Showing papers on "Multi-objective optimization published in 2010"

The weighted sum method for multi-objective optimization: new insights

Abstract: As a common concept in multi-objective optimization, minimizing a weighted sum constitutes an independent method as well as a component of other methods. Consequently, insight into characteristics of the weighted sum method has far reaching implications. However, despite the many published applications for this method and the literature addressing its pitfalls with respect to depicting the Pareto optimal set, there is little comprehensive discussion concerning the conceptual significance of the weights and techniques for maximizing the effectiveness of the method with respect to a priori articulation of preferences. Thus, in this paper, we investigate the fundamental significance of the weights in terms of preferences, the Pareto optimal set, and objective-function values. We determine the factors that dictate which solution point results from a particular set of weights. Fundamental deficiencies are identified in terms of a priori articulation of preferences, and guidelines are provided to help avoid blind use of the method.

Evolutionary multi-criterion optimization

Abstract: GECCO-2010 Tutorial on EMO Portland, USA (8 July'10) 2 Kalyanmoy Deb holds Deva Raj Chair Professor at Indian Institute of Technology Kanpur in India. He is the recipient of the MCDM Edgeworth-Pareto award by the Multiple Criterion Decision Making (MCDM) Society. He has also received Shanti Swarup Bhatnagar Prize in Engineering Sciences for the year 2005 from Govt. of India. He has also received the `Thomson Citation Laureate Award' for having highest number of citations in Computer Science during the past ten years in India. He is a fellow of Indian National Academy of Engineering (INAE), Indian National Academy of Sciences, and International Society of Genetic and Evolutionary Computation (ISGEC). He has received Fredrick Wilhelm Bessel Research award from Alexander von Humboldt Foundation in 2003. He has written more than 240 international journal and conference research papers. More information about his research can be found from http://www.iitk.ac.in/kangal/deb.htm

Expensive Multiobjective Optimization by MOEA/D With Gaussian Process Model

Abstract: In some expensive multiobjective optimization problems (MOPs), several function evaluations can be carried out in a batch way. Therefore, it is very desirable to develop methods which can generate multipler test points simultaneously. This paper proposes such a method, called MOEA/D-EGO, for dealing with expensive multiobjective optimization. MOEA/D-EGO decomposes an MOP in question into a number of single-objective optimization subproblems. A predictive model is built for each subproblem based on the points evaluated so far. Effort has been made to reduce the overhead for modeling and to improve the prediction quality. At each generation, MOEA/D is used for maximizing the expected improvement metric values of all the subproblems, and then several test points are selected for evaluation. Extensive experimental studies have been carried out to investigate the ability of the proposed algorithm.

Bioinspired Computation in Combinatorial Optimization: Algorithms and Their Computational Complexity

Abstract: Bioinspired computation methods, such as evolutionary algorithms and ant colony optimization, are being applied successfully to complex engineering and combinatorial optimization problems, and it is very important that we understand the computational complexity of these algorithms. This tutorials explains the most important results achieved in this area.The presenters show how runtime behavior can be analyzed in a rigorous way, in particular for combinatorial optimization. They present well-known problems such as minimum spanning trees, shortest paths, maximum matching, and covering and scheduling problems. Classical single objective optimization is examined first. They then investigate the computational complexity of bioinspired computation applied to multiobjective variants of the considered combinatorial optimization problems, and in particular they show how multiobjective optimization can help to speed up bioinspired computation for single-objective optimization problems.The tutorial is based on a book written by the authors with the same title. Further information about the book can be found at www.bioinspiredcomputation.com.

Multi-Objective Optimization Design of In-Wheel Switched Reluctance Motors in Electric Vehicles

Abstract: The method of the optimization design with multi-objectives for switched reluctance motors (SRMs) in electric vehicles (EVs) is proposed in this paper. It is desired that electric motors for EVs have high torque, high efficiency, and high torque density. Thus, the developed optimization function is selected as the correct compromise between the maximum average torque, maximum average torque per copper loss, and maximum average torque per motor lamination volume, by using three weight factors and three base values. The stator and rotor pole arc angles are selected as the optimized variables. Furthermore, the authors also discuss the design requirements and some constraints on the optimization design. The results of the optimization design show that the proposed method meets the requirements of EVs on electric motors well. A prototype of the optimally designed in-wheel SRM for EVs has been manufactured. This paper provides a valuable method to implement the optimal design of SRMs for EVs.

Short-Term Scheduling and Control of Active Distribution Systems With High Penetration of Renewable Resources

Abstract: Among the innovative contributions to electric distribution systems, one of the most promising and qualified is the possibility to manage and control distributed generation. Therefore, the latest distribution management systems tend to incorporate optimization functions for the short-term scheduling of the various energy and control resources available in the network (e.g., embedded generators, reactive power compensators and transformers equipped with on-load tap changers). The short-term scheduling procedure adopted in the paper is composed by two stages: a day-ahead scheduler for the optimization of distributed resources production during the following day, an intra-day scheduler that every 15 min adjusts the scheduling in order to take into account the operation requirements and constraints of the distribution network. The intra-day scheduler solves a non-linear multi-objective optimization problem by iteratively applying a mixed-integer linear programming (MILP) algorithm. The linearization of the optimization function and the constraints is achieved by the use of sensitivity coefficients obtained from the results of a three-phase power flow calculation. The paper shows the application of the proposed approach to a medium-voltage 120 buses network with five wind plants, one photovoltaic field, ten dispatchable generators, and two transformers equipped with on-load tap changers.

