A hybrid multiobjective immune algorithm with region preference for decision makers
ABSTRACT Recently, one of the main tools of decision maker (DM) preference incorporation in the multiobjective optimization (MOO) has been using reference points and achievement scalarizing functions (ASF). The core idea of these methods is converting the original multiobjective problem (MOP) into single objective problem by using ASF to find a single preferred point. However, many DMs not only interest in a single point but also a set of efficient points in their preferred region. In this paper, we introduce a hybrid multiobjective immune algorithm (HMIA) for DM. It combines the immune inspired algorithm and region preference based on a novel dominance concept called region-dominance without ASF. The new algorithm can let DMs flexibly decide the number of reference points and accurately determine the preferred region with its simple and effective interactive methods. To exemplify its advantages, simulated results of HMIA are shown with some well-known problems.
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ABSTRACT: One of the main tools for including decision maker (DM) preferences in the multiobjective optimization (MO) literature is the use of reference points and achievement scalarizing functions [A.P. Wierzbicki, The use of reference objectives in multiobjective optimization, in: G. Fandel, T. Gal (Eds.), Multiple-Criteria Decision Making Theory and Application, Springer-Verlag, New York, 1980, pp. 469–486.]. The core idea in these approaches is converting the original MO problem into a single-objective optimization problem through the use of a scalarizing function based on a reference point. As a result, a single efficient point adapted to the DM’s preferences is obtained. However, a single solution can be less interesting than an approximation of the efficient set around this area, as stated for example by Deb in [K. Deb, J. Sundar, N. Udaya Bhaskara Rao, S. Chaudhuri, Reference point based multiobjective optimization using evolutionary algorithms, International Journal of Computational Intelligence Research, 2(3) (2006) 273–286]. In this paper, we propose a variation of the concept of Pareto dominance, called g-dominance, which is based on the information included in a reference point and designed to be used with any MO evolutionary method or any MO metaheuristic. This concept will let us approximate the efficient set around the area of the most preferred point without using any scalarizing function. On the other hand, we will show how it can be easily used with any MO evolutionary method or any MO metaheuristic (just changing the dominance concept) and, to exemplify its use, we will show some results with some state-of-the-art-methods and some test problems.European Journal of Operational Research 09/2009; · 1.84 Impact Factor
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ABSTRACT: The content of the book provides a general overview of the field now called evolutionary multiobjective optimization, which refers to the use of the evolutionary algorithms of any sort to solve multiobjective optimization problems. It covers also other metaheuristics that have been used to solve multiobjective optimization problems. This book should be of interest to the many disciplines that have to deal with multiobjective optimization. Each chapter is complemented by discussion questions and several ideas meant to trigger novel research paths. Chapter 1 presents the basic terminology and nomenclature for use throughout the rest of the book. Chapter 2 provides an overview of the different multi-objective evolutionary (MOEAs) currently available. Chapter 3 discusses both coevolutionary MOEAs and hybridizations of MOEAs with local search procedures. A variety of MOEA implementations within each of these two types of approaches are presented summarized, categorized and analyzed. Chapter 4 presents a detailed developement of MOP test suites ranging from numerical functions to discrete NP-Complete problems and real-world applications. MOEA performance comparisons are presented in Chapter 5. Chapter 6 summarizes the MOEA theoretical results found in the literature. Chapter 7 attempts to group and classify the wide variety of applications found in the literature. Chapter 8 classifies and analyzes the existing research on parallel MOEAs. Chapter 9 describes the most representative research regarding the incorporation of preferences articulation into MOEAs. Chapter 10 discusses multiobjective extensions of other metaheuristics used for optimization. The first edition was published in 2002 (see Zbl 1130.90002).2nd 01/2007; Springer, New York.