This paper presents a new simplex-type algorithm for linear programming with the following two main characteristics: (i) the algorithm computes basic solutions which are neither primal or dual feasible, nor monotonica...
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This paper presents a new simplex-type algorithm for linear programming with the following two main characteristics: (i) the algorithm computes basic solutions which are neither primal or dual feasible, nor monotonically improving and (ii) the sequence of these basic solutions is connected with a sequence of monotonically improving interior points to construct a feasible direction at each iteration. We compare the proposed algorithm with the state-of-the-art commercial CPLEX and Gurobi Primal-Simplex optimizers on a collection of 93 well known benchmarks. The results are promising, showing that the new algorithm competes versus the state-of-the-art solvers in the total number of iterations required to converge.
This paper considers a linear optimisation problem under uncertainty with at least one element modelled as a non-probabilistic uncertainty. The uncertainty is expressed in the coefficient matrices of constraints and/o...
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This paper considers a linear optimisation problem under uncertainty with at least one element modelled as a non-probabilistic uncertainty. The uncertainty is expressed in the coefficient matrices of constraints and/or coefficients of goal function. Previous work converts such problems to classical (linear) optimisation problems and eliminates uncertainty by converting the linear programming under uncertainty problem to a decision problem using imprecise probability and imprecise decision theory. Our aim here is to generalise this approach numerically and present three methods to calculate the solution. We investigate what numerical results can be obtained for interval and fuzzy types of uncertainty models and compare them to classical probabilistic cases - for two different optimality criteria: maximinity and maximality. We also provide an efficient method to calculate the maximal solutions in the fuzzy set model. A numerical example is considered for illustration of the results.
In order to accurately assess the reliability of a real-world complex system, the joint distribution of component events is needed. In reality, however, such complete information to model the joint distributions of sy...
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In order to accurately assess the reliability of a real-world complex system, the joint distribution of component events is needed. In reality, however, such complete information to model the joint distributions of system components is rarely available. As a way to resort only to the available information while excluding any assumptions on the form of distributions, a linear programming (LP) bounds method was developed in 2003, which computes the narrowest bounds possible for given information regarding marginal and joint failure probabilities. However, the number of variables of the optimization problem exponentially increases as that of component events increases, requiring an insurmountable memory for larger systems. In order to overcome such memory issue, an alternative formulation of the LP bounds method is proposed in this paper. Specifically, an iteration of binary integer programming (BIP) is formulated based on the inclusion relationships between the events of consideration. As a result, the memory requirement can be significantly alleviated with the trade-off of the computational cost required for repeated optimizations of smaller BIP problems. Then, the major bottleneck is changed from the number of component events to that of constraints given as information to narrow the bounds. This paper also provides empirical suggestions on the selection of a subset of constraints to further extend the applicability of the proposed methodology to even larger systems. Five numerical examples of series, parallel, and general system reliability problems are provided to demonstrate the method and its applications.
Photovoltaic (PV) technology is highly adopted within buildings, as it is proven for reducing electricity bills. However, with the 2010/31/EU directive all new buildings shall be nearly Zero Energy Buildings (nZEB) fr...
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Photovoltaic (PV) technology is highly adopted within buildings, as it is proven for reducing electricity bills. However, with the 2010/31/EU directive all new buildings shall be nearly Zero Energy Buildings (nZEB) from 2020 onward, with the requirement to maintain their energy consumption at low levels. For further embedding the nZEB concept in an integrated, holistic and efficient energy system, to overcome any application problems, one should not only focus on building energy efficiency designs, but also on smart and effective energy management techniques. For instance, as energy storage may contribute a key solution towards nZEB, a novel approach able to adapt to a given PV generation and load demand and individually control the battery and the net grid energy, is presented. This is achieved through linear programming (LP), a convex optimization tool, along with a weighted sum approach. Using real data, simulation results demonstrate that, choosing the right weight values based on the given generation and demand profiles, the LP model controls the building's import energy, export energy and the battery accordingly. Hence, the net grid electrical energy is maintained to the minimum possible level. Finally, the LP model is crossed-checked with the freeware System Advisor Model (SAM) showing a normalized Root Mean Squared Error (nRMSE) of 2.10% for the annual battery dispatch. The analysis shows that the LP model combined with SAM, for addressing the non-linearity of the storage and to account for the power conversion losses, gives a lower annual net grid energy use than SAM's automated target controller by 2.0%. (C) 2020 Elsevier Ltd. All rights reserved.
In this paper, we investigate how energy storage can be used to increase the value of community energy schemes through cost reductions, infrastructure support, increased scheme membership, and reduced carbon emissions...
