This paper considers the problem of designing a multilevel pulse width modulated (PWM) waveform with a prescribed harmonic content. Multilevel PWM design plays a major role in many diverse engineering disciplines. In ...
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This paper considers the problem of designing a multilevel pulse width modulated (PWM) waveform with a prescribed harmonic content. Multilevel PWM design plays a major role in many diverse engineering disciplines. In power electronics, multilevel PWM design corresponds to determining the inverter switching times and levels for selective harmonic elimination and harmonic compensation. In mechatronics, the same design corresponds to shaping input signals to damp residual vibrations in flexible structures. More generally, in many applications, the aim of PWM design is to minimise the total harmonic distortion while adhering to a prescribed harmonic content. The solution approach presented in this paper is based on linear programming with the objective of minimising the total harmonic distortion. This objective is achieved within an arbitrarily small bound of the optimal solution of the related convex optimisation problem. In addition, the linear programming formulation makes the design of such switching waveforms computationally tractable and efficient. Simulations and experiments are provided for corroboration.
For interior-point algorithms in linear programming,it is well known that the selection of the centering parameter is crucial for proving polynomiality in theory and for efficiency in ***,the selection of the centerin...
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For interior-point algorithms in linear programming,it is well known that the selection of the centering parameter is crucial for proving polynomiality in theory and for efficiency in ***,the selection of the centering parameter is usually by heuristics and separated from the selection of the line-search step *** heuristics are quite different while developing practically efficient algorithms,such as Mehrotra’s predictor–corrector(MPC)algorithm,and theoretically efficient algorithms,such as short-step path-following *** introduces a dilemma that some algorithms with the best-known polynomial bound are least efficient in practice,and some most efficient algorithms may not be convergent in polynomial ***,in this paper,we propose a systematic way to optimally select the centering parameter and linesearch step size at the same time,and we show that the algorithm based on this strategy has the best-known polynomial bound and may be very efficient in computation for real problems.
Classical planning in Artificial Intelligence is a computationally expensive problem of finding a sequence of actions that transforms a given initial state of the problem to a desired goal situation. Lack of informati...
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Classical planning in Artificial Intelligence is a computationally expensive problem of finding a sequence of actions that transforms a given initial state of the problem to a desired goal situation. Lack of information about the initial state leads to conditional and conformant planning that is more difficult than classical one. A parallel plan is the plan in which some actions can be executed in parallel, usually leading to decrease of the plan execution time but increase of the difficulty of finding the plan. This paper is focused on three planning problems which are computationally difficult: conditional, conformant and parallel conformant. To avoid these difficulties a set of transformations to linear programming Problem (LPP), illustrated by examples, is proposed. The results show that solving LPP corresponding to the planning problem can be computationally easier than solving the planning problem by exploring the problem state space. The cost is that not always the LPP solution can be interpreted directly as a plan.
In a construction environment, project scheduling is an essential tool to measure the success of all projects. This research paper will use project crashing of Activity to decrease the project completion schedule thro...
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In a construction environment, project scheduling is an essential tool to measure the success of all projects. This research paper will use project crashing of Activity to decrease the project completion schedule through the CPM method of time-cost trade-off and to minimize project cost. It includes linear programming with the aid of Microsoft Excel Solver to determine the result. And at the end of the research paper, it will show the impact of crashing the activities for the HVAC mechanical installation in a project for both normal and crash time, which displays that the selected Activity that had been crashed generated an increase of 9.8 % total cost from the total project cost.
A bipolar single-valued neutrosophic set can deal with the hesitation relevant to the information of any decision making problem in real life scenarios,where bipolar fuzzy sets may fail to handle those hesitation *** ...
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A bipolar single-valued neutrosophic set can deal with the hesitation relevant to the information of any decision making problem in real life scenarios,where bipolar fuzzy sets may fail to handle those hesitation *** this study,we first develop a new method for solving linear programming problems based on bipolar singlevalued neutrosophic ***,we apply the score function to transform bipolar single-valued neutrosophic problems into crisp linear programming ***,we apply the proposed technique to solve fully bipolar single-valued neutrosophic linear programming problems with non-negative triangular bipolar single-valued neutrosophic numbers(TBSvNNs)and non-negative trapezoidal bipolar single-valued neutrosophic numbers(TrBSvNNs).
This paper presents a new dimension reduction strategy for medium and large-scale linear programming problems. The proposed method uses a subset of the original constraints and combines two algorithms: the weighted av...
