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An Efficient and Accurate Solution Methodology for Bilevel Multi-Objective programming Problems Using a Hybrid Evolutionary-Local-Search Algorithm

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EVOLUTIONARY COMPUTATION 2010年第3期18卷 403-449页

作者： Deb, Kalyanmoy Sinha, Ankur Indian Inst Technol Kanpur Dept Mech Engn Kanpur 208016 Uttar Pradesh India Aalto Univ Sch Econ Dept Business Technol Helsinki 00076 Finland

Bilevel optimization problems involve two optimization tasks (upper and lower level), in which every feasible upper level solution must correspond to an optimal solution to a lower level optimization problem. These problems commonly appear in many practical problem solving tasks including optimal control, process optimization, game-playing strategy developments, transportation problems, and others. However, they are commonly converted into a single level optimization problem by using an approximate solution procedure to replace the lower level optimization task. Although there exist a number of theoretical, numerical, and evolutionary optimization studies involving single-objective bilevel programming problems, not many studies look at the context of multiple conflicting objectives in each level of a bilevel programming problem. In this paper, we address certain intricate issues related to solving multi-objective bilevel programming problems, present challenging test problems, and propose a viable and hybrid evolutionary-cum-local-search based algorithm as a solution methodology. The hybrid approach performs better than a number of existing methodologies and scales well up to 40-variable difficult test problems used in this study. The population sizing and termination criteria are made self-adaptive, so that no additional parameters need to be supplied by the user. The study indicates a clear niche of evolutionary algorithms in solving such difficult problems of practical importance compared to their usual solution by a computationally expensive nested procedure. The study opens up many issues related to multi-objective bilevel programming and hopefully this study will motivate EMO and other researchers to pay more attention to this important and difficult problem solving activity.

关键词： Bilevel optimization evolutionary multi-objective optimization NSGA-II test problem development problem difficulties hybrid evolutionary algorithms self-adaptive algorithm sequential quadratic programming

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Endgame Problem Part 2: Multibody Technique and the Tisserand-Poincare Graph

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2010年第2期33卷 476-486页

作者： Campagnola, Stefano Russell, Ryan P. Univ So Calif Los Angeles CA 90089 USA Georgia Inst Technol Gugenheim Sch Aerosp Engn Atlanta GA 30332 USA

This two-part series studies the anatomy of the endgame problem, the last part of the spacecraft trajectory before the orbit-insertion maneuver into the science orbit. The endgame provides large savings in the capture Delta v, and therefore it is an important element in the design of ESA and NASA missions to the moons of Jupiter and Saturn. The endgame problem has been approached in different ways with different results: the v(infinity)-leveraging-maneuver approach leads to high-Delta v, short-time-of-flight transfers, and the multibody technique leads to low-Delta v, long-time-of-flight transfers. This paper series investigates the link between the two approaches, giving a new insight to the complex dynamics of the multibody gravity-assist problem. In this paper we focus on the multibody approach using a new graphical tool, the Tisserand-Poincare graph. The Tisserand-Poincare graph shows that ballistic endgames are energetically possible and it explains why they require resonant orbits patched with high-altitude flybys, whereas in the v(infinity)-leveraging-maneuver approach, flybys alone are not effective without impulsive maneuvers in between them. We then use the Tisserand-Poincare graph to design quasi-ballistic transfers. Unlike previous methods, the Tisserand-Poincare graph provides a valuable energy-based target point for the design of the endgame and begin-game and a simple way to patch them. Finally, we present two transfers. The first transfer is between low-altitude orbits at Europa and Ganymede using almost half the Delta v of the Hohmann transfer;the second transfer is a 300-day quasi-ballistic transfer between halo orbits of the Jupiter-Ganymede and Jupiter-Europa. With approximately 50 m/s the transfer can be reduced by two months.

