A review of optimization techniques in spacecraft flight trajectory design

For most atmospheric or exo-atmospheric spacecraft flight scenarios, a well-designed trajectory is usually a key for stable flight and for improved guidance and control of the vehicle. Although extensive research work has been carried out on the design of spacecraft trajectories for different mission profiles and many effective tools were successfully developed for optimizing the flight path, it is only in the recent five years that there has been a growing interest in planning the flight trajectories with the consideration of multiple mission objectives and various model errors/uncertainties. It is worth noting that in many practical spacecraft guidance, navigation and control systems, multiple performance indices and different types of uncertainties must frequently be considered during the path planning phase. As a result, these requirements bring the development of multi-objective spacecraft trajectory optimization methods as well as stochastic spacecraft trajectory optimization algorithms. This paper aims to broadly review the state-of-the-art development in numerical multi-objective trajectory optimization algorithms and stochastic trajectory planning techniques for spacecraft flight operations. A brief description of the mathematical formulation of the problem is firstly introduced. Following that, various optimization methods that can be effective for solving spacecraft trajectory planning problems are reviewed, including the gradient-based methods, the convexification-based methods, and the evolutionary/metaheuristic methods. The multi-objective spacecraft trajectory optimization formulation, together with different class of multi-objective optimization algorithms, is then overviewed. The key features such as the advantages and disadvantages of these recently-developed multi-objective techniques are summarised. Moreover, attentions are given to extend the original deterministic problem to a stochastic version. Some robust optimization strategies are also outlined to deal with the stochastic trajectory planning formulation. In addition, a special focus will be given on the recent applications of the optimized trajectory. Finally, some conclusions are drawn and future research on the development of multi-objective and stochastic trajectory optimization techniques is discussed

State-of-the-Art Report on Systems Analysis Methods for Resolution of Conflicts in Water Resources Management

Water is an important factor in conflicts among stakeholders at the local, regional, and even international level. Water conflicts have taken many forms, but they almost always arise from the fact that the freshwater resources of the world are not partitioned to match the political borders, nor are they evenly distributed in space and time. Two or more countries share the watersheds of 261 major rivers and nearly half of the land area of the wo rld is in international river basins. Water has been used as a military and political goal. Water has been a weapon of war. Water systems have been targets during the war. A role of systems approach has been investigated in this report as an approach for resolution of conflicts over water. A review of systems approach provides some basic knowledge of tools and techniques as they apply to water management and conflict resolution. Report provides a classification and description of water conflicts by addressing issues of scale, integrated water management and the role of stakeholders. Four large-scale examples are selected to illustrate the application of systems approach to water conflicts: (a) hydropower development in Canada; (b) multipurpose use of Danube river in Europe; (c) international water conflict between USA and Canada; and (d) Aral See in Asia. Water conflict resolution process involves various sources of uncertainty. One section of the report provides some examples of systems tools that can be used to address objective and subjective uncertainties with special emphasis on the utility of the fuzzy set theory. Systems analysis is known to be driven by the development of computer technology. Last section of the report provides one view of the future and systems tools that will be used for water resources management. Role of the virtual databases, computer and communication networks is investigated in the context of water conflicts and their resolution.https://ir.lib.uwo.ca/wrrr/1005/thumbnail.jp

Virtual power plant models and electricity markets - A review

In recent years, the integration of distributed generation in power systems has been accompanied by new facility operations strategies. Thus, it has become increasingly important to enhance management capabilities regarding the aggregation of distributed electricity production and demand through different types of virtual power plants (VPPs). It is also important to exploit their ability to participate in electricity markets to maximize operating profits. This review article focuses on the classification and in-depth analysis of recent studies that propose VPP models including interactions with different types of energy markets. This classification is formulated according to the most important aspects to be considered for these VPPs. These include the formulation of the model, techniques for solving mathematical problems, participation in different types of markets, and the applicability of the proposed models to real case studies. From the analysis of the studies, it is concluded that the most recent models tend to be more complete and realistic in addition to featuring greater diversity in the types of electricity markets in which VPPs participate. The aim of this review is to identify the most profitable VPP scheme to be applied in each regulatory environment. It also highlights the challenges remaining in this field of study

APLIKASI FUZZY PADA PERMASALAHAN PROGRAM TAK-LINIER

One of the most purpose of non linear programing is to determine the optimal solution of its objective function. If the objective function of a certain non linear programing only possess a uniqe value function, it is easy to calculate its optimal solution. However, if the objective function of non linier programing possess multi functions, so there are two possibilities to determine their optimal solutions. Theses depend on whether there are conflic among them or not. In order to make them more easier, the fuzzy parameter could be applied to calculate the optimal solution

