Modern Trends in Multiobjective Optimization

  in Special Issue   Posted on June 3, 2020

Information for the Special Issue

Submission Deadline: Tue 30 Jun 2020
Journal Impact Factor : 2.600
Journal Name : Computers and Operations Research
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Special Issue Call for Papers:

Computers and Operations Research

Guest Editors:

Carlos M. Fonseca (University of Coimbra, Portugal)
Kathrin Klamroth (Universität Wuppertal, Germany)
Margaret M. Wiecek (Clemson University, United States)

Submission deadline: June 30, 2020

Multiobjective optimization (MO), which strives for the simultaneous consideration of conflicting objectives and complicating constraints, has become an indispensable tool in complex decision-making situations in many areas of human activity in business, management, and engineering. Complexity in decision-making results from the rapid technological and economic growth that improves our lives but simultaneously creates new challenges such as environmental pollution, limited healthcare and security services, shortage of water and energy resources, and others. The growth is accompanied by the ongoing production of big amounts of data but also by increasing computational power. Due to the new or continuing demands and requirements, but also opportunities, we have recently experienced a shift of paradigm from decision-making problems of a simple structure with relatively few variables and constraints, and two or three objective functions, to large-scale problems composed of interacting subproblems and involving many variables, many objective functions and constraints, and many decision makers. In view of these growing practical needs, development of MO models and solution approaches with specific features, as a decisive characteristic for future applicability and success of MO, has thus become crucial. Consequently, for this special issue we invite original research contributions to the theory, computation, and practice of MO that address the following current trends in multiobjective optimization, and the relationships between them. Relevant solution approaches include mathematical programming as well as heuristic and meta-heuristic approaches, such as evolutionary algorithms.

Complexity in Multiobjective Optimization Complexity in MO can originate from mathematical modeling, the real-life situation being modeled, or limitations in data collection.

(i) MO problems are complex by their mathematical nature; optimization problems that are easy to solve in the single objective case are often intractable and highly complex already in the biobjective case. Algorithms for challenging problems such as MO problems with heterogeneous objective functions and/or mixed-integer variables and semidefinite MO problems, among others, are of interest to this special issue.

(ii) MO problems become complex also because they model and provide decision-making methods for man-made complex systems such as financial markets, social networks, communication systems, public health providers, cybersecurity systems, and global corporations. Since such systems are composed of subsystems, decision-making is difficult because optimal decisions for the subsystems may not be optimal for the overall system and vice versa. A unique optimal decision for the system may not exist, or if it exists, it may be extremely difficult to be identified. Furthermore, a solution methodology for finding optimal decisions for the overall system may not exist either, or if it does, it may be prohibitively expensive due to difficulties such as heterogeneous functions, integrality of variables, nested problems in a bilevel structure, cost of simulation, etc. Due to these challenges, it is of interest to develop distributed MO algorithms for computing optimal decisions for subsystems without ever dealing with the overall system in its entirety, but such that they are suboptimal or optimal to the overall system.

(iii) Another type of complexity arises when an objective or constraint can be evaluated only by black box algorithms, in which case MO simulation optimization becomes a relevant methodology. The recent availability of mature and efficient single-objective simulation optimization algorithms, coupled with ubiquitously available parallel computing power, makes solving MO simulation optimization problems a realistic goal and papers proposing this class of algorithms are welcome.

(iv) Yet another type of complexity arises when an objective or constraint can be observed only with a stochastic error, or when the computed solutions can only be realized up to some inaccuracies, for example, due to the production process. Uncertain MO is a quickly growing research area with a multitude of practical applications. Deterministic counterpart models are usually highly complex optimization problems, that demand for the development of novel and efficient solution paradigms.

Scalability in Multiobjective Optimization Scalability is an important issue in optimization problems in terms of volume, variety, and variability. As large data sets are necessary for modeling large-scale societal challenges, scalability becomes a critical concern in MO methodology. Consequently, it is of interest to propose MO models and methods that are scalable with respect to the large amounts of data, many objective functions, many variables, and many decision makers.

(i) MO problems with a large number of objective functions are highly challenging, since usually the number of solutions grows exponentially with the number of objectives (as long as these are conflicting). Current solution techniques usually do not scale well with the number of objectives and/or constraints. Topics of interest thus include, but are not limited to, model building, identification of agreement and conflict, representations and approximations, as well as algorithm development and parallelization.

(ii) Many approaches for preference elicitation and interactive decision support are based on a one-to-one interaction with a single decision maker, and hence do not scale well with an increasing number of decision makers. Novel concepts for preference modelling, preference elicitation in group decision making, and utility function extraction are required that aim at complicated and complex decision-making situations.

(iii) MO with a large number of variables and/or based on large amounts of data occur, for example, in the context of (multiobjective) machine learning and the (multiobjective) training of artificial neural networks.

Invariance in Multiobjective Optimization Intimately related to complexity and scalability is the notion of invariance. The more the size and complexity of MO problems grows, the more important it is that solution approaches are not detrimentally affected by redundant aspects of the MO problem formulation, nor by certain transformations leading to equivalent formulations of the same problem. Similarly, decision making methods should be insensitive to the presence of irrelevant alternatives, and the elicited preferences of a decision maker should not depend on the method used to elicit them.

(i) Due to dependencies among decision variables, the set of independent variables required to formulate a given MO problem, or even their scale, may not be unique. Invariance to such decision-space transformations offers greater flexibility at the modeling stage.

(ii) Real-world problems involving many objectives are often such that only a few objectives are conflicting at any given point in the decision space, although their number may vary, and conflicting objectives at one point may become non-conflicting at another point. Invariance with respect to non-conflicting objectives is therefore a desirable property of MO solution methods.

(iii) Objective scaling and the sets of alternatives made available to the Decision Maker may influence preference elicitation and decision outcomes in unwanted ways. Descriptive invariance and procedural invariance are properties that contribute to more reliable decisions.

All researchers worldwide working on the topics indicated above are invited to contribute to this special issue. The submitted papers shall comply with the aims and scope of Computers & Operations Research. Authors should follow the Instructions for Authors of Computers and Operations Research ( and submit their high quality manuscript via the Elsevier online submission and editorial system by June 30, 2020.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere. The submitted manuscripts are sent to reviewers as they arrive but the editors reserve the right to reject any manuscript that does not present a high level of scholarship before the manuscript is sent to reviewers. Papers accepted for publication are made electronically available before the Special Issue is published. Further inquiries should be sent to the Guest Editors:

Carlos M. Fonseca (

Kathrin Klamroth (

Margaret M. Wiecek (

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