Showing papers in "Optimization and Engineering in 2011"
TL;DR: A database of approximate maximin and Audze-Eglais Latin hypercube designs for up to ten dimensions and for up-to 300 design points is constructed.
Abstract: In the area of computer simulation, Latin hypercube designs play an important role. In this paper the classes of maximin and Audze-Eglais Latin hypercube designs are considered. Up to now only several two-dimensional designs and a few higher dimensional designs for these classes have been published. Using periodic designs and the Enhanced Stochastic Evolutionary algorithm of Jin et al. (J. Stat. Plan. Interference 134(1):268–687, 2005), we obtain new results which we compare to existing results. We thus construct a database of approximate maximin and Audze-Eglais Latin hypercube designs for up to ten dimensions and for up to 300 design points. All these designs can be downloaded from the website http://www.spacefillingdesigns.nl.
165 citations
TL;DR: This paper presents a Sequential Approximate Optimization (SAO) procedure that uses the Radial Basis Function (RBF) network and proposes a sampling strategy that can be found with a small number of function evaluations.
Abstract: This paper presents a Sequential Approximate Optimization (SAO) procedure that uses the Radial Basis Function (RBF) network. If the objective and constraints are not known explicitly but can be evaluated through a computationally intensive numerical simulation, the response surface, which is often called meta-modeling, is an attractive method for finding an approximate global minimum with a small number of function evaluations. An RBF network is used to construct the response surface. The Gaussian function is employed as the basis function in this paper. In order to obtain the response surface with good approximation, the width of this Gaussian function should be adjusted. Therefore, we first examine the width. Through this examination, some sufficient conditions are introduced. Then, a simple method to determine the width of the Gaussian function is proposed. In addition, a new technique called the adaptive scaling technique is also proposed. The sufficient conditions for the width are satisfied by introducing this scaling technique. Second, the SAO algorithm is developed. The optimum of the response surface is taken as a new sampling point for local approximation. In addition, it is necessary to add new sampling points in the sparse region for global approximation. Thus, an important issue for SAO is to determine the sparse region among the sampling points. To achieve this, a new function called the density function is constructed using the RBF network. The global minimum of the density function is taken as the new sampling point. Through the sampling strategy proposed in this paper, the approximate global minimum can be found with a small number of function evaluations. Through numerical examples, the validities of the width and sampling strategy are examined in this paper.
156 citations
TL;DR: In the context of growing environmental concerns, hybrid-electric vehicles appear to be one of the most promising technologies for reducing fuel consumption and pollutant emissions as discussed by the authors, and they have been shown to be a promising technology for reducing greenhouse gas emissions.
Abstract: In the context of growing environmental concerns, hybrid-electric vehicles appear to be one of the most promising technologies for reducing fuel consumption and pollutant emissions.
106 citations
TL;DR: An adaptive penalty technique (APM), which has been shown to be quite effective within genetic algorithms, is adopted for constraint handling within differential evolution, and automatically defines, for each constraint, its corresponding penalty coefficient.
Abstract: Differential Evolution is a simple and efficient stochastic population-based heuristics for global optimization over continuous spaces. As with other nature inspired techniques, there is no provision for constraint handling in its original formulation, and a few possibilities have been proposed in the literature. In this paper an adaptive penalty technique (APM), which has been shown to be quite effective within genetic algorithms, is adopted for constraint handling within differential evolution. The technique, which requires no extra parameters, is based on feedback obtained from the current status of the population of candidate solutions, and automatically defines, for each constraint, its corresponding penalty coefficient. Equality as well as inequality constraints can be dealt with. In this paper we additionally introduce a mechanism for dynamically selecting the mutation operator, according to its performance, among several variants commonly used in the literature. In order to assess the applicability and performance of the proposed procedure, several test-problems from the structural and mechanical engineering optimization literature are considered.
53 citations
TL;DR: This paper shows that the optimal design of a stationary storage device can be regarded as a classical isoperimetric problem, whose solution is very attractive in order to determine also the optimal allocation of the storage device.
