Search results for "Mathematical optimization"
showing 10 items of 1300 documents
A model for designing callable bonds and its solution using tabu search
1997
Abstract We formulate the problem of designing callable bonds as a non-linear, global, optimization problem. The data of the model are obtained from simulations of holding-period returns of a given bond design, which are used to compute a certainty equivalent return, viz., some target assets. The design specifications of the callable bond are then adjusted so that the certainty equivalent return is maximized. The resulting problem is multi-modal, and a tabu search procedure, implemented on a distributed network of workstations, is used to optimize the bond design. The model is compared with the classical portfolio immunization model, and the tabu search solution technique is compared with s…
The Random-Time Binomial Model
1999
In this paper we study Binomial Models with random time steps. We explain, how calculating values for European and American Call and Put options is straightforward for the Random-Time Binomial Model. We present the conditions to ensure weak-convergence to the Black-Scholes setup and convergence of the values for European and American put options. Differently to the CRR-model the convergence behaviour is extremely smooth in our model. By using extrapolation we therefore achieve order of convergence two. This way it is an efficient tool for pricing purposes in the Black-Scholes setup, since the CRR model and its extrapolations typically achieve order one. Moreover our model allows in a straig…
A problem-adjusted genetic algorithm for flexibility design
2013
Many present markets for goods and services have highly volatile demand due to short life cycles and strong competition in saturated environments. Determination of capacity levels is difficult because capacities often need to be set long before demand realizes. In order to avoid capacity-demand mismatches, operations managers employ mix-flexible resources which allow them to shift excess demands to unused capacities. The Flexibility Design Problem (FDP) models the decision on the optimal configuration of a flexible (manufacturing) network. FDP is a difficult stochastic optimization problem, for which traditional exact approaches are not able to solve but the smallest instances in reasonable…
A naïve approach to speed up portfolio optimization problem using a multiobjective genetic algorithm
2012
a b s t r a c t Genetic algorithms (GAs) are appropriate when investors have the objective of obtaining mean-variance (VaR) efficient frontier as minimising VaR leads to non-convex and non-differential risk-return optimisation problems. However GAs are a time-consuming optimisation technique. In this paper, we propose to use a naive approach consisting of using samples split by quartile of risk to obtain complete efficient frontiers in a reasonable computation time. Our results show that using reduced problems which only consider a quartile of the assets allow us to explore the efficient frontier for a large range of risk values. In particular, the third quartile allows us to obtain efficie…
Strategic sharing of a costly network
2012
We study minimum cost spanning tree problems for a set of users connected to a source. Prim’s algorithm provides a way of finding the minimum cost tree mm. This has led to several definitions in the literature, regarding how to distribute the cost. These rules propose different cost allocations, which can be understood as compensations and/or payments between players, with respect to the status quo point: each user pays for the connection she uses to be linked to the source. In this paper we analyze the rationale behind a distribution of the minimum cost by defining an a priori transfer structure. Our first result states the existence of a transfer structure such that no user is willing to …
The closed-form solution for a family of four-dimension nonlinear MHDS
2008
In this article we propose a method for solving a general class of four-dimension nonlinear modified Hamiltonian dynamic systems in closed form. This method may be used to study several intertemporal optimization problems sharing a common structure, which involves unbounded technological constraints as well as multiple controls and state variables. The method is developed by solving the first-order conditions associated with the planner's problem corresponding to the Lucas [1988. On the mechanics of economic development. Journal of Monetary Economics 22, 3-42] two-sector model of endogenous growth, and allows for explicitly showing the transitional dynamics of the model. Despite the externa…
Passive congregation based particle swam optimization (pso) with self-organizing hierarchical approach for non-convex economic dispatch
2017
This paper proposes a passive congregation based PSO with self-organizing hierarchical algorithm approach for solving the economic dispatch problem of power system, where some of the units have prohibited operating zones. This Algorithm is known to perform better than conventional gradient based optimization methods for non-convex optimization problems. Conventional PSO algorithm is a population based heuristic search, employing problem of premature convergence. In this work, an innovative approach based on the concept of passive congregation based PSO with self-organizing hierarchical approach is employed to overcome the problem of premature convergence in classical PSO method.
Econo- Environmental Dispatch Solutions for Power Systems Integrated with Renewable Energy Resources
2020
Due to the global initiatives for sustainable energy supply, the electric grids are increasingly integrated with environment-friendly and renewable energy resources. Hence, the power dispatch strategies are to be timely modified by incorporating the environmental aspects of generation along with the economic considerations. In this paper, we propose such an Econo- Environmental dispatch (EED) system for a power grids, which are integrated with renewable energy sources. The EED problem is formulated with two objective functions which aims at minimizing the unit cost of generation as well as minimizing the emissions caused during the power production. For attaining these objectives, cost and …
Training Artificial Neural Networks With Improved Particle Swarm Optimization
2020
Particle Swarm Optimization (PSO) is popular for solving complex optimization problems. However, it easily traps in local minima. Authors modify the traditional PSO algorithm by adding an extra step called PSO-Shock. The PSO-Shock algorithm initiates similar to the PSO algorithm. Once it traps in a local minimum, it is detected by counting stall generations. When stall generation accumulates to a prespecified value, particles are perturbed. This helps particles to find better solutions than the current local minimum they found. The behavior of PSO-Shock algorithm is studied using a known: Schwefel's function. With promising performance on the Schwefel's function, PSO-Shock algorithm is util…
Corrective meshless particle formulations for time domain Maxwell's equations
2007
AbstractIn this paper a meshless approximation of electromagnetic (EM) field functions and relative differential operators based on particle formulation is proposed. The idea is to obtain numerical solutions for EM problems by passing up the mesh generation usually required to compute derivatives, and by employing a set of particles arbitrarily placed in the problem domain. The meshless Smoothed Particle Hydrodynamics method has been reformulated for solving the time domain Maxwell's curl equations. The consistency of the discretized model is investigated and improvements in the approximation are obtained by modifying the numerical process. Corrective algorithms preserving meshless consiste…