions. We propose a method of equivalent transformation of these models under discrete distribution of random parameters to mixed-integer programming problems. The number of additional integer (Boolean) variables in these problems equals to the number of possible values of the vector of random parameters. The obtained mixedoptimizationproblems can be solved by powerful standard discrete optimization software. To illustrate the approach, the results of numerical experiment for the problem of small dimension are presented.
In the Payment Cost Minimization (PCM) mechanism [4] payment costs are minimized directly, thus the payment costs that results from selected offers can be significantly reduced compared to the costs obtained by minimi...
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ISBN:
(纸本)9781457710018
In the Payment Cost Minimization (PCM) mechanism [4] payment costs are minimized directly, thus the payment costs that results from selected offers can be significantly reduced compared to the costs obtained by minimizing total bid costs. The PCM can be solved efficiently using standard LP software packages (e. g., CPLEX) only for a limited number of offers. Lagrangian relaxation (LR) has been a powerful technique to solve discrete and mixed-integer optimization problems. For complex problems, such as the PCM, the surrogate subgradient method is frequently used within Lagrangian relaxation approach to update multipliers (e. g., [6], [4]). In the surrogate subgradient approach a proper direction is obtained without fully minimizing the relaxed problem. This paper presents a modified Lagrangian relaxation and the surrogate optimization approach for obtaining a good feasible solution within a reasonable CPU time. The difficulty of the standard surrogate optimization method primarily arises due to the lack of prior knowledge about the optimal dual value, which is used in the definition of a step size. In order to overcome this difficulty, a new method is proposed. The main purpose of the modified surrogate subgradient approach is to obtain a "good" direction quickly and independently of the optimal dual value at each iteration. In this paper it is achieved by introducing a formula for updating the multipliers such that the exact minimization of the Lagrangian leads to a convergent result. Then an approximate formula for updating the multipliers is developed so that the exact optimization of the Lagrangian leads to a convergent result under certain optimality conditions. Lastly, the notion of the surrogate subgradient is used for ensuring the convergence within the reasonable CPU time. An analogue of the surrogate subgradient condition guarantees the convergence on the surrogate subgradient method. Numerical examples are provided to demonstrate the method's effectiveness
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