Abstract: Recently a great interest has been paid in the relevant literature to the use of energy storage systems for the performance improvement of electrified light transit systems. In this context, the main targets are the increase of the energetic efficiency and the reduction of pantograph voltage drops. Therefore, it can be very interesting the determination of the optimal characteristics of a storage device for satisfying these objectives, both in stationary and onboard case. In this paper, this problem is approached for a sample case study, by showing that the optimal design of a stationary storage device can be regarded as a classical isoperimetric problem, whose solution is very attractive in order to determine also the optimal allocation of the storage device. For more complex configurations of the transit system, the methodology presented can be extended by solving a constrained optimization problem, which in a quite general manner is capable of matching all the assigned technical requirements. The reported simulations confirm the validity of the proposed design approach.
49 citations
TL;DR: This work describes some variants of the PSO method, and presents results of several experiments performed to analyze the behavior of its parameters, trying to improve the performance of the method and tailor it for the application to the design of riser systems.
Abstract: In offshore oil production activities, risers are employed to connect the wellheads at the sea-bottom to a floating platform at the sea surface. The design of risers is a very important issue for the petroleum industry; many aspects are involved in the design of such structures, related to safety and cost savings, thus requiring the use of optimization tools. In this context, this work presents studies on the application of the Particle Swarm Optimization method (PSO) to the design of steel catenary risers in a lazy-wave configuration. The PSO method has shown good efficiency for some applications, but its performance is dependent on the values selected for the parameters of the algorithm. Therefore, this work describes some variants of the method, and presents results of several experiments performed to analyze the behavior of its parameters, trying to improve the performance of the method and tailor it for the application to the design of riser systems. The resulting method and its best set of parameters can then be taken as the default values in an implementation of the PSO method in the in-house OtimRiser computational tool, oriented to the design of risers, and also incorporating other optimization methods based on evolutionary concepts.
43 citations
TL;DR: In this article, material selection is considered together with shape and sizing optimization in a framework of multiobjective optimization of tracking the Pareto curve, where continuous variables refer to structural parameters such as thickness, diameter and spring elastic constants while material ID is defined as binary design variable for each material.
Abstract: In this work, we explore simultaneous designs of materials selection and structural optimization. As the material selection turns out to be a discrete process that finds the optimal distribution of materials over the design domain, it cannot be performed with common gradient-based optimization methods. In this paper, material selection is considered together with the shape and sizing optimization in a framework of multiobjective optimization of tracking the Pareto curve. The idea of mixed variables is often introduced in the case of mono-objective optimization. However, in the case of multi-objective optimization, we still face some hard key points related to the convexity and the continuity of the Pareto domain, which underline the originality of this work. In addition to the above aspect, there is a lack in the literature concerning the industrial applications that consider the mixed parameters. Continuous variables refer to structural parameters such as thickness, diameter and spring elastic constants while material ID is defined as binary design variable for each material. Both mechanical and thermal loads are considered in this work with the aim of minimizing the maximum stress and structural weight simultaneously. The efficiency of the design procedure is demonstrated through various numerical examples.
28 citations
TL;DR: Two new approaches to address the optimization problem associated with engine calibration are presented, one of which relies on a global formulation and the other on a local formulation, which allows the whole driving cycle to be taken into account while remaining single-objective.
Abstract: We present two new approaches to address the optimization problem associated with engine calibration. In this area, the tuning parameters are traditionally determined in a local way, i.e., at each engine operating point, via a single-objective minimization problem. To overcome these restrictions, the first method we propose is able to cope with several objective functions simultaneously in the local formulation. The second method we put forward relies on a global formulation, which allows the whole driving cycle to be taken into account while remaining single-objective. At the practical level, the two methods are implemented by combining various existing techniques such as the LoLiMoT (Local Linear Model Tree) parameterization and the MO-CMA-ES (Multi-Objective Covariance Matrix Adaptation Evolution Strategy) algorithm. A better compromise appears to be achieved on real case applications.
27 citations
TL;DR: A rigorous proof of the optimal properties of a straight pipeline system based on nonlinear programming optimality conditions is proposed within a more general framework than before.
