Ingrid Vieira Saldanha · LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) · 2020
This work aims to present three strategies for solving problems of optimization, involving some geometric concepts such as areas of flat figures and volume geometric solids. We will present a method using differential calculus and, two others without the use of calculus. For this, we will initially deal with the main theorems to be respect to calculation and then some concepts of geometry, fundamental to the solving the problems that will be presented. Based on that, two resolution strategies, one with the use of maximum and minimum values of a function quadratic and, later, another, through the use of inequality of means. We will end with the third strategy, addressing geometric problems, using the theorems calculations presented at the beginning. For this work, the methodology used was the bibliographic research. Through this research, we were able to conclude that, despite the three presented, the calculation takes on great importance for the resolution of this type of problem, since there are a lot of situations that cannot be solved through the inequality of means, nor with the use of the quadratic function.
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AH Gee · 1993
previously seemed, since they can be successfully applied to only a limited number of problems exhibiting special, amenable properties. Combinatorial optimization, neural networks, mean eld annealing. i optimization networks Key words: Summary I am greatly indebted to my supervisor, Richard Prager, for initially allowing me the freedom to explore various research areas, and subsequently providing invaluable support as my work progressed. Members of the Speech, Vision and Robotics Group at the Cambridge University Department of Engineering have provided a stimulating and friendly environment to work in: special thanks must go to Patrick Gosling and Tony Robinson for maintaining a superb computing service, and to Sree Aiyer for both setting me on the right course and for numerous helpful discussions since then. I would like to thank the Science and Engineering Research Council of Great Britain, the Cambridge University Department of Engineering and Queen
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Basim Rabaa Jumaa, Ahmed Sabah Al-Jilawi · Journal of Physics Conference Series · 2020
Abstract The goal of this paper is to find a better method that converges faster of Max-Cut problem. One strategy is to the comparison between Bundle Method and the Augmented Lagrangian method. We have also developed the theoretical convergence properties of these methods.
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Paul D. Kaplan · Financial Planning Review · 2025
ABSTRACT The mean–variance optimization (MVO) model of Harry M. Markowitz is the foundation of quantitative portfolio construction and asset allocation. While Markowitz originally developed MVO for forming portfolios of tradable assets in isolation, it has been adapted for creating portfolios of tradable assets in the presence of non‐tradable assets and liabilities. In a series of publications, Paul D. Kaplan and Thomas M. Idzorek further extend MVO to the household economic balance sheet. The extended MVO model is the net worth optimization (NWO) model. In NWO, human capital is modeled as an asset mix held long, and, as in surplus optimization, liabilities are modeled as an asset mix held short. NWO operates in terms of net worth returns rather than in the returns on the financial assets. Kaplan and Idzorek maximize an approximation for expected utility developed by Haim Levy and Harry M. Markowitz. In this article, I show how to achieve this by combining existing quadratic programming techniques with nonlinear equation solution techniques in a novel way. I also discuss and demonstrate how NWO differs from the discretionary wealth approach (DWA) introduced by Jarrod Wilcox.
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Gregory Sell, Malcolm Slaney · IEEE Transactions on Audio Speech and Language Processing · 2010
We introduce two new methods for the demodulation of acoustic signals by posing the problem in a convex optimization framework. This allows the parameters of the modulator and carrier to be explicitly defined as constraints in an optimization problem. We first show the theory used to define the demodulation relationship within the rules of convex programming. Then, for the two approaches introduced, we derive specific cost functions and constraints to solve for modulators specifically motivated by perceptual rules. The methods described here perform well with simple, harmonic, and stochastic carriers, and also in the presence of noise.
