| 1. |
- Aittokoski, Timo, et al.
(författare)
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Clustering aided approach for decision making in computationally expensive multiobjective optimization
- 2009
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Ingår i: Optimization Methods and Software. - : Informa UK Limited. - 1055-6788 .- 1029-4937. ; 24:2, s. 157-174
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Tidskriftsartikel (refereegranskat)abstract
- Typically, industrial optimization problems need to be solved in an efficient, multiobjective and global manner, because they are often computationally expensive (as function values are typically based on simulations), they may contain multiple conflicting objectives, and they may have several local optima. Solving such problems may be challenging and time consuming when the aim is to find the most preferred Pareto optimal solution. In this study, we propose a method where we use an advanced clustering technique to reveal essential characteristics of the approximation of the Pareto optimal set, which has been generated beforehand. Thus, the decision maker (DM) is involved only after the most time consuming computation is finished. After the initiation phase, a moderate number of cluster prototypes projected to the Pareto optimal set is presented to the DM to be studied. This allows him/her to rapidly gain an overall understanding of the main characteristics of the problem without placing too much cognitive load on the DM. Furthermore, we also suggest some ways of applying our approach to different types of problems and demonstrate it with an example related to internal combustion engine design.
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| 2. |
- Aittokoski, Timo, et al.
(författare)
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Cost Effective Simulation-Based Multiobjective Optimization in Performance of Internal Combustion Engine
- 2008
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Ingår i: Engineering optimization (Print). - : Informa UK Limited. - 0305-215X .- 1029-0273. ; 40:7, s. 593-612
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Tidskriftsartikel (refereegranskat)abstract
- Solving real-life engineering problems requires often multiobjective, global, and efficient (in terms of objective function evaluations) treatment. In this study, we consider problems of this type by discussing some drawbacks of the current methods and then introduce a new population-based multiobjective optimization algorithm UPS-EMOA which produces a dense (not limited to the population size) approximation of the Pareto-optimal set in a computationally effective manner.
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| 3. |
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| 4. |
- Aittokoski, Timo, et al.
(författare)
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Efficient Evolutionary Method to Approximate the Pareto Optimal Set in Multiobjective Optimization
- 2008
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Ingår i: Proceedings of the International Conference on Engineering Optimization EngOpt 2008.
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- Solving real-life engineering problems requires often multiobjective, global and efficient (in terms of ob-jective function evaluations) treatment. In this study, we consider problems of this type by discussingsome drawbacks of the current methods and then introduce a new population based multiobjective op-timization algorithm which produces a dense (not limited to the population size) approximation of thePareto optimal set in a computationally effective manner.
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| 5. |
- Deb, K., et al.
(författare)
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A Hybrid Integrated Multi-Objective Optimization Procedure for Estimating Nadir Point
- 2009
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Ingår i: Evolutionary Multi-Criterion Optimization. - Berlin, Heidelberg : Springer. - 9783642010194 ; , s. 569-583
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Konferensbidrag (refereegranskat)abstract
- A nadir point is constructed by the worst objective values of the solutions of the entire Pareto-optimal set. Along with the ideal point, the nadir point provides the range ofobjective values within which all Pareto-optimal solutions must lie. Thus, a nadir point is an important point to researchers and practitioners interested in multi-objectiveoptimization. Besides, if the nadir point can be computed relatively quickly, it can be used to normalize objectives in many multi-criterion decision making tasks. Importantly,estimating the nadir point is a challenging and unsolved computing problem in case of more than two objectives. In this paper, we revise a previously proposed serial application of an EMO and a local search method and suggest an integrated approach for finding the nadir point. A local search procedure based on the solution of a bi-level achievement scalarizing function is employed to extreme solutions in stabilized populations in an EMO procedure. Simulation results on a number of problems demonstrate the viability and working of the proposed procedure.
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| 6. |
- Deb, Kalyanmoy, et al.