Abstract: In this paper, we consider the optimal design of a straight pipeline system. Suppose a gas pipeline is to be designed to transport a specified flowrate from the entry point to the gas demand point. Physical and contractual requirements at supply and delivery nodes are known as well as the costs to buy and lay a pipeline or build a compressor station. In order to minimize the overall cost of creation of this mainline, the following design variables need to be determined: the number of compressor stations, the lengths of pipeline segments between compressor stations, the diameters of the pipeline segments, the suction and discharge pressures at each compressor station. To facilitate the calculation of the design of a pipeline, gas engineers proposed, in several handbooks, to base their cost-assessments on some optimal properties from previous experiences and usual engineering practices: the distance between compressors is constant, all diameters are equal, and all inlet (resp. outlet) pressures are equal. The goals of this paper are (1) to state on which assumptions we can consider that the optimal properties are valid and (2) to propose a rigorous proof of the optimal properties (based on nonlinear programming optimality conditions) within a more general framework than before.
23 citations
TL;DR: An efficient parallel algorithm for the computation of parametric sensitivities for differential-algebraic equations (DAEs) with a focus on dynamic optimization problems is presented and can almost be reduced to the computational effort of the pure state integration.
Abstract: An efficient parallel algorithm for the computation of parametric sensitivities for differential-algebraic equations (DAEs) with a focus on dynamic optimization problems is presented. A speedup of about 4 can be obtained for process models of more than 13500 DAEs and 75 parameters employing 8 processor cores in parallel using a Windows based system. The algorithm obtains its efficiency by decoupling the sensitivity equations from the state equations of the DAE. Furthermore, the costly Jacobian matrices are computed separately by other processes. The computational effort for a combined state and sensitivity integration can almost be reduced to the computational effort of the pure state integration, which is the theoretical limit of the suggested approach.
23 citations
TL;DR: In this paper, the gradient of an objective function with respect to a deformation of the shape can be computed as a boundary integral without any additional "mesh sensitivities" or volume quantities.
Abstract: Aerodynamic design based on the Hadamard representation of shape gradients is considered. Using this approach, the gradient of an objective function with respect to a deformation of the shape can be computed as a boundary integral without any additional “mesh sensitivities” or volume quantities. The resulting very fast gradient evaluation procedure greatly supports a one-shot optimization strategy and coupled with an appropriate shape Hessian approximation, a very efficient shape optimization procedure is created that does not deteriorate with an increase in the number of design parameters. As such, all surface mesh nodes are used as shape design parameters for optimizing a variety of lifting and non-lifting airfoil shapes using the compressible Euler equations to model the fluid.
TL;DR: In this work different multi-objective techniques are used to the conceptual design of a new kind of space radiator which has an effective variable emittance which makes it able to reduce or avoid the demand for heater power to warm up equipment during cold case operations in orbit.
Abstract: In this work different multi-objective techniques are used to the conceptual design of a new kind of space radiator. Called VESPAR (Variable Emittance Space Radiator), the radiator has an effective variable emittance which makes it able to reduce or avoid the demand for heater power to warm up equipment during cold case operations in orbit. The multi-objective approach was aimed on obtaining a radiator that minimize its mass while at the same time minimize the need for heater power during cold case. Four multi-objective algorithms were used: Elitist Non-dominated Sorting Genetic Algorithm (NSGA-II), Multi-Objective Genetic Algorithm (MOGA), Multi-Objective Simulating Annealing (MOSA) and Multi-Objective Generalized Extremal Optimization (M-GEO). The first three algorithms were used under the modeFrontier® optimization software package, while M-GEO is a recently proposed multi-objective implementation of the Generalized Extremal Optimization (GEO) algorithm. The Pareto frontier showing the trade-off solutions between radiator mass and heater power consumption is obtained by the four algorithms and the results compared. An assessment of the performance of M-GEO on this problem, compared to the other well-known multi-objective algorithms is also made.
TL;DR: In this article, the problem of optimally determining an investment portfolio for an energy company owning a network of gas pipelines, and in charge of purchasing, selling and distributing gas is considered.
Abstract: We consider the problem of optimally determining an investment portfolio for an energy company owning a network of gas pipelines, and in charge of purchasing, selling and distributing gas. We propose a two stage stochastic investment model which hedges risk by means of Conditional Value at Risk constraints. The model, solved by a decomposition method, is assessed on a real-life case, of a Brazilian integrated company that operates on the oil, gas, and energy sectors.
