scholarly journals Diversity in Kemeny Rank Aggregation: A Parameterized Approach

2021 ◽  
Author(s):  
Emmanuel Arrighi ◽  
Henning Fernau ◽  
Daniel Lokshtanov ◽  
Mateus de Oliveira Oliveira ◽  
Petra Wolf
Keyword(s):  
Social Choice Theory ◽  
Optimization Theory ◽  
Optimal Solution ◽  
General Setting ◽  
Solution Space ◽  
Order Theory ◽  
Rank Aggregation ◽  
Main Concern ◽  
Traditional Setting ◽  
The Impact

In its most traditional setting, the main concern of optimization theory is the search for optimal solutions for instances of a given computational problem. A recent trend of research in artificial intelligence, called solution diversity, has focused on the development of notions of optimality that may be more appropriate in settings where subjectivity is essential. The idea is that instead of aiming at the development of algorithms that output a single optimal solution, the goal is to investigate algorithms that output a small set of sufficiently good solutions that are sufficiently diverse from one another. In this way, the user has the opportunity to choose the solution that is most appropriate to the context at hand. It also displays the richness of the solution space. When combined with techniques from parameterized complexity theory, the paradigm of diversity of solutions offers a powerful algorithmic framework to address problems of practical relevance. In this work, we investigate the impact of this combination in the field of Kemeny Rank Aggregation, a well-studied class of problems lying in the intersection of order theory and social choice theory and also in the field of order theory itself. In particular, we show that KRA is fixed-parameter tractable with respect to natural parameters providing natural formalizations of the notions of diversity and of the notion of a sufficiently good solution. Our main results work both when considering the traditional setting of aggregation over linearly ordered votes, and in the more general setting where votes are partially ordered.

scholarly journals On the Optimal Efficiency of Cost-Algebraic A*

2019 ◽  
Vol 33 ◽  
pp. 2288-2295
Author(s):  
Robert C. Holte ◽  
Sandra Zilles
Keyword(s):  
Shortest Path ◽  
Optimal Solution ◽  
General Setting ◽  
Algebraic Setting ◽  
Optimal Efficiency ◽  
The Cost ◽  
Traditional Setting

Edelkamp et al. (2005) proved that A*, given an admissible heuristic, is guaranteed to return an optimal solution in any cost algebra, not just in the traditional shortest path setting. In this paper, we investigate cost-algebraic A*’s optimal efficiency: in the cost-algebraic setting, under what conditions is A* guaranteed to expand the fewest possible states? In the traditional setting, this question was examined in detail by Dechter & Pearl (1985). They identified five different situations in which A* was optimally efficient. We show that three of them continue to hold in the cost-algebraic setting, but that one does not. We also show that one of them is false, it does not hold even in the traditional setting. We introduce an alternative that does hold in the cost-algebraic setting. Finally, we show that a well-known result due to Nilsson does not hold in the general cost-algebraic setting but does hold in a slightly less general setting.

scholarly journals Empirical Stochastic Model of Multi-GNSS Measurements

Sensors ◽  
2021 ◽  
Vol 21 (13) ◽  
pp. 4566
Author(s):  
Dominik Prochniewicz ◽  
Kinga Wezka ◽  
Joanna Kozuchowska
Keyword(s):  
Stochastic Model ◽  
Density Ratio ◽  
Functional Model ◽  
Optimal Solution ◽  
Global Navigation Satellite Systems ◽  
Unknown Parameters ◽  
Short Baseline ◽  
Stochastic Parameters ◽  
Dependent Model ◽  
The Impact

The stochastic model, together with the functional model, form the mathematical model of observation that enables the estimation of the unknown parameters. In Global Navigation Satellite Systems (GNSS), the stochastic model is an especially important element as it affects not only the accuracy of the positioning model solution, but also the reliability of the carrier-phase ambiguity resolution (AR). In this paper, we study in detail the stochastic modeling problem for Multi-GNSS positioning models, for which the standard approach used so far was to adopt stochastic parameters from the Global Positioning System (GPS). The aim of this work is to develop an individual, empirical stochastic model for each signal and each satellite block for GPS, GLONASS, Galileo and BeiDou systems. The realistic stochastic model is created in the form of a fully populated variance-covariance (VC) matrix that takes into account, in addition to the Carrier-to-Noise density Ratio (C/N0)-dependent variance function, also the cross- and time-correlations between the observations. The weekly measurements from a zero-length and very short baseline are utilized to derive stochastic parameters. The impact on the AR and solution accuracy is analyzed for different positioning scenarios using the modified Kalman Filter. Comparing the positioning results obtained for the created model with respect to the results for the standard elevation-dependent model allows to conclude that the individual empirical stochastic model increases the accuracy of positioning solution and the efficiency of AR. The optimal solution is achieved for four-system Multi-GNSS solution using fully populated empirical model individual for satellite blocks, which provides a 2% increase in the effectiveness of the AR (up to 100%), an increase in the number of solutions with errors below 5 mm by 37% and a reduction in the maximum error by 6 mm compared to the Multi-GNSS solution using the elevation-dependent model with neglected measurements correlations.