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This paper presents a new dimension reduction strategy for medium and large-scale linear programming problems. The proposed method uses a subset of the original constraints and combines two algorithms: the weighted average and the cosine simplex algorithm. The first approach identifies binding constraints by using the weighted average of each constraint, whereas the second algorithm is based on the cosine similarity between the vector of the objective function and the constraints. These two approaches are complementary, and when used together, they locate the essential subset of initial constraints required for solving medium and large-scale linear programming problems. After reducing the dimension of the linear programming problem using the subset of the essential constraints, the solution method can be chosen from any suitable method for linear programming. The proposed approach was applied to a set of well-known benchmarks as well as more than 2000 random medium and large-scale linear programming problems. The results are promising, indicating that the new approach contributes to the reduction of both the size of the problems and the total number of iterations required. A tree-based classification model also confirmed the need for combining the two approaches. A detailed numerical example, the general numerical results, and the statistical analysis for the decision tree procedure are presented.
Multiple instance learning (MIL) aims to classify objects with complex structures and covers a wide range of real-world data mining applications. In MIL, objects are represented by a bag of instances instead of a sing...
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Multiple instance learning (MIL) aims to classify objects with complex structures and covers a wide range of real-world data mining applications. In MIL, objects are represented by a bag of instances instead of a single instance, and class labels are provided only for the bags. Some of the earlier MIL methods focus on solving MIL problem under the standard MIL assumption, which requires at least one positive instance in positive bags and all remaining instances are negative. This study proposes a linear programming framework to learn instance level contributions to bag label without emposing the standart assumption. Each instance of a bag is mapped to a pseudo-class membership estimate and these estimates are aggregated to obtain the bag-level class membership in an optimization framework. A simple linear mapping enables handling various MIL assumptions with adjusting instance contributions. Our experiments with instance-dissimilarity based data representations verify the effectiveness of the proposed MIL framework. Proposed mathematical models can be solved efficiently in polynomial time.
For static traffic assignment problems, it is well known that (1) for some users the experienced travel time in a system optimum assignment can be substantially higher than the experienced travel time in a user equili...
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For static traffic assignment problems, it is well known that (1) for some users the experienced travel time in a system optimum assignment can be substantially higher than the experienced travel time in a user equilibrium assignment, and (2) the total travel time in user equilibrium can be substantially higher than the total travel time in system optimum. By seeking system optimal traffic flows subject to user constraints, a compromise assignment can be obtained that balances system and user objectives. To this aim, a linear model and an efficient heuristic algorithm are proposed in this paper. A computational study shows that the proposed model, along with the heuristic algorithm, is able to provide fair solutions with near-optimal total travel time within very short computational time. (C) 2021 The Authors. Published by Elsevier B.V.
In this paper, we propose a new framework to implement interior point method (IPM) in order to solve some very large-scale linear programs (LPs). Traditional IPMs typically use Newton's method to approximately sol...
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In this paper, we propose a new framework to implement interior point method (IPM) in order to solve some very large-scale linear programs (LPs). Traditional IPMs typically use Newton's method to approximately solve a subproblem that aims to minimize a log-barrier penalty function at each iteration. Due its connection to Newton's method, IPM is often classified assecond-order method- a genre that is attached with stability and accuracy at the expense of scalability. Indeed, computing a Newton step amounts to solving a large system of linear equations, which can be efficiently implemented if the input data are reasonably sized and/or sparse and/or well-structured. However, in case the above premises fail, then the challenge still stands on the way for a traditional IPM. To deal with this challenge, one approach is to apply the iterative procedure, such as preconditioned conjugate gradient method, to solve the system of linear equations. Since the linear system is different in each iteration, it is difficult to find good pre-conditioner to achieve the overall solution efficiency. In this paper, an alternative approach is proposed. Instead of applying Newton's method, we resort to the alternating direction method of multipliers (ADMM) to approximately minimize the log-barrier penalty function at each iteration, under the framework of primal-dual path-following for a homogeneous self-dual embedded LP model. The resulting algorithm is an ADMM-Based Interior Point Method, abbreviated asABIPin this paper. The new method inherits stability from IPM and scalability from ADMM. Because of its self-dual embedding structure,ABIPis set to solve any LP without requiring prior knowledge about its feasibility. We conduct extensive numerical experiments testingABIPwith large-scale LPs from NETLIB and machine learning applications. The results demonstrate thatABIPcompares favourably with other LP solvers includingSDPT3,MOSEK,DSDP-CGandSCS.
Multi-objective programming is frequently used in forest management research to reconcile conflicting policy objectives. Given the frequent occurrence of fire in Pinus canariensis forests in the Canary Islands, forest...
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