TL;DR: In this paper, a modified Evolutionary Structural Optimization (ESO) algorithm for optimal design of topologies for complex structures is presented, where a new approach for adaptively controlling the material elimination and a "gauss point average stress" is used as the ESO criterion in order to reduce the generation of checkerboard patterns in the resultant optimal topologies.
Abstract: The paper demonstrates the application of a modified Evolutionary Structural Optimisation (ESO) algorithm for optimal design of topologies for complex structures. A new approach for adaptively controlling the material elimination and a ‘gauss point average stress’ is used as the ESO criterion in order to reduce the generation of checkerboard patterns in the resultant optimal topologies. Also, a convergence criterion is used to examine the uniformity of strength throughout a structure. The ESO algorithm is validated by comparing the ESO based solution with the result obtained using another numerical optimisation method (SIMP).
TL;DR: In this article, the problem of power plant preventive maintenance scheduling is studied from a reliability perspective, which consists of ascertaining which generating units must halt production to be examined regularly for safety.
Abstract: The problem of power plant preventive maintenance scheduling is studied in this paper. A reliability perspective is considered. This problem consists of ascertaining which generating units must halt production to be examined regularly for safety. It is very important because a failure in a power station may cause a general breakdown in an electric network. The main consequence is that the electricity demand of customers will not be satisfied in such cases. Therefore, reliability is the key point used in the methodology presented. The problem is approached under the operations research perspective as an optimization issue. 0/1 mixed integer linear programming is used to solve the model reached. An application study is included. The model is put to use in a real power plant setting, representative of the Spanish one. The result obtained is a schedule that allows the efficient organization of preventive maintenance over a specific time horizon.
TL;DR: In this article, the problem of compressor scheduling in gas-lifted oil fields is formulated as a mixed-integer, nonconvex, nonlinear programming problem that generalizes the standard facility location problem.
Abstract: In gas-lifted oil fields, high pressure gas is injected at the bottom of the production tubing of the wells to artificially lift oil to the surface. Lift-gas should enter each well at a certain mass flow and pressure, giving rise to the problem of deciding which compressors (facilities) should be installed and how they supply the demands of the wells (clients). This compressor scheduling is a mixed-integer, nonconvex, nonlinear programming problem that generalizes the standard facility location problem. By piecewise-linearizing the performance curve of each compressor—a function relating output mass flow and discharge pressure, the problem is recast as a mixed-integer linear program. This paper presents this linear reformulation, proposes families of valid inequalities, and reports on results from the application of these inequalities to solve representative instances of the compressor scheduling problem.
TL;DR: The Continuous Derivative Free algorithm fits naturally to the solution of discretized models arising from continuous models, and finds stationary points of real problems with continuous and discrete variables.
Abstract: In this paper we extend Continuous Derivative Free (CDF) algorithms that solve optimization models with continuous variables to the solution of optimization models with both continuous and discrete variables. The algorithm fits naturally to the solution of discretized models arising from continuous models. Roughly speaking, the finer the discretization, the closer the discretized solution is to its continuous counterpart. The algorithm also finds stationary points of real problems with continuous and discrete variables. Encouraging results are reported on an access point communication problem and on models solved with a Field Programmable Gate Array (FPGA) device, which generally forces a fixed point discretization of the problem.
TL;DR: In this paper, an integrated optimization approach, using a finite element code together with a numerical optimization program, was employed to solve the problem of parameter identification and shape optimization in metal forming.