Optimal Sizing and Location of Static and Dynamic Reactive Power Compensation

The key of reactive power planning (RPP), or Var planning, is the optimal allocation of reactive power sources considering location and size. Traditionally, the locations for placing new Var sources were either simply estimated or directly assumed. Recent research works have presented some rigorous optimization-based methods in RPP. Different constraints are the key of various optimization models, identified as Optimal Power Flow (OPF) model, Security Constrained OPF (SCOPF) model, and Voltage Stability Constrained OPF model (VSCOPF). First, this work investigates the economic benefits from local reactive power compensation including reduced losses, shifting reactive power flow to real power flow, and increased transfer capability. Then, the benefits in the three categories are applied to Var planning considering different locations and amounts of Var compensation in an enumeration method, but many OPF runs are needed. Then, the voltage stability constrained OPF (VSCOPF) model with two sets of variables is used to achieve an efficient model. The two sets of variables correspond to the “normal operating point (o)” and “collapse point (*)” respectively. Finally, an interpolation approximation method is adopted to simplify the previous VSCOPF model by approximating the TTC function, therefore, eliminating the set of variables and constraints related to the “collapse point”. In addition, interpolation method is compared with the least square method in the literature to show its advantages. It is also interesting to observe that the test results from a seven-bus system show that it is not always economically efficient if Var compensation increases continuously

Lost in optimisation of water distribution systems? A literature review of system operation

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.Optimisation of the operation of water distribution systems has been an active research field for almost half a century. It has focused mainly on optimal pump operation to minimise pumping costs and optimal water quality management to ensure that standards at customer nodes are met. This paper provides a systematic review by bringing together over two hundred publications from the past three decades, which are relevant to operational optimisation of water distribution systems, particularly optimal pump operation, valve control and system operation for water quality purposes of both urban drinking and regional multiquality water distribution systems. Uniquely, it also contains substantial and thorough information for over one hundred publications in a tabular form, which lists optimisation models inclusive of objectives, constraints, decision variables, solution methodologies used and other details. Research challenges in terms of simulation models, optimisation model formulation, selection of optimisation method and postprocessing needs have also been identified

Fuzzy Bilevel Optimization

In the dissertation the solution approaches for different fuzzy optimization problems are presented. The single-level optimization problem with fuzzy objective is solved by its reformulation into a biobjective optimization problem. A special attention is given to the computation of the membership function of the fuzzy solution of the fuzzy optimization problem in the linear case. Necessary and sufficient optimality conditions of the the convex nonlinear fuzzy optimization problem are derived in differentiable and nondifferentiable cases. A fuzzy optimization problem with both fuzzy objectives and constraints is also investigated in the thesis in the linear case. These solution approaches are applied to fuzzy bilevel optimization problems. In the case of bilevel optimization problem with fuzzy objective functions, two algorithms are presented and compared using an illustrative example. For the case of fuzzy linear bilevel optimization problem with both fuzzy objectives and constraints k-th best algorithm is adopted.:1 Introduction 1 1.1 Why optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Fuzziness as a concept . . . . . . . . . . . . . . . . . . . . .. . . . . . . 2 1.3 Bilevel problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2 Preliminaries 11 2.1 Fuzzy sets and fuzzy numbers . . . . . . . . . . . . . . . . . . . . . 11 2.2 Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3 Fuzzy order . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.4 Fuzzy functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17 3 Optimization problem with fuzzy objective 19 3.1 Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.2 Solution method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.3 Local optimality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.4 Existence of an optimal solution . . . . . . . . . . . . . . . . . . . . 25 4 Linear optimization with fuzzy objective 27 4.1 Main approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 4.2 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 4.3 Optimality conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 4.4 Membership function value . . . . . . . . . . . . . . . . . . . . . . . . 34 4.4.1 Special case of triangular fuzzy numbers . . . . . . . . . . . . 36 4.4.2 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .39 5 Optimality conditions 47 5.1 Differentiable fuzzy optimization problem . . . . . . . . . . .. . . . 48 5.1.1 Basic notions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 5.1.2 Necessary optimality conditions . . . . . . . . . . . . . . . . . . .. 49 5.1.3 Suffcient optimality conditions . . . . . . . . . . . . . . . . . . . . . . 49 5.2 Nondifferentiable fuzzy optimization problem . . . . . . . . . . . . 51 5.2.1 Basic notions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 5.2.2 Necessary optimality conditions . . . . . . . . . . . . . . . . . . . 52 5.2.3 Suffcient optimality conditions . . . . . . . . . . . . . . . . . . . . . . 54 5.2.4 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 6 Fuzzy linear optimization problem over fuzzy polytope 59 6.1 Basic notions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 6.2 The fuzzy polytope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .63 6.3 Formulation and solution method . . . . . . . . . . . . . . . . . . .. . 65 6.4 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 7 Bilevel optimization with fuzzy objectives 73 7.1 General formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 7.2 Solution approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .74 7.3 Yager index approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 7.4 Algorithm I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 7.5 Membership function approach . . . . . . . . . . . . . . . . . . . . . . .78 7.6 Algorithm II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .80 7.7 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 8 Linear fuzzy bilevel optimization (with fuzzy objectives and constraints) 87 8.1 Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 8.2 Solution approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 8.3 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 8.4 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 9 Conclusions 95 Bibliography 9