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Hisashi Shimosaka, Tomoyuki Hiroyasu, Mitsunori Miki · Sekkei Kougaku, Shisutemu Bumon Kouenkai kouen rombunshuu/Sekkei Kogaku, Shisutemu Bumon Koenkai koen ronbunshu · 2003
In this paper, an optimization problem solving system on the Grid and its APIs are proposed. Generally, to solve the optimization problems, high calculation cost due to many iterations of analyzation and several libraries for optimization and analyzation are required. Therefore, the optimization system on the Grid is very efficient. In the proposed system, the GridRPC system is used for exchanging the informations among the optimization and analyzing libraries. The GridRPC system is a Grid middleware and provides useful RPC based programming model. In addition, the APIs for the proposed system are prepared. These APIs make it easy for the end-users to use the services provided by the proposed system and can offer the same services that do not depend on the Grid middleware. Therefore, the proposed system is expected to be the efficient optimization system on the Grid.
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Dragon, Ondřej · Brno University of Technology Digital Library (Brno University of Technology) · 2014
Tato práce je věnována evolučním algoritmům a řešením globálních optimalizačních problémů, a to hlavně problému obchodního cestujícího. Problém obchodního cestujícího je podrobně rozebrán stejně jako metody jeho řešení, kterými jsou: teorie grafů, heuristické metody a evoluční algoritmy. Hlavní optimalizační metodou této práce, je Inver - over operátor. V závěru jsou implementovány vybrané metody a je provedeno jejich testování a vyhodnocení na jednotlivých datových souborech.
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Wielkopolska Digital Library · 2014
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GT Parks, P.J. Turinsky, GI Maldonado · Cambridge University Engineering Department Publications Database · 1992
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Robert F. Dell · 2008
This paper presents new bounds, heuristics, and an exact algorithm for the Pallet Loading Problem (PLP). PLP maximizes the number of boxes placed on a rectangular pallet. All boxes have identical rectangular dimensions and, when placed, must be located completely within the pallet. Boxes may be rotated 90� so long as they are placed with edges parallel to the pallet’s edges. The set of all PLP instances with an area ratio (pallet area divided by box area) less than 101 boxes can be represented by 3,080,730 equivalent classes. Our G5-heuristic finds optimal solutions to 3,073,724 of these 3,080,730 classes and in the remaining 7006 classes only differs from the best known bound by one box. We develop three other heuristics that solve another 54 instances. Finally, we solve the 6952 remaining classes with our exact HVZ algorithm. Only a subset of these classes has been solved previously. � 2006 Elsevier B.V. All rights reserved.
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Xiaohui Ji, Zhuo Huang · 2010
This paper presents a new method that solves a mixed constraints problem by transforming it into a mixed integer programming problem. The method builds the connection between the feasibility of a mixed constraint problem and the solution to a mixed integer programming problem. The correctness of this method is proven. This method will be beneficial for the further integration of constraint programming and optimization methods.
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R. Akerkar · 2008
Purpose of these notes is to discuss the optimization problem. An optimization problem consists of finding the best (cheapest, heaviest, etc.) element in a large set P, called the feasible region and usually specified implicitly, where the quality of elements of the set are evaluated using a function f(x), the objective function, usually something fairly simple. The element that minimizes (or maximizes) this function is said to be an optimal solution of the objective function at this element is the optimal value. The greedy approach is a technique in which an optimal solution is obtained by means of the set of choices. A greedy algorithm always makes the choice that looks best at that moment. In this lecture, we will discuss greedy approach. To determine whether the greedy approach will yield the optimal solution the basics of matroid theory are presented.
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Braekers, Kris, Janssens, Gerrit K. · Advances in data mining and database management book series · 2018
In a vehicle routing problem (VRP) with time windows, the start of service needs to take place within the customer time window. Due to uncertainty on travel times, vehicles might arrive late at a customer’s site. A VRP is mostly solved to minimize a total cost criterion (travel time, travel distance, fixed and variable vehicle costs). But the dispatcher might also take into consideration the risk of non-conformance with the service agreement to start service within the time window. Therefore, a measure of risk, called “vulnerability of a solution,” is developed to serve as a \nsecond criterion. This chapter develops such a measure based on a distance metric and investigates its strengths and weaknesses.