Abstract: Simulation of metal forming processes using the Finite Element Method (FEM) is a well established procedure, being nowadays possible to develop alternative approaches, such as inverse methodologies, in solving complex problems. In the present paper, two types of inverse approaches will be discussed, namely the parameter identification and the shape optimization problems. The aim of the former is to evaluate the input parameters for material constitutive models that would lead to the most accurate set of results respecting physical experiments. The second category involves determining the initial geometry of a given specimen leading to a desired final geometry after the forming process. The purpose of the present work is then to formulate these inverse problems as optimization problems, introducing a straightforward methodology of process optimization in engineering applications such as metal forming and structural analysis. To reach this goal, an integrated optimization approach, using a finite element code together with a numerical optimization program, was employed. A gradient-based optimization method, as a combination of the steepest-descent method and the Levenberg-Marquardt techniques, was used. Numerical applications in the parameter optimization category include, namely, the characterization of a non-linear elasto-plastic hardening model and the determination of the parameters for a nonlinear hyperelastic model. It is also discussed the simultaneous identification of both constitutive material model parameters and the friction coefficient parameters. From the point of view of shape optimization problems, the determination of the initial geometry of a specimen in a upsetting billing problem as well as a methodology for defining the most suited blank shape to be formed in a square cup, are discussed. The final results for both categories show that this kind of algorithms have great potential for future developments in more demanding and realistic benchmarks. It is also worth noting that the presented integrated methodology can be easily applied to a first introduction of optimization techniques and numerical simulation to undergraduate courses in engineering.
TL;DR: The real structured singular value (RSSV) problem is formulated as a nonlinear programming problem and a new computation technique, F-modified subgradient (F-MSG) algorithm, is used for its lower bound computation.
Abstract: The real structured singular value (RSSV, or real μ) is a useful measure to analyze the robustness of linear systems subject to structured real parametric uncertainty, and surely a valuable design tool for the control systems engineers. We formulate the RSSV problem as a nonlinear programming problem and use a new computation technique, F-modified subgradient (F-MSG) algorithm, for its lower bound computation. The F-MSG algorithm can handle a large class of nonconvex optimization problems and requires no differentiability. The RSSV computation is a well known NP hard problem. There are several approaches that propose lower and upper bounds for the RSSV. However, with the existing approaches, the gap between the lower and upper bounds is large for many problems so that the benefit arising from usage of RSSV is reduced significantly. Although the F-MSG algorithm aims to solve the nonconvex programming problems exactly, its performance depends on the quality of the standard solvers used for solving subproblems arising at each iteration of the algorithm. In the case it does not find the optimal solution of the problem, due to its high performance, it practically produces a very tight lower bound. Considering that the RSSV problem can be discontinuous, it is found to provide a good fit to the problem. We also provide examples for demonstrating the validity of our approach.
TL;DR: In this article, a generalized method to find multiple optimal solutions of SDP problems with free variables is proposed, where variable substitution and convexification strategies are used to solve the problem.
Abstract: With the increasing reliance on mathematical programming based approaches in various fields, signomial discrete programming (SDP) problems occur frequently in real applications. Since free variables are often introduced to model problems and alternative optima are practical for decision making among multiple strategies, this paper proposes a generalized method to find multiple optimal solutions of SDP problems with free variables. By means of variable substitution and convexification strategies, an SDP problem with free variables is first converted into another convex mixed-integer nonlinear programming problem solvable to obtain an exactly global optimum. Then a general cut is utilized to exclude the previous solution and an algorithm is developed to locate all alternative optimal solutions. Finally, several illustrative examples are presented to demonstrate the effectiveness of the proposed approach.
TL;DR: In this article, the authors deal with a chance-constrained programming formulation and approximate resolution of an offer-demand equilibrium problem in the context of electricity markets, which is in fact a stochastic multi-knapsack problem.
Abstract: This paper deals with a Chance-Constrained Programming formulation and approximate resolution of an offer-demand equilibrium problem in the context of electricity markets. First, we state the probabilistic model. Computing the coefficients of the problem matrix is easy for financial assets, but a challenging task for physical assets. By introducing maximal production capacities, the computation becomes tractable for thermal plants but still leads to a combinatorial problem for hydraulic production. The obtained problem matrix is sparse, large scale and with random coefficients describing underlying uncertainty factors affecting the available power of assets. Second, we suggest some ways for approximately solving the obtained combinatorial chance-constrained program, which is in fact a stochastic multi-knapsack problem. A formal link between joint and individual chance constraints is exhibited and may lead to a simplified processing of the problem. Finally we illustrate our approximate algorithm on a stylized example.
TL;DR: A metaheuristic algorithm is presented that adapts techniques from the area of integer linear programming based on a rolling horizon strategy to solve the problem of finding an efficient production plan to schedule the different processes needed to the manufacture of pieces.