The r-Dominance: A New Dominance Relation for Interactive Evolutionary Multicriteria Decision Making

Abstract: Evolutionary multiobjective optimization (EMO) methodologies have gained popularity in finding a representative set of Pareto optimal solutions in the past decade and beyond. Several techniques have been proposed in the specialized literature to ensure good convergence and diversity of the obtained solutions. However, in real world applications, the decision maker is not interested in the overall Pareto optimal front since the final decision is a unique solution. Recently, there has been an increased emphasis in addressing the decision-making task in searching for the most preferred alternatives. In this paper, we introduce a new variant of the Pareto dominance relation, called r-dominance, which has the ability to create a strict partial order among Pareto-equivalent solutions. This fact makes such a relation able to guide the search toward the interesting parts of the Pareto optimal region based on the decision maker's preferences expressed as a set of aspiration levels. After integrating the new dominance relation in the NSGA-II methodology, the efficacy and the usefulness of the modified procedure are assessed through two to ten-objective test problems a priori and interactively. Moreover, the proposed approach provides competitive and better results when compared to other recently proposed preference-based EMO approaches.

Multi-objective self-adaptive differential evolution with elitist archive and crowding entropy-based diversity measure

Abstract: A self-adaptive differential evolution algorithm incorporate Pareto dominance to solve multi-objective optimization problems is presented. The proposed approach adopts an external elitist archive to retain non-dominated solutions found during the evolutionary process. In order to preserve the diversity of Pareto optimality, a crowding entropy diversity measure tactic is proposed. The crowding entropy strategy is able to measure the crowding degree of the solutions more accurately. The experiments were performed using eighteen benchmark test functions. The experiment results show that, compared with three other multi-objective optimization evolutionary algorithms, the proposed MOSADE is able to find better spread of solutions with better convergence to the Pareto front and preserve the diversity of Pareto optimal solutions more efficiently.

An Interactive Evolutionary Multiobjective Optimization Method Based on Progressively Approximated Value Functions

Abstract: This paper suggests a preference-based methodology, which is embedded in an evolutionary multiobjective optimization algorithm to lead a decision maker (DM) to the most preferred solution of her or his choice. The progress toward the most preferred solution is made by accepting preference based information progressively from the DM after every few generations of an evolutionary multiobjective optimization algorithm. This preference information is used to model a strictly monotone value function, which is used for the subsequent iterations of the evolutionary multiobjective optimization (EMO) algorithm. In addition to the development of the value function which satisfies DM's preference information, the proposed progressively interactive EMO-approach utilizes the constructed value function in directing EMO algorithm's search to more preferred solutions. This is accomplished using a preference-based domination principle and utilizing a preference-based termination criterion. Results on two- to five-objective optimization problems using the progressively interactive NSGA-II approach show the simplicity of the proposed approach and its future promise. A parametric study involving the algorithm's parameters reveals interesting insights of parameter interactions and indicates useful parameter values. A number of extensions to this paper are also suggested.

On Set-Based Multiobjective Optimization

Abstract: Assuming that evolutionary multiobjective optimization (EMO) mainly deals with set problems, one can identify three core questions in this area of research: 1) how to formalize what type of Pareto set approximation is sought; 2) how to use this information within an algorithm to efficiently search for a good Pareto set approximation; and 3) how to compare the Pareto set approximations generated by different optimizers with respect to the formalized optimization goal. There is a vast amount of studies addressing these issues from different angles, but so far only a few studies can be found that consider all questions under one roof. This paper is an attempt to summarize recent developments in the EMO field within a unifying theory of set-based multiobjective search. It discusses how preference relations on sets can be formally defined, gives examples for selected user preferences, and proposes a general preference-independent hill climber for multiobjective optimization with theoretical convergence properties. Furthermore, it shows how to use set preference relations for statistical performance assessment and provides corresponding experimental results. The proposed methodology brings together preference articulation, algorithm design, and performance assessment under one framework and thereby opens up a new perspective on EMO.

HCS: A New Local Search Strategy for Memetic Multiobjective Evolutionary Algorithms

Abstract: In this paper, we propose and investigate a new local search strategy for multiobjective memetic algorithms. More precisely, we suggest a novel iterative search procedure, known as the Hill Climber with Sidestep (HCS), which is designed for the treatment of multiobjective optimization problems, and show further two possible ways to integrate the HCS into a given evolutionary strategy leading to new memetic (or hybrid) algorithms. The pecularity of the HCS is that it is intended to be capable both moving toward and along the (local) Pareto set depending on the distance of the current iterate toward this set. The local search procedure utilizes the geometry of the directional cones of such optimization problems and works with or without gradient information. Finally, we present some numerical results on some well-known benchmark problems, indicating the strength of the local search strategy as a standalone algorithm as well as its benefit when used within a MOEA. For the latter we use the state of the art algorithms Nondominated Sorting Genetic Algorithm-II and Strength Pareto Evolutionary Algorithm 2 as base MOEAs.