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Babatunde Opesemowo, Chika Yinka-Banjo · Journal of Computer Science and Its Application · 2020
The increasing demand of optimization to various aspect of real-life complex combinatorial problems have seen a directly increase proportion of the use of metaheuristics as a technique many researchers applied to solve such problems. This is as a result of its flexibility, yet a complex approach that takes into consideration domain specific entities on how the problems are solve. One of such combinatorial problem applicable to real life issues is the facility location problem. Hence, this study sought to describe the concept of facility location problem, the techniques used to solve FLP (facility location problem) and real life application of FLP. Particle swarm optimization, genetic algorithm and tabu search are the most common metaheuristics used as solution tools to solving facility location problem from the review carried out. From the review, we recommended the application of more hybridized techniques to solve FLP in other to achieve better result.Keywords: Metaheuristics, Facility Location Problem (FLP), Optimization
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Mohammed Alhanjouri · International Journal of Advanced Research in Computer Science and Software Engineering · 2017
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Colletta, Stephen, Hamilton, Nathan, Cruz, David et al. · DigitalCommons - Kennesaw State University (Kennesaw State University) · 2024
Combinatorial optimization problems prevail in engineering and industry. Some are NP-hard and thus become difficult to solve on edge devices due to limited power and computing resources. Quadratic Unconstrained Binary Optimization (QUBO) problem is a valuable emerging model that can formulate numerous combinatorial problems, such as Max-Cut, traveling salesman problems, and graphic coloring. QUBO model also reconciles with two emerging computation models, quantum computing and neuromorphic computing, which can potentially boost the speed and energy efficiency in solving combinatorial problems. In this work, we explore neuromorphic QUBO solver composed of a swarm of spiking neural networks (SNN) that conduct a population-based meta-heuristic search for solutions. The proposed model can achieve about x20 40 speedup on large QUBO problems in terms of time steps compared to a traditional neural network solver. We also explore the hardware-software codesign for the proposed solver via high level synthesis.
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Yasunari Obuchi, Hironari Masui, Masaru Ohki · Neural Networks · 1996
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Hasan Abdulraheem Jubair, Saad Shakir Mahmood, Alan Jalal Abdulqader · AIP conference proceedings · 2023
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Hira Zaheer, Millie Pant · 2016
Portfolio theories best describes the asset management. Several investment offers are available to a customer and the task is to select the most appropriate option to gain the maximum financial benefit. The investor requires a thorough comparative study to decide the best possible option where the return is maximum and the risk is minimum. Portfolio optimization can help in the process of decision making by bringing out the selected options beneficial for the investor. In this paper we have considered the Markovitz's Mean Variance portfolio optimization model and the data is considered from National Stock Exchange (NSE), Mumbai. Differential Evolution, a population based metaheuristics is applied for obtaining the optimal portfolio.
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Omar Muhammed Neda, Alfian Ma’arif · International Journal of Robotics and Control Systems · 2022
The losses in electrical power systems are a great problem. Multiple methods have been utilized to decrease power losses in transmission lines. The proper adjusting of reactive power resources is one way to minimize the losses in any power system. Reactive Power Optimization (RPO) problem is a nonlinear and complex optimization problem and contains equality and inequality constraints. The RPO is highly essential in the operation and control of power systems. Therefore, the study concentrates on the Optimal Load Flow calculation in solving RPO problems. The Simple Particle Swarm Optimization (PSO) often falls into the local optima solution. To prevent this limitation and speed up the convergence for the Simple PSO algorithm, this study employed an improved hybrid algorithm based on Chaotic theory with PSO, called Chaotic PSO (CPSO) algorithm. Undeniably, this merging of chaotic theory in PSO algorithm can be an efficient method to slip very easily from local optima compared to Simple PSO algorithm due to remarkable behavior and high ability of the chaos. In this study, the CPSO algorithm was utilized as an optimization tool for solving the RPO problem; the main objective in this study is to decrease the power loss and enhance the voltage profile in the power system. The presented algorithm was tested on IEEE Node-14 system. The simulation implications for this system reveal that the CPSO algorithm provides the best results. It had a high ability to minimize transmission line losses and improve the system's voltage profile compared to the Simple PSO and other approaches in the literature.
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