关键词： Callisto Orbital Elements Saturn Spacecraft Trajectories Hohmann Transfer Pericenter Potentially Hazardous Asteroids Low Energy Transfer sequential quadratic programming Keplerian Orbit

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A SECOND DERIVATIVE SQP METHOD: GLOBAL CONVERGENCE

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SIAM JOURNAL ON OPTIMIZATION 2010年第4期20卷 2023-2048页

作者： Gould, Nicholas I. M. Robinson, Daniel P. Rutherford Appleton Lab Numer Anal Grp Didcot OX11 0QX Oxon England Univ Oxford Inst Math Oxford OX1 3LB England

sequential quadratic programming (SQP) methods form a class of highly efficient algorithms for solving nonlinearly constrained optimization problems. Although second derivative information may often be calculated, there is little practical theory that justifies exact-Hessian SQP methods. In particular, the resulting quadratic programming (QP) subproblems are often nonconvex, and thus finding their global solutions may be computationally nonviable. This paper presents a second derivative SQP method based on quadratic subproblems that are either convex, and thus may be solved efficiently, or need not be solved globally. Additionally, an explicit descent-constraint is imposed on certain QP subproblems, which "guides" the iterates through areas in which nonconvexity is a concern. Global convergence of the resulting algorithm is established.

关键词： nonlinear programming nonlinear inequality constraints sequential quadratic programming l(1)-penalty function nonsmooth optimization

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Optimizing smart well controls under geologic uncertainty

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JOURNAL OF PETROLEUM SCIENCE AND ENGINEERING 2010年第1-2期73卷 107-121页

作者： Alhuthali, Ahmed H. Datta-Gupta, Akhil Yuen, Bevan Fontanilla, Jerry P. Texas A&M Univ Dept Petr Engn TAMU 3116 College Stn TX 77843 USA Saudi Aramco Dhahran 31311 Saudi Arabia

Waterflood optimization via rate control is receiving increased interest because of rapid developments in the smart well completions and i-field technology. The use of inflow control valves (ICV) allows us to optimize the production/injection rates of various segments along the wellbore, thereby maximizing sweep efficiency and delaying water breakthrough. A major challenge for practical field implementation of this technology is dealing with geologic uncertainty. in practice, the reservoir geology is known only in a probabilistic sense: hence, the optimization of smart wells should be carried out in a stochastic framework to account for geologic uncertainty. We propose a practical and efficient approach for computing optimal injection and production rates accounting for geological uncertainty. The approach relies on equalizing arrival time of the waterfront at all producers using multiple geologic realizations. The main objective is to improve sweep efficiency and thereby improve oil production and recovery. We account for geologic uncertainty using two optimization schemes. The first one is to formulate the objective function in a stochastic form which relies on a combination of expected value and standard deviation combined with a risk attitude coefficient. The second one is to minimize the worst case scenario using a min-max problem formulation. The optimization is performed under operational and facility constraints using a sequential quadratic programming approach. A major advantage of our approach is the analytical computation of the gradient and Hessian of the objective function which makes it computationally efficient and suitable for large field cases. Multiple examples are presented to support the robustness and efficiency of the proposed optimization scheme. These include 2D synthetic examples for validation and a 3D field-scale application. The role of geologic uncertainty in the outcome of the optimization is demonstrated both during the early stage and

关键词： optimal rate control geologic uncertainty time-of-flight arrival time sensitivity sequential quadratic programming

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Particle Swarm Optimization of Suction and Blowing on Airfoils at Transonic Speeds

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JOURNAL OF AIRCRAFT 2010年第6期47卷 1955-1965页

作者： Pehlivanoglu, Y. Volkan Yagiz, Bedri Kandil, O. Baysal, O. Turkish AF Acad TR-34149 Istanbul Turkey Old Dominion Univ Dept Aerosp Engn Norfolk VA 23529 USA Old Dominion Univ Batten Coll Engn & Technol Norfolk VA 23529 USA