scholarly journals Improving PV Resilience by Dynamic Reconfiguration in Distribution Grids: Problem Complexity and Computation Requirements

Energies ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 830
Author(s):  
Filipe F. C. Silva ◽  
Pedro M. S. Carvalho ◽  
Luís A. F. M. Ferreira
Keyword(s):  
Distributed Generation ◽  
Optimal Solution ◽  
Dynamic Reconfiguration ◽  
Scheduling Problem ◽  
Low Carbon ◽  
Distribution Grid ◽  
Medium Voltage ◽  
Classical Computing ◽  
The Impact ◽  
Distribution Grids

The dissemination of low-carbon technologies, such as urban photovoltaic distributed generation, imposes new challenges to the operation of distribution grids. Distributed generation may introduce significant net-load asymmetries between feeders in the course of the day, resulting in higher losses. The dynamic reconfiguration of the grid could mitigate daily losses and be used to minimize or defer the need for network reinforcement. Yet, dynamic reconfiguration has to be carried out in near real-time in order to make use of the most updated load and generation forecast, this way maximizing operational benefits. Given the need to quickly find and update reconfiguration decisions, the computational complexity of the underlying optimal scheduling problem is studied in this paper. The problem is formulated and the impact of sub-optimal solutions is illustrated using a real medium-voltage distribution grid operated under a heavy generation scenario. The complexity of the scheduling problem is discussed to conclude that its optimal solution is infeasible in practical terms if relying upon classical computing. Quantum computing is finally proposed as a way to handle this kind of problem in the future.

scholarly journals Efficient Operative Cost Reduction in Distribution Grids Considering the Optimal Placement and Sizing of D-STATCOMs Using a Discrete-Continuous VSA

2021 ◽  
Vol 11 (5) ◽  
pp. 2175
Author(s):  
Oscar Danilo Montoya ◽  
Walter Gil-González ◽  
Jesus C. Hernández
Keyword(s):  
Objective Function ◽  
Reactive Power ◽  
Programming Model ◽  
Search Algorithm ◽  
Solution Space ◽  
Distribution Networks ◽  
Optimal Placement ◽  
Mixed Integer ◽  
Solution Vector ◽  
The Impact

The problem of reactive power compensation in electric distribution networks is addressed in this research paper from the point of view of the combinatorial optimization using a new discrete-continuous version of the vortex search algorithm (DCVSA). To explore and exploit the solution space, a discrete-continuous codification of the solution vector is proposed, where the discrete part determines the nodes where the distribution static compensator (D-STATCOM) will be installed, and the continuous part of the codification determines the optimal sizes of the D-STATCOMs. The main advantage of such codification is that the mixed-integer nonlinear programming model (MINLP) that represents the problem of optimal placement and sizing of the D-STATCOMs in distribution networks only requires a classical power flow method to evaluate the objective function, which implies that it can be implemented in any programming language. The objective function is the total costs of the grid power losses and the annualized investment costs in D-STATCOMs. In addition, to include the impact of the daily load variations, the active and reactive power demand curves are included in the optimization model. Numerical results in two radial test feeders with 33 and 69 buses demonstrate that the proposed DCVSA can solve the MINLP model with best results when compared with the MINLP solvers available in the GAMS software. All the simulations are implemented in MATLAB software using its programming environment.

scholarly journals Exploring optimal control of epidemic spread using reinforcement learning

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Abu Quwsar Ohi ◽  
M. F. Mridha ◽  
Muhammad Mostafa Monowar ◽  
Md. Abdul Hamid
Keyword(s):  
Reinforcement Learning ◽  
Economic Crisis ◽  
Transmission Rate ◽  
Optimal Solution ◽  
Short Length ◽  
Reproduction Rate ◽  
Economic Factors ◽  
Epidemic Spread ◽  
The Impact ◽  
Individual Human