A multiple objective optimization approach to quality control

The use of product quality as the performance criteria for manufacturing system control is explored. The goal in manufacturing, for economic reasons, is to optimize product quality. The problem is that since quality is a rather nebulous product characteristic, there is seldom an analytic function that can be used as a measure. Therefore standard control approaches, such as optimal control, cannot readily be applied. A second problem with optimizing product quality is that it is typically measured along many dimensions: there are many apsects of quality which must be optimized simultaneously. Very often these different aspects are incommensurate and competing. The concept of optimality must now include accepting tradeoffs among the different quality characteristics. These problems are addressed using multiple objective optimization. It is shown that the quality control problem can be defined as a multiple objective optimization problem. A controller structure is defined using this as the basis. Then, an algorithm is presented which can be used by an operator to interactively find the best operating point. Essentially, the algorithm uses process data to provide the operator with two pieces of information: (1) if it is possible to simultaneously improve all quality criteria, then determine what changes to the process input or controller parameters should be made to do this; and (2) if it is not possible to improve all criteria, and the current operating point is not a desirable one, select a criteria in which a tradeoff should be made, and make input changes to improve all other criteria. The process is not operating at an optimal point in any sense if no tradeoff has to be made to move to a new operating point. This algorithm ensures that operating points are optimal in some sense and provides the operator with information about tradeoffs when seeking the best operating point. The multiobjective algorithm was implemented in two different injection molding scenarios: tuning of process controllers to meet specified performance objectives and tuning of process inputs to meet specified quality objectives. Five case studies are presented

A new hybrid algorithm for multi‐objective reactive power planning via facts devices and renewable wind resources

The power system planning problem considering system loss function, voltage profile function, the cost function of FACTS (flexible alternating current transmission system) devices, and stability function are investigated in this paper. With the growth of electronic technologies, FACTS devices have improved stability and more reliable planning in reactive power (RP) planning. In addition, in modern power systems, renewable resources have an inevitable effect on power system planning. Therefore, wind resources make a complicated problem of planning due to conflicting functions and non-linear constraints. This confliction is the stochastic nature of the cost, loss, and voltage functions that cannot be summarized in function. A multi-objective hybrid algorithm is proposed to solve this problem by considering the linear and non-linear constraints that combine particle swarm optimization (PSO) and the virus colony search (VCS). VCS is a new optimization method based on viruses’ search function to destroy host cells and cause the penetration of the best virus into a cell for reproduction. In the proposed model, the PSO is used to enhance local and global search. In addition, the non-dominated sort of the Pareto criterion is used to sort the data. The optimization results on different scenarios reveal that the combined method of the proposed hybrid algorithm can improve the parameters such as convergence time, index of voltage stability, and absolute magnitude of voltage deviation, and this method can reduce the total transmission line losses. In addition, the presence of wind resources has a positive effect on the mentioned issue

A MPC Strategy for the Optimal Management of Microgrids Based on Evolutionary Optimization

In this paper, a novel model predictive control strategy, with a 24-h prediction horizon, is proposed to reduce the operational cost of microgrids. To overcome the complexity of the optimization problems arising from the operation of the microgrid at each step, an adaptive evolutionary strategy with a satisfactory trade-off between exploration and exploitation capabilities was added to the model predictive control. The proposed strategy was evaluated using a representative microgrid that includes a wind turbine, a photovoltaic plant, a microturbine, a diesel engine, and an energy storage system. The achieved results demonstrate the validity of the proposed approach, outperforming a global scheduling planner-based on a genetic algorithm by 14.2% in terms of operational cost. In addition, the proposed approach also better manages the use of the energy storage system.Ministerio de Economía y Competitividad DPI2016-75294-C2-2-RUnión Europea (Programa Horizonte 2020) 76409