To improve the aerodynamic performance, the control applied to the transonic flow past an airfoil is optimized. The flow is simulated by solving the Navier-Stokes equations and a turbulence model. The control is applied using flow suction or blowing on the airfoil surface. The design variables are set to be the location and the angle of the suction/blowing port and the mass flow coefficient at this port. To validate the computational methodology, successful comparisons have been made with available experimental data. The focus of the present study is on the application of a selected design optimization methodology. Therefore, the particle swarm optimization algorithm is also validated by comparing its results with those from a more traditional approach: that is, a gradient-based method with sequential quadratic programming. It is observed that the aerodynamic performance is increased by over 20% as a result of optimizing the location, angle, and mass flow coefficient of the suction and blowing control ports on the airfoil surface at transonic speeds.

关键词： sequential quadratic programming Optimal design Airfoils Flow coefficient Particle swarm optimization aerodynamic performance MASS FLOW blowing design variable Navier-Stokes equations

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Semi-analytical solutions for optimal distributions of sensors and actuators in smart structure vibration control

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SMART STRUCTURES AND SYSTEMS 2010年第7期6卷 767-792页

作者： Jin, Zhanli Yang, Yaowen Soh, Chee Kiong Nanyang Technol Univ Sch Civil & Environm Engn Singapore 639798 Singapore Nanyang Technol Univ Sch Elect & Elect Engn Singapore 639798 Singapore

In this paper, the optimal design of vibration control system for smart structures has been investigated semi-analytically via the optimization of geometric parameters like the placements and sizes of piezoelectric sensors and actuators (S/As) bonded on the structures. The criterion based on the maximization of energy dissipation was adopted for the optimization of the control system. Based on the sensing and actuating equations, the total energy stored in the system which is used as the objective function was analytically derived with design variables explicitly presented. Two cases of single and combined vibration modes were addressed for a simply supported beam and a simply supported cylindrical shell. For single vibration mode, the optimal distributions of the piezoelectric S/As could be obtained analytically. However, the sequential quadratic programming (SQP) method has to be employed to solve those which violated the prescribed constraints and to solve the case of combined vibration modes. The results of three examples, which include a simply supported beam, a simply supported cylindrical shell and a simply supported plate, showed good agreement with those obtained by the Genetic Algorithm (GA) method. Moreover, in comparison with the GA method, the proposed method is more effective in obtaining better optimization results and is much more efficient in terms of computation time.

关键词： optimization vibration control sequential quadratic programming smart structures

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Hybrid SOA-SQP algorithm for dynamic economic dispatch with valve-point effects

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ENERGY 2010年第12期35卷 5031-5036页

作者： Sivasubramani, S. Swarup, K. S. Indian Inst Technol Dept Elect Engn Madras 600036 Tamil Nadu India

This paper proposes a hybrid technique combining a new heuristic algorithm named seeker optimization algorithm (SOA) and sequential quadratic programming (SQP) method for solving dynamic economic dispatch problem with valve-point effects. The SOA is based on the concept of simulating the act of human searching, where the search direction is based on the empirical gradient (EG) by evaluating the response to the position changes and the step length is based on uncertainty reasoning by using a simple fuzzy rule. In this paper, SOA is used as a base level search, which can give a good direction to the optimal global region and SQP as a local search to fine tune the solution obtained from SOA. Thus SQP guides SOA to find optimal or near optimal solution in the complex search space. Two test systems i.e., 5 unit with losses and 10 unit without losses, have been taken to validate the efficiency of the proposed hybrid method. Simulation results clearly show that the proposed method outperforms the existing method in terms of solution quality. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： Seeker optimization algorithm sequential quadratic programming Dynamic economic dispatch Valve-point effects

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Integration of SQP and PSO for optimal planning of harmonic filters

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EXPERT SYSTEMS WITH APPLICATIONS 2010年第3期37卷 2522-2530页

