Search results for "optimization"
showing 10 items of 2824 documents
On the definition of viscosity solutions for parabolic equations
2001
In this short note we suggest a refinement for the definition of viscosity solutions for parabolic equations. The new version of the definition is equivalent to the usual one and it better adapts to the properties of parabolic equations. The basic idea is to determine the admissibility of a test function based on its behavior prior to the given moment of time and ignore what happens at times after that.
A genetic algorithm for scratch removal in static images
2002
This paper investigates the removal of line scratches from old moving pictures and gives a twofold contribution. First, it presents a simple technique for detecting the scratches, based on an analysis of the statistics of the grey levels. Second, the scratch removal is approached as an optimisation problem, which is solved by using a genetic algorithm. The method can be classified as a static approach, as it works independently on each single frame of the sequence. It does not require any a-priori knowledge of the absolute position of the scratch, nor an external starting population of chromosomes for the genetic algorithm. The central column of the line scratch once detected is changed wit…
Multi-Objective and Multi-Criteria Analysis for Optimal Pump Scheduling in Water Systems
2018
This contribution focuses on the problem of optimal pump scheduling, a fundamental element in pursuing operation optimization of water distribution systems. A combined approach of multi-objective optimization and multi-criteria analysis is herein suggested to first find the Pareto front of non-dominated solutions and then to rank them based on a set of weighted criteria. The Non-Dominated Sorting Genetic Algorithm (NSGA-II) is proposed to solve the multi-objective problem, while the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) is used to achieve the final ranking.
k-out-of-n systems: an exact formula for the stationary availability and multi-objective configuration design based on mathematical programming and T…
2018
[EN] Reliability and availability analyses are recognized as essential for guiding decision makers in the implementation of actions addressed to improve the technical and economical performance of complex systems. For industrial systems with reparable components, the most interesting parameter used to drive maintenance is the stationary availability. In this regard, the present paper proposes an exact formula for computing the system stationary availability of a k-out-of-n system. Such a formula is proved to be in agreement with the fundamental theorem of Markov chains. Then, a multi-objective mathematical model is formulated for choosing the optimal system configuration design. The Pareto …
Response determination of linear dynamical systems with singular matrices: A polynomial matrix theory approach
2017
Abstract An approach is developed based on polynomial matrix theory for formulating the equations of motion and for determining the response of multi-degree-of-freedom (MDOF) linear dynamical systems with singular matrices and subject to linear constraints. This system modeling may appear for reasons such as utilizing redundant DOFs, and can be advantageous from a computational cost perspective, especially for complex (multi-body) systems. The herein developed approach can be construed as an alternative to the recently proposed methodology by Udwadia and coworkers, and has the significant advantage that it circumvents the use of pseudoinverses in determining the system response. In fact, ba…
SMAA in Robustness Analysis
2016
Stochastic multicriteria acceptability analysis (SMAA) is a simulation based method for discrete multicriteria decision aiding problems where information is uncertain, imprecise, or partially missing. In SMAA, different kind of uncertain information is represented by probability distributions. Because SMAA considers simultaneously the uncertainty in all parameters, it is particularly useful for robustness analysis. Depending on the problem setting, SMAA determines all possible rankings or classifications for the alternatives, and quantifies the possible results in terms of probabilities. This chapter describes SMAA in robustness analysis using a real-life decision problem as an example. Bas…
On deterministic solutions for multi-marginal optimal transport with Coulomb cost
2022
In this paper we study the three-marginal optimal mass transportation problem for the Coulomb cost on the plane $\R^2$. The key question is the optimality of the so-called Seidl map, first disproved by Colombo and Stra. We generalize the partial positive result obtained by Colombo and Stra and give a necessary and sufficient condition for the radial Coulomb cost to coincide with a much simpler cost that corresponds to the situation where all three particles are aligned. Moreover, we produce an infinite class of regular counterexamples to the optimality of this family of maps.
Demonstrating the Applicability of PAINT to Computationally Expensive Real-life Multiobjective Optimization
2011
We demonstrate the applicability of a new PAINT method to speed up iterations of interactive methods in multiobjective optimization. As our test case, we solve a computationally expensive non-linear, five-objective problem of designing and operating a wastewater treatment plant. The PAINT method interpolates between a given set of Pareto optimal outcomes and constructs a computationally inexpensive mixed integer linear surrogate problem for the original problem. We develop an IND-NIMBUS R PAINT module to combine the interactive NIMBUS method and the PAINT method and to find a preferred solution to the original problem. With the PAINT method, the solution process with the NIMBUS method take …
Genetic Algorithms: A Decision Tool in Industrial Disassembly
2008
In the recycling process of the Waste Electrical and Electronic Equipment (WEEE) the disassembly process has a central role. Disassembly is not the reverse of the assembly process, real difficulties occur in the tasks assignment process of the disassembly operations. Since this is a multi objective optimization problem, we prove that genetic algorithms provide a useful multi-criteria decision tool in the industrial disassembly process.
On Generalizing Lipschitz Global Methods forMultiobjective Optimization
2015
Lipschitz global methods for single-objective optimization can represent the optimal solutions with desired accuracy. In this paper, we highlight some directions on how the Lipschitz global methods can be extended as faithfully as possible to multiobjective optimization problems. In particular, we present a multiobjective version of the Pijavskiǐ-Schubert algorithm.