Abstract: This paper describes a real problem in a market-driven medium sized foundry delivering a wide range of castings to different markets. The problem consists of finding an efficient production plan to schedule the different processes (moulding, furnacing, cutting, tooling, etc.) needed to the manufacture of the pieces. Different objectives and resources and technical constraints must be taken into account. To solve this problem we have first developed a more classical integer linear programming approach based on a rolling horizon strategy. The most innovative contribution of the paper is that it models the problem as a project scheduling problem. Based on this model we present a metaheuristic algorithm that adapts techniques from the area. Computational experiments comparing both approaches are provided on instances created by a generator simulating real instances.
TL;DR: This paper presents the design of a large water system within the production and packaging areas of a brewery based on a Mixed Integer Nonlinear Programming (MINLP) formulation from the open literature, which enabled the investigation of several integration options.
Abstract: This paper presents the design of a large water system within the production and packaging areas of a brewery. In order to accomplish the task, mathematical models were developed based on a Mixed Integer Nonlinear Programming (MINLP) formulation from the open literature. These models enable the investigation of several integration options: a) direct water re-use between batch and semi-continuous consumers operating within the same time interval and b) regeneration re-use options, by designing and scheduling an on-site wastewater treatment system. A multilevel strategy was applied for this large-scale industrial problem, which firstly decomposes design problem into several smaller integration problems concerning water consumers within each section of the brewery. At the following level, water re-use and regeneration re-use opportunities between the brewhouse and the packaging areas were explored for each working day. Finally, the design of an integrated water system was performed over the entire working week by fixing identified intra-daily matches between sections. An optimum water integration scheme is proposed based on the results obtained. © 2011 Springer Science+Business Media, LLC.
TL;DR: In this article, an alternative constraint-handling technique that converts a non-linear constrained programming problem into an unconstrained multi-objective optimisation problem was presented for a propeller optimization problem.
Abstract: The paper presents an alternative constraint-handling technique that converts a nonlinear constrained programming problem into an unconstrained multi-objective optimisation problem. The technique is derived from the behavioural memory constraint-handling method, which was originally implemented for single-objective optimisation with genetic algorithms. We compare our presented technique with two other popular constraint-handling concepts and demonstrate its superiority over them when applied to a propeller optimisation problem. We conclude that the multi-objective behavioural memory constraint-handling technique conjugated with the non-dominated sorting genetic algorithm (NSGA-II) is a prudent method to apply to problems with an infeasible initial design and where constraints have a natural order of satisfaction, which, if not conformed to, would lead to unrealistic designs that impair the search by GA.
TL;DR: A fast simulation tool of the variable-speed induction machine, based on electrical, mechanical, acoustic and thermal analytical models, has been elaborated and validated at different stages with both tests and finite element method (FEM) simulations.
Abstract: Squirrel cage induction motors design requires making numerous trade-offs, especially between its audible electromagnetic noise level, its efficiency and its material cost. However, adding the vibro-acoustic and thermal models to the usual electrical model of the motor drastically increases the simulation time. A finite element approach is then inconceivable, especially if the model has to be coupled to an evolutionary optimization algorithm.
TL;DR: This study investigates the optimal routing strategy in case where network providers charge ISPs according to top-percentile pricing, and explores the solution of the TpTRP as a stochastic dynamic programming problem by a discretization of the state space.
Abstract: Multi-homing is a technology used by Internet Service Provider (ISP) to connect to the Internet via different network providers. To make full use of the underlying networks with minimum cost, an optimal routing strategy is required by ISPs. This study investigates the optimal routing strategy in case where network providers charge ISPs according to top-percentile pricing. We call this problem the Top-percentile Traffic Routing Problem (TpTRP). The TpTRP is a multistage stochastic optimisation problem in which routing decision should be made before knowing the amount of traffic that is to be routed in the following time period. The stochastic nature of the problem forms the critical difficulty of this study. In this paper several approaches are investigated in modelling and solving the problem. We begin by modelling the TpTRP as a multistage stochastic programming problem, which is hard to solve due to the integer variables introduced by top-percentile pricing. Several simplifications of the original TpTRP are then explored in the second part of this work. Some of these allow analytical solutions which lead to bounds on the achievable optimal solution. We also establish bounds by investigation several “naive” routing policies. In the end, we explore the solution of the TpTRP as a stochastic dynamic programming problem by a discretization of the state space. This allows us to solve medium size instances of TpTRP to optimality and to improve on any naive routing policy.