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In this paper, we investigate how energy storage can be used to increase the value of community energy schemes through cost reductions, infrastructure support, increased scheme membership, and reduced carbon emissions. A linear programming optimisation framework is developed to schedule the operation of behind-the-meter energy storage such that costs are minimised, while keeping peak demands within allowable limits. This is also extended to model generation-integrated energy storage systems, where the storage is located in the flow of energy from primary source (e.g. wind) to a usable form (e.g. electricity). To demonstrate the potential of energy storage within a real community energy scheme, we present a case study of a community hydro scheme in North Wales, considering both battery storage and a reservoir-based storage system. It is found that either system can be used to substantially increase the membership of the scheme while avoiding impacts on the electricity network, but that storage remains prohibitively expensive when used for self-consumption of renewables and arbitrage. We also investigate the impacts of energy storage on the community's carbon emissions, showing that storage operation appears to provide very little additional reduction in emissions when grid average emissions factors are used.
The linear programming (LP) approach to solve the Bellman equation in dynamic programming is a well-known option for finite state and input spaces to obtain an exact solution. However, with function approximation or c...
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The linear programming (LP) approach to solve the Bellman equation in dynamic programming is a well-known option for finite state and input spaces to obtain an exact solution. However, with function approximation or continuous state spaces, refinements are necessary. This paper presents a methodology to make approximate dynamic programming via LP work in practical control applications with continuous state and input spaces. There are some guidelines on data and regressor choices needed to obtain meaningful and well-conditioned value function estimates. The work discusses the introduction of terminal ingredients and computation of lower and upper bounds of the value function. An experimental inverted-pendulum application will be used to illustrate the proposal and carry out a suitable comparative analysis with alternative options in the literature.
A new multiple attribute decision making method based on the q-rung orthopair hesitant fuzzy sets has been developed. The evaluation values are given as q-rung orthopair hesitant fuzzy values. Then some weighted simil...
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A new multiple attribute decision making method based on the q-rung orthopair hesitant fuzzy sets has been developed. The evaluation values are given as q-rung orthopair hesitant fuzzy values. Then some weighted similarity functions are defined. A linear programming model is proposed to derive attribute weights based on the similarity functions for the case of partly known attribute weight information and a formula is given to determine attribute weight based on similarity function and the Lagrange function for completely unknown attribute weights. Finally, TOPSIS method is used to rank alternatives. The application of the proposed approach is explored by the application of purchase self-service book sterilizer problem. Some comparisons are also conducted to demonstrate advantages of the proposed method.
The coordination of directional overcurrent relays (DOCRs) is a constrained and nonlinear optimization problem which consists in finding suitable plug and time dial settings so that the relay operational times are min...
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The coordination of directional overcurrent relays (DOCRs) is a constrained and nonlinear optimization problem which consists in finding suitable plug and time dial settings so that the relay operational times are minimized, keeping selectivity and sensitivity characteristics. Recently, several efforts have been devoted to automate the coordination of DOCRs. This paper proposes a hybrid technique entitled simulated annealing linear programming (SA-LP) to achieve the optimal coordination of DOCRs. Five test-systems (IEEE-3, IEEE-6, IEEE-8, IEEE-15 and IEEE-30 bus) are used to verify the effectiveness of the proposed technique. Results obtained with the SA-LP are confronted against other optimization techniques reported in specialized literature, under identical conditions. The proposed approach presented good quality solutions, low computational processing times and great convergence towards the optimum solution, presenting an advantage over adaptive coordination tendency by enhancing monitoring, communication capabilities and grid control.
In the last few years, there has been a growing interest in the disassembly scheduling problem to fulfil the demands of individual disassembled parts over a given planning horizon. An analysis of the literature shows ...
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Traditional linear program (LP) models are deterministic. The way that constraint limit uncertainty is handled is to compute the range of feasibility. After the optimal solution is obtained, typically by the simplex m...
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Traditional linear program (LP) models are deterministic. The way that constraint limit uncertainty is handled is to compute the range of feasibility. After the optimal solution is obtained, typically by the simplex method, one considers the effect of varying each constraint limit, one at a time. This yields the range of feasibility within which the solution remains feasible. This sensitivity analysis is useful for helping the analyst get a feel for the problem. However, it is unrealistic because some constraint limits can vary randomly. These are typically constraint limits based on expected inventory. Inventory may fall short if there are overdue deliveries, unplanned machine failure, spoilage, etc. A realistic LP is created for simultaneously randomizing the constraint limits from any probability distribution. The corresponding distribution of objective function values is created. This distribution is examined directly for central tendencies, spread, skewness and extreme values for the purpose of risk analysis. The spreadsheet design presented is ideal for teaching Monte Carlo simulation and risk analysis to graduate students in business analytics with no specialized programming language requirement.
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