A survey of current continuous nonlinear multi-objective optimization (MOO) concepts and methods is presented. It consolidates and relates seemingly different terminology and methods. The methods are divided into three major categories: methods with a priori articulation of preferences, methods with a posteriori articulation of preferences, and methods with no articulation of preferences. Genetic algorithms are surveyed as well. Commentary is provided on three fronts, concerning the advantages and pitfalls of individual methods, the different classes of methods, and the field of MOO as a whole. The Characteristics of the most significant methods are summarized. Conclusions are drawn that reflect often-neglected ideas and applicability to engineering problems. It is found that no single approach is superior. Rather, the selection of a specific method depends on the type of information that is provided in the problem, the user’s preferences, the solution requirements, and the availability of software.

Survey of multi-objective optimization methods for engineering

After using evolutionary techniques for single-objective optimization during more than two decades, the incorporation of more than one objective in the fitness function has finally become a popular area of research. As a consequence, many new evolutionary-based approaches and variations of existing techniques have recently been published in the technical literature. The purpose of this paper is to summarize and organize the information on these current approaches, emphasizing the importance of analyzing the operations research techniques in which most of them are based, in an attempt to motivate researchers to look into these mathematical programming approaches for new ways of exploiting the search capabilities of evolutionary algorithms. Furthermore, a summary of the main algorithms behind these approaches is provided, together with a brief criticism that includes their advantages and disadvantages, degree of applicability, and some known applications. Finally, further trends in this area and some possible paths for further research are also addressed.

An updated survey of GA-based multiobjective optimization techniques

This paper is an update of a paper that five of us published in 1992. The areas of multiple criteria decision making (MCDM) and multiattribute utility theory (MAUT) continue to be active areas of management science research and application. This paper extends the history of these areas and discusses topics we believe to be important for the future of these fields.

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Multiple Criteria Decision Making, Multiattribute Utility Theory: Recent Accomplishments and What Lies Ahead

Goal programming for decision making: an overview of the current state-of-the-art

The use of evolutionary algorithms (EAs) to solve problems with multiple objectives (known as multi-objective optimization problems (MOPs)) has attracted much attention. Being population based approaches, EAs offer a means to find a group of Pareto-optimal solutions in a single run. Differential evolution (DE) is an EA that was developed to handle optimization problems over continuous domains. The objective of this paper is to introduce a novel Pareto-frontier differential evolution (PDE) algorithm to solve MOPs. The solutions provided by the proposed algorithm for two standard test problems, outperform the Strength Pareto Evolutionary Algorithm, one of the state-of-the-art evolutionary algorithms for solving MOPs.

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PDE: a Pareto-frontier differential evolution approach for multi-objective optimization problems

(1962). Management Models and Industrial Applications of Linear Programming. Journal of the Operational Research Society: Vol. 13, No. 3, pp. 274-275.

https://link.springer.com/content/pdf/10.1057%2Fjors.1962.42.pdf

K. B. Williams

Papers

Management Models and Industrial Applications of Linear Programming