作者： Chang, Ying-Pin Nan Kai Univ Technol Tsaotun Dept Elect Engn Nantou 542 Taiwan

This paper presents an approach of combined sequential quadratic programming and particle swarm optimization (SQP-PSO) to optimize the planning of large-scale passive harmonic filters (PHF). The optimal filter scheme can be obtained for a system under abundant harmonic current sources where harmonic amplification problems should be avoided. The objective is to minimize the cost of the filter, filters loss, the total demand distortion of harmonic currents and the total harmonic distortion of voltages at each bus simultaneously. Meanwhile, based on the concept of multi-objective optimization, how to define the fitness function of the PSO to include different performance criteria is also discussed. The designed heuristic SQP-PSO is applied to a practical harmonic problem in a steel plant, where both AC and DC arc furnaces are used and a static var compensator (SVC) is installed. Three design schemes are compared to demonstrate the performance of the SQP-PSO. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： Harmonic filter Harmonic currents Particle swarm optimization sequential quadratic programming

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A TRUNCATED SQP METHOD BASED ON INEXACT INTERIOR-POINT SOLUTIONS OF SUBPROBLEMS

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SIAM JOURNAL ON OPTIMIZATION 2010年第5期20卷 2584-2613页

作者： Izmailov, A. F. Solodov, M. V. Moscow MV Lomonosov State Univ Fac Computat Math & Cybernet Dept Operat Res Moscow 119899 Russia Inst Matematica Pura & Aplicada BR-22460320 Rio De Janeiro Brazil

We consider sequential quadratic programming (SQP) methods applied to optimization problems with nonlinear equality constraints and simple bounds. In particular, we propose and analyze a truncated SQP algorithm in which subproblems are solved approximately by an infeasible predictor-corrector interior-point method, followed by setting to zero some variables and some multipliers so that complementarity conditions for approximate solutions are enforced. Verifiable truncation conditions based on the residual of optimality conditions of subproblems are developed to ensure both global and fast local convergence. Global convergence is established under assumptions that are standard for linesearch SQP with exact solution of subproblems. The local superlinear convergence rate is shown under the weakest assumptions that guarantee this property for pure SQP with exact solution of subproblems, namely, the strict Mangasarian-Fromovitz constraint qualification and second-order sufficiency. Local convergence results for our truncated method are presented as a special case of the local convergence for a more general perturbed SQP framework, which is of independent interest and is applicable even to some algorithms whose subproblems are not quadratic programs. For example, the framework can also be used to derive sharp local convergence results for linearly constrained Lagrangian methods. Preliminary numerical results confirm that it can be indeed beneficial to solve subproblems approximately, especially on early iterations.

关键词： sequential quadratic programming inexact sequential quadratic programming truncated sequential quadratic programming interior-point method superlinear convergence

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Optimal self-scheduling of hydro producer in the electricity market

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ENERGY CONVERSION AND MANAGEMENT 2010年第12期51卷 2523-2530页

作者： Yuan, Xiaohui Wang, Yunyan Xie, Jun Qi, Xiwen Nie, Hao Su, Anjun Huazhong Univ Sci & Technol Sch Hydropower & Informat Engn Wuhan 430074 Peoples R China

This paper proposes an efficient method to solve the profit-based optimal self-scheduling of a hydroelectric company in the pool-based day-ahead electricity market by integrating cultural algorithm (CA) with feasible sequential quadratic programming (SQP). The proposed method is developed in such a way that CA is applied as a based level search, which can give a good direction to the optimal global region, and a local search SQP is used as a fine-tuning to determine the optimal solution at the final. Finally, optimal self-scheduling of hydro company with several cascaded hydro plants along a river basin is used to illustrate the effectiveness of the proposed method. Results from the proposed method are compared with those obtained by other optimization methods in terms of solution precision. It is shown that the proposed method is capable of yielding higher quality solutions. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： Cultural algorithm sequential quadratic programming Optimal self-scheduling Hydro producer

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