AbstractPandemic defines the global outbreak of a disease having a high transmission rate. The impact of a pandemic situation can be lessened by restricting the movement of the mass. However, one of its concomitant circumstances is an economic crisis. In this article, we demonstrate what actions an agent (trained using reinforcement learning) may take in different possible scenarios of a pandemic depending on the spread of disease and economic factors. To train the agent, we design a virtual pandemic scenario closely related to the present COVID-19 crisis. Then, we apply reinforcement learning, a branch of artificial intelligence, that deals with how an individual (human/machine) should interact on an environment (real/virtual) to achieve the cherished goal. Finally, we demonstrate what optimal actions the agent perform to reduce the spread of disease while considering the economic factors. In our experiment, we let the agent find an optimal solution without providing any prior knowledge. After training, we observed that the agent places a long length lockdown to reduce the first surge of a disease. Furthermore, the agent places a combination of cyclic lockdowns and short length lockdowns to halt the resurgence of the disease. Analyzing the agent’s performed actions, we discover that the agent decides movement restrictions not only based on the number of the infectious population but also considering the reproduction rate of the disease. The estimation and policy of the agent may improve the human-strategy of placing lockdown so that an economic crisis may be avoided while mitigating an infectious disease.

scholarly journals Time-jerk optimal trajectory planning of hydraulic robotic excavator

2021 ◽  
Vol 13 (7) ◽  
pp. 168781402110346
Author(s):  
Yunyue Zhang ◽  
Zhiyi Sun ◽  
Qianlai Sun ◽  
Yin Wang ◽  
Xiaosong Li ◽  
...  
Keyword(s):  
Angular Velocity ◽  
Trajectory Planning ◽  
Optimal Trajectory ◽  
High Efficiency ◽  
Optimal Solution ◽  
Optimal Time ◽  
Target Point ◽  
Robotic Excavator ◽  
The Impact ◽  
Optimal Trajectory Planning

Due to the fact that intelligent algorithms such as Particle Swarm Optimization (PSO) and Differential Evolution (DE) are susceptible to local optima and the efficiency of solving an optimal solution is low when solving the optimal trajectory, this paper uses the Sequential Quadratic Programming (SQP) algorithm for the optimal trajectory planning of a hydraulic robotic excavator. To achieve high efficiency and stationarity during the operation of the hydraulic robotic excavator, the trade-off between the time and jerk is considered. Cubic splines were used to interpolate in joint space, and the optimal time-jerk trajectory was obtained using the SQP with joint angular velocity, angular acceleration, and jerk as constraints. The optimal angle curves of each joint were obtained, and the optimal time-jerk trajectory planning of the excavator was realized. Experimental results show that the SQP method under the same weight is more efficient in solving the optimal solution and the optimal excavating trajectory is smoother, and each joint can reach the target point with smaller angular velocity, and acceleration change, which avoids the impact of each joint during operation and conserves working time. Finally, the excavator autonomous operation becomes more stable and efficient.

scholarly journals Control of Discrete Event Systems by Means of Discrete Optimization and Disjunctive Colored PNs: Application to Manufacturing Facilities

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
Juan-Ignacio Latorre-Biel ◽  
Emilio Jiménez-Macías ◽  
Mercedes Pérez de la Parte ◽  
Julio Blanco-Fernández ◽  
Eduardo Martínez-Cámara
Keyword(s):  
Discrete Event ◽  
Optimal Solution ◽  
Solution Space ◽  
Discrete Systems ◽  
Discrete Control ◽  
Classic Approach ◽  
Event Dynamic ◽  
Time Required ◽  
Computational Resources ◽  
Control Methodology

Artificial intelligence methodologies, as the core of discrete control and decision support systems, have been extensively applied in the industrial production sector. The resulting tools produce excellent results in certain cases; however, the NP-hard nature of many discrete control or decision making problems in the manufacturing area may require unaffordable computational resources, constrained by the limited available time required to obtain a solution. With the purpose of improving the efficiency of a control methodology for discrete systems, based on a simulation-based optimization and the Petri net (PN) model of the real discrete event dynamic system (DEDS), this paper presents a strategy, where a transformation applied to the model allows removing the redundant information to obtain a smaller model containing the same useful information. As a result, faster discrete optimizations can be implemented. This methodology is based on the use of a formalism belonging to the paradigm of the PN for describing DEDS, the disjunctive colored PN. Furthermore, the metaheuristic of genetic algorithms is applied to the search of the best solutions in the solution space. As an illustration of the methodology proposal, its performance is compared with the classic approach on a case study, obtaining faster the optimal solution.

Predictive Search for Capacitated Multi-Item Lot Sizing Problems

2021 ◽  
Author(s):  
Tao Wu
Keyword(s):  
Mathematical Programming ◽  
Heuristic Search ◽  
Lot Sizing ◽  
Optimal Solution ◽  
Solution Space ◽  
Search Method ◽  
Benchmark Problems ◽  
Solution Quality ◽  
Programming Technique ◽  
Advanced Analytics

