Management science and decision science have grown exponentially since midcentury. Two closely-related fields central to this growth are multiple criteria decision making MCDM and multiattribute utility theory MAUT. This paper comments on the history of MCDM and MAUT and discusses topics we believe are important in their continued development and usefulness to management science over the next decade. Our aim is to identify exciting directions and promising areas for future research.

Multiple Criteria Decision Making, Multiattribute Utility Theory: The Next Ten Years

Many-objective optimization refers to the optimization problems containing large number of objectives, typically more than four. Non-dominance is an inadequate strategy for convergence to the Pareto front for such problems, as almost all solutions in the population become non-dominated, resulting in loss of convergence pressure. However, for some problems, it may be possible to generate the Pareto front using only a few of the objectives, rendering the rest of the objectives redundant. Such problems may be reducible to a manageable number of relevant objectives, which can be optimized using conventional multiobjective evolutionary algorithms (MOEAs). For dimensionality reduction, most proposals in the paper rely on analysis of a representative set of solutions obtained by running a conventional MOEA for a large number of generations, which is computationally overbearing. A novel algorithm, Pareto corner search evolutionary algorithm (PCSEA), is introduced in this paper, which searches for the corners of the Pareto front instead of searching for the complete Pareto front. The solutions obtained using PCSEA are then used for dimensionality reduction to identify the relevant objectives. The potential of the proposed approach is demonstrated by studying its performance on a set of benchmark test problems and two engineering examples. While the preliminary results obtained using PCSEA are promising, there are a number of areas that need further investigation. This paper provides a number of useful insights into dimensionality reduction and, in particular, highlights some of the roadblocks that need to be cleared for future development of algorithms attempting to use few selected solutions for identifying relevant objectives.

A Pareto Corner Search Evolutionary Algorithm and Dimensionality Reduction in Many-Objective Optimization Problems

Various difficulties have been encountered in using decision set-based vector maximization methods to solve a multiple objective linear programming problem (MOLP). Motivated by these difficulties, some researchers in recent years have suggested that outcome set-based approaches should instead be developed and used to solve problem (MOLP). In this article, we present a finite algorithm, called the Outer Approximation Algorithm, for generating the set of all efficient extreme points in the outcome set of problem (MOLP). To our knowledge, the Outer Approximation Algorithm is the first algorithm capable of generating this set. As a by-product, the algorithm also generates the weakly efficient outcome set of problem (MOLP). Because it works in the outcome set rather than in the decision set of problem (MOLP), the Outer Approximation Algorithm has several advantages over decision set-based algorithms. It is also relatively easy to implement. Preliminary computational results for a set of randomly-generated problems are reported. These results tangibly demonstrate the usefulness of using the outcome set approach of the Outer Approximation Algorithm instead of a decision set-based approach.

An Outer Approximation Algorithm for Generating AllEfficient Extreme Points in the Outcome Set of a Multiple ObjectiveLinear Programming Problem

Many-objective problems represent a major challenge in the field of evolutionary multiobjective optimization---in terms of search efficiency, computational cost, decision making, visualization, and so on. This leads to various research questions, in particular whether certain objectives can be omitted in order to overcome or at least diminish the difficulties that arise when many, that is, more than three, objective functions are involved. This study addresses this question from different perspectives.

First, we investigate how adding or omitting objectives affects the problem characteristics and propose a general notion of conflict between objective sets as a theoretical foundation for objective reduction. Second, we present both exact and heuristic algorithms to systematically reduce the number of objectives, while preserving as much as possible of the dominance structure of the underlying optimization problem. Third, we demonstrate the usefulness of the proposed objective reduction method in the context of both decision making and search for a radar waveform application as well as for well-known test functions.

Objective reduction in evolutionary multiobjective optimization: Theory and applications

On the convergence of multiobjective evolutionary algorithms

A general method for determining the set of all efficient solutions to a linear vectormaximum problem

Redundant objective functions in linear vector maximum problems and their determination

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A general method for determining the set of all efficient solutions to a linear vectormaximum problem

Redundant objective functions in linear vector maximum problems and their determination