TL;DR: Analysis of 〈X,M〉 and 》X,R〉 models serves as parts of a general scheme for multicriteria decision making under information uncertainty, which is also associated with a generalization of the classic approach to considering the uncertainty of information.
Abstract: There exist two classes of problems, which need the use of a multicriteria approach: problems whose solution consequences cannot be estimated with a single criterion and problems that, initially, may require a single criterion or several criteria, but their unique solutions are unachievable, due to decision uncertainty regions, which can be contracted using additional criteria. According to this, two classes of models (〈X,M〉 and 〈X,R〉 models) can be constructed. Analysis of 〈X,M〉 and 〈X,R〉 models (based on applying the Bellman-Zadeh approach to decision making in a fuzzy environment and using fuzzy preference modeling techniques, respectively) serves as parts of a general scheme for multicriteria decision making under information uncertainty. This scheme is also associated with a generalization of the classic approach to considering the uncertainty of information (based on analyzing payoff matrices constructed for different combinations of solution alternatives and states of nature) in monocriteria decision making to multicriteria problems. The paper results are of a universal character and are illustrated by an example.
TL;DR: In this article, the authors used genetic algorithms to design minimum time curing cycles for composite patch repair in the aircraft industry, where the optimization is subjected to the following constraints: (1) Maximum allowed temperature in order to avoid residual stresses, (2) Minimum temperature to initiate the cure reaction, (3) Sufficient degree of cure at the end of the process and (4) Maximum heat generation rate that can be achieved by the device.
Abstract: The aim of this contribution is the optimization of some parameters of the composite patch repair technique (CPR). This technique is mainly used by the aircraft industry, as it offers high reliability, short repair times and reduced cost in compare to other methods, such as the riveted joints. CPR consists of adhesively bonding thin composite patches over cracked or corroded areas with heat supply. As the polymer-matrix composite patch is heated, it cures and toughens. Proper curing insures structural reliability of the repair. Short duration curing cycles are of great importance for the aircraft availability. With the use of Genetic Algorithms, we design minimum time curing cycles. The optimization is subjected to the following constraints: (1) Maximum allowed temperature in order to avoid residual stresses, (2) Minimum temperature in order to initiate the cure reaction, (3) Sufficient degree of cure at the end of the process and (4) Maximum heat generation rate that can be achieved by the device. Our design vector contains the duration of the plateau stage of the cure cycle and the characteristic thermal profile. The degree of cure is estimated with the use of the Kamal cure rate model for thermosetting polymers. For the numerical time integration of the cure rate equation, a second order, implicit Runge-Kutta scheme is employed.
TL;DR: A novel dynamic Cournot game model with bounded rationality of electricity market that considers the constraints of realistic power networks is proposed in this paper, represented by discrete difference equations embedded within the optimization problem of consumption benefits.
Abstract: In order to accurately simulate the dynamic decision-making behaviors of market participants, a novel dynamic Cournot game model with bounded rationality of electricity market that considers the constraints of realistic power networks is proposed in this paper. This model is represented by discrete difference equations embedded within the optimization problem of consumption benefits. The Nash equilibrium of electricity market and its stability are quantitatively analyzed. It is found that there are different Nash equilibriums with different market parameters corresponding to different operating conditions of power network, i.e. congestion and non-congestion, and even in some cases there is no Nash equilibrium at all. Numerical simulations with the 2-node and IEEE 30-node systems are carried out to evaluate the dynamic behaviors of electricity market, especially the periodic and chaotic behaviors when the market parameters are beyond the stability region of Nash equilibrium.
TL;DR: In this paper, counter-examples to two triality results are provided, and one of the before mentioned results is corrected and improved, in addition to a corrected version of the triality result.
Abstract: In this note counter-examples to two triality results are provided. In addition, one of the before mentioned results is corrected and improved.