MA-SW-Chains: Memetic algorithm based on local search chains for large scale continuous global optimization

Abstract: Memetic algorithms are effective algorithms to obtain reliable and accurate solutions for complex continuous optimization problems. Nowadays, high dimensional optimization problems are an interesting field of research. The high dimensionality introduces new problems for the optimization process, requiring more scalable algorithms that, at the same time, could explore better the higher domain space around each solution. In this work, we proposed a memetic algorithm, MA-SW-Chains, for large scale global optimization. This algorithm assigns to each individual a local search intensity that depends on its features, by chaining different local search applications. MA-SW-Chains is an adaptation to large scale optimization of a previous algorithm, MA-CMA-Chains, to improve its performance on high-dimensional problems. Finally, we present the results obtained by our proposal using the benchmark problems defined in the Special Session of Large Scale Global Optimization on the IEEE Congress on Evolutionary Computation in 2010.

Multi-objective optimization of a mixed renewable system with demand-side management

Abstract: The 2001/77/CE European Commission Directive sets the target of 22% of gross electricity generation from renewables for the Europe, by 2010. In a scenario of large scale penetration of renewable production from wind and other intermittent resources, it is fundamental that the electric system has appropriate means to compensate the effects of the variability and randomness of the wind, solar and hydro power availability. The paper proposes a novel multi-objective method to optimize the mix of the renewable system maximizing its contribution to the peak load, while minimizing the combined intermittence, at a minimum cost. In such model the contribution of the large-scale demand-side management and demand response technologies are also considered.

Multi-Objective Optimization Using Surrogates

Abstract: Until recently, optimization was regarded as a discipline of rather theoretical interest, with limited real-life applicability due to the computational or experimental expense involved. Practical multiobjective optimization was considered almost as a utopia even in academic studies due to the multiplication of this expense. This paper discusses the idea of using surrogate models for multiobjective optimization. With recent advances in grid and parallel computing more companies are buying inexpensive computing clusters that work in parallel. This allows, for example, efficient fusion of surrogates and finite element models into a multiobjective optimization cycle. The research presented here demonstrates this idea using several response surface methods on a pre-selected set of test functions. We aim to show that there are number of techniques which can be used to tackle difficult problems and we also demonstrate that a careful choice of response surface methods is important when carrying out surrogate assisted multiobjective search.

Sensitivity Versus Accuracy in Multiclass Problems Using Memetic Pareto Evolutionary Neural Networks

Abstract: This paper proposes a multiclassification algorithm using multilayer perceptron neural network models. It tries to boost two conflicting main objectives of multiclassifiers: a high correct classification rate level and a high classification rate for each class. This last objective is not usually optimized in classification, but is considered here given the need to obtain high precision in each class in real problems. To solve this machine learning problem, we use a Pareto-based multiobjective optimization methodology based on a memetic evolutionary algorithm. We consider a memetic Pareto evolutionary approach based on the NSGA2 evolutionary algorithm (MPENSGA2). Once the Pareto front is built, two strategies or automatic individual selection are used: the best model in accuracy and the best model in sensitivity (extremes in the Pareto front). These methodologies are applied to solve 17 classification benchmark problems obtained from the University of California at Irvine (UCI) repository and one complex real classification problem. The models obtained show high accuracy and a high classification rate for each class.

Analog circuit design optimization through the particle swarm optimization technique

Abstract: This paper details the Particle Swarm Optimization (PSO) technique for the optimal design of analog circuits. It is shown the practical suitability of PSO to solve both mono-objective and multiobjective discrete optimization problems. Two application examples are presented: maximizing the voltage gain of a low noise amplifier for the UMTS standard and computing the Pareto front of a bi-objective problem, maximizing the high current cut off frequency and minimizing the parasitic input resistance of a second generation current conveyor. The aptness of PSO to optimize difficult circuit problems, in terms of numbers of parameters and constraints, is shown.

An efficient and accurate solution methodology for bilevel multi-objective programming problems using a hybrid evolutionary-local-search algorithm

Abstract: 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.

A multi-objective PSO for job-shop scheduling problems

Abstract: Most previous research into the job-shop scheduling problem has concentrated on finding a single optimal solution (e.g., makespan), even though the actual requirement of most production systems requires multi-objective optimization. The aim of this paper is to construct a particle swarm optimization (PSO) for an elaborate multi-objective job-shop scheduling problem. The original PSO was used to solve continuous optimization problems. Due to the discrete solution spaces of scheduling optimization problems, the authors modified the particle position representation, particle movement, and particle velocity in this study. The modified PSO was used to solve various benchmark problems. Test results demonstrated that the modified PSO performed better in search quality and efficiency than traditional evolutionary heuristics.