(författare)
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A Review of Nadir Point Estimation Procedures Using Evolutionary Approaches : A Tale of Dimensionality Reduction
- 2008
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Estimation of the nadir objective vector is an important task, particularly for multi-objective optimization problems having more than two conflicting objectives. Along with the ideal point, nadir point can be used to normalize the objectives so that multi-objective optimization algorithms can be used more reliably. The knowledge of the nadir point is also a pre-requisite to many multiple criteria decision making methodologies.Moreover, nadir point is useful for an aid in interactive methodologies and visualization softwares catered for multi-objective optimization. However, the computation of exact nadir point formore than two objectives is not an easy matter, simply because nadir point demands the knowledge of extreme Paretooptimal solutions. In the past few years, researchers have proposed several nadir point estimation procedures using evolutionary optimization methodologies. In this paper, we review the past studies and reveal an interesting chronicle of events in this direction. To make the estimation procedure computationally faster and more accurate, the methodologies were refined one after the other by mainly focusing on increasingly lower dimensional subset of Pareto-optimal solutions. Simulation results on a number of numerical test problems demonstrate better efficacy of the approach which aims to find only the extreme Pareto-optimal points compared to its higher-dimensional counterparts.
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| 7. |
- Deb, Kalyanmoy, et al.
(författare)
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An Estimation of Nadir Objective Vector using a Hybrid Evolutionary-Cum-Local-Search Procedure
- 2009
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- A nadir objective vector is constructed from the worstPareto-optimal objective values in a multi-objectiveoptimization problem and is an important entity tocompute because of its significance in estimating therange of objective values in the Pareto-optimal frontand also in executing a number of interactive multi-objective optimization techniques. Along with theideal objective vector, it is also needed for the purposeof normalizing different objectives, so as to facilitatea comparison and agglomeration of the objectives.However, the task of estimating the nadir objectivevector necessitates information about the completePareto-optimal front and has been reported to be adifficult task, and importantly an unsolved and openresearch issue. In this paper, we propose certain mod-ifications to an existing evolutionary multi-objectiveoptimization procedure to focus its search towardsthe extreme objective values and combine it with areference-point based local search approach to con-stitute a couple of hybrid procedures for a reliableestimation of the nadir objective vector. With upto 20-objective optimization test problems and on athree-objective engineering design optimization prob-lem, one of the proposed procedures is found to becapable of finding the nadir objective vector reliably.The study clearly shows the significance of an evolu-tionary computing based search procedure in assist-ing to solve an age-old important task in the field ofmulti-objective optimization.
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| 8. |
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| 9. |
- Deb, Kalyanmoy, et al.
(författare)
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Towards Estimating Nadir Objective Vector using Evolutionary Approaches
- 2006
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Ingår i: GECCO 2006. - New York : The Association of Computing Machinery. - 9781595931863 ; , s. 643-650
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Konferensbidrag (refereegranskat)abstract
- Nadir point plays an important role in multi-objective optimization because of its importance in estimating the range of objective values corresponding to desired Pareto-optimal solutions and also in using many classical interactive optimization techniques. Since this point corresponds to the worst Pareto-optimal solution of each objective, the task of estimating the nadir point necessitates information about the whole Pareto optimal frontier and is reported to be a difficult task using classical means. In this paper, for the first time, we have proposed a couple of modifications to an existing evolutionary multi-objective optimization procedure to focus its search towards the extreme objective values front-wise. On up to 20-objective optimization problems, both proposed procedures are found to be capable of finding a near nadir point quickly and reliably. Simulation results are interesting and should encourage further studies and applications in estimating the nadir point, a process which should lead to a better interactive procedure of finding and arriving at a desired Pareto-optimal solution.
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| 10. |
- Erkki, Heikkola, et al.
(författare)
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Multiobjective Optimization of an Ultrasonic Transducer using NIMBUS
- 2006
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Ingår i: Ultrasonics. - : Elsevier BV. - 0041-624X .- 1874-9968. ; 44:4, s. 368-380
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Tidskriftsartikel (refereegranskat)abstract
- The optimal design of an ultrasonic transducer is a multiobjective optimization problem since the final outcome needs to satisfy several conflicting criteria. Simulation tools are often used to avoid expensive and time-consuming experiments, but even simulations may be inefficient and lead to inadequate results if they are based only on trial and error. In this work, the interactive multiobjective optimization method NIMBUS is applied in designing a high-power ultrasonic transducer. The performance of the transducer is simulated with a finite element model, and three design goals are formulated as objective functions to be minimized. To find an appropriate compromise solution, additional preference information is needed from a decision maker, who in our case is an expert in transducer design. A realistic design problem is formulated, and an interactive solution process is described. Our findings demonstrate that interactive multiobjective optimization methods, combined with numerical simulation models, can efficiently help in finding new solution approaches and possibilities as well as new understanding of real-life problems as entirenesses. In this case, the decision maker found a solution that was better with respect to all three objectives than the conventional unoptimized design.
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