For capacitated multi-item lot sizing problems, we propose a predictive search method that integrates machine learning/advanced analytics, mathematical programming, and heuristic search into a single framework. Advanced analytics can predict the probability that an event will happen and has been applied to pressing industry issues, such as credit scoring, risk management, and default management. Although little research has applied such technique for lot sizing problems, we observe that advanced analytics can uncover optimal patterns of setup variables given properties associated with the problems, such as problem attributes, and solution values yielded by linear programming relaxation, column generation, and Lagrangian relaxation. We, therefore, build advanced analytics models that yield information about how likely a solution pattern is the same as the optimum, which is insightful information used to partition the solution space into incumbent, superincumbent, and nonincumbent regions where an analytics-driven heuristic search procedure is applied to build restricted subproblems. These subproblems are solved by a combined mathematical programming technique to improve solution quality iteratively. We prove that the predictive search method can converge to the global optimal solution point. The discussion is followed by computational tests, where comparisons with other methods indicate that our approach can obtain better results for the benchmark problems than other state-of-the-art methods. Summary of Contribution: In this study, we propose a predictive search method that integrates machine learning/advanced analytics, mathematical programming, and heuristic search into a single framework for capacitated multi-item lot sizing problems. The advanced analytics models are used to yield information about how likely a solution pattern is the same as the optimum, which is insightful information used to divide the solution space into incumbent, superincumbent, and nonincumbent regions where an analytics-driven heuristic search procedure is applied to build restricted subproblems. These subproblems are solved by a combined mathematical programming technique to improve solution quality iteratively. We prove that the predictive search method can converge to the global optimal solution point. Through computational tests based on benchmark problems, we observe that the proposed approach can obtain better results than other state-of-the-art methods.

Pulp mill process closure: a review of global technology developments and mill experiences in the 1990s

2004 ◽  
Vol 50 (3) ◽  
pp. 183-194 ◽  
Author(s):  
S.C. Stratton ◽  
P.L. Gleadow ◽  
A.P. Johnson
Keyword(s):  
Manufacturing Industry ◽  
Pollution Prevention ◽  
Optimal Solution ◽  
Pulp Mill ◽  
Thermomechanical Pulp ◽  
Pulp Mills ◽  
Oxygen Delignification ◽  
Manufacturing Operations ◽  
The Impact ◽  
Mill Process

The impact of effluent discharges continues to be an important issue for the pulp manufacturing industry. Considerable progress has been made in pollution prevention to minimize waste generation, so-called manufacturing “process closure.” Since the mid-1980s many important technologies have been developed and implemented, many of these in response to organochlorine concerns. Zero effluent operation is now a reality for a few bleached chemi-thermomechanical pulp (BCTMP) pulp mills. In kraft pulp manufacturing, important developments include widespread adoption of new cooking techniques, oxygen delignification, closed screening, improved process control, new bleaching methods, and systems that minimize pulping liquor losses. Coupled to this is a commitment to reduce water use and maximize reuse of in-mill process streams. Some companies pursued bleach plant closure, and many have been successful in eliminating a portion of their bleaching wastewaters. However, the difficulties inherent in closing bleach plants are considerable. For many mills the optimal solution has been found to be a high degree of closure coupled with external biological treatment of the remaining process effluent. No bleach plants at papergrade bleached kraft mills are known to be operating effluent-free on a continuous basis. This paper reviews the important worldwide technological developments and mill experiences in the 1990s that were focused on minimizing environmental impacts of pulp manufacturing operations.

scholarly journals Decision Support Tool for Offshore Wind Farm Vessel Routing under Uncertainty

Energies ◽  
2018 ◽  
Vol 11 (9) ◽  
pp. 2190 ◽  
Author(s):  
Rafael Dawid ◽  
David McMillan ◽  
Matthew Revie
Keyword(s):  
Wind Farm ◽  
Real Life ◽  
Synthetic Data ◽  
Optimal Solution ◽  
Decision Support Tool ◽  
Offshore Wind ◽  
Offshore Wind Farm ◽  
Support Tool ◽  
Trade Offs ◽  
The Impact

This paper for the first time captures the impact of uncertain maintenance action times on vessel routing for realistic offshore wind farm problems. A novel methodology is presented to incorporate uncertainties, e.g., on the expected maintenance duration, into the decision-making process. Users specify the extent to which these unknown elements impact the suggested vessel routing strategy. If uncertainties are present, the tool outputs multiple vessel routing policies with varying likelihoods of success. To demonstrate the tool’s capabilities, two case studies were presented. Firstly, simulations based on synthetic data illustrate that in a scenario with uncertainties, the cost-optimal solution is not necessarily the best choice for operators. Including uncertainties when calculating the vessel routing policy led to a 14% increase in the number of wind turbines maintained at the end of the day. Secondly, the tool was applied to a real-life scenario based on an offshore wind farm in collaboration with a United Kingdom (UK) operator. The results showed that the assignment of vessels to turbines generated by the tool matched the policy chosen by wind farm operators. By producing a range of policies for consideration, this tool provided operators with a structured and transparent method to assess trade-offs and justify decisions.

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