TY - JOUR

T1 - Fifty years of multi-objective optimization and decision-making

T2 - From mathematical programming to evolutionary computation

AU - Ehrgott, Matthias

AU - Köksalan, Murat

AU - Kadziński, Miłosz

AU - Deb, Kalyanmoy

PY - 2025/6/10

Y1 - 2025/6/10

N2 - We review major developments in multi-objective optimization over the past decades. Although mathematical foundations and basic concepts have been established earlier, substantial progress in methods for constructing and identifying preferred solutions started in the late 1950s. We classify these approaches into two broad categories: mathematical programming-based and population-based. The former originated in the late 1950s, and its growth accelerated from the 1970s onward. We differentiate between approaches dealing with problems that operate in a continuous solution space and combinatorial problems where some variables are restricted to integer values. Population-based approaches flourished in the 1990s. Our focus is on evolutionary computation techniques that either aim to discover the entire Pareto front or incorporate the decision maker's preferences to select the most favorable solution(s) or bias the search toward preferred regions. For all categories, we discuss those approaches that, in our opinion, have made major impacts. We examine current research trends and speculate on future directions in the field.

AB - We review major developments in multi-objective optimization over the past decades. Although mathematical foundations and basic concepts have been established earlier, substantial progress in methods for constructing and identifying preferred solutions started in the late 1950s. We classify these approaches into two broad categories: mathematical programming-based and population-based. The former originated in the late 1950s, and its growth accelerated from the 1970s onward. We differentiate between approaches dealing with problems that operate in a continuous solution space and combinatorial problems where some variables are restricted to integer values. Population-based approaches flourished in the 1990s. Our focus is on evolutionary computation techniques that either aim to discover the entire Pareto front or incorporate the decision maker's preferences to select the most favorable solution(s) or bias the search toward preferred regions. For all categories, we discuss those approaches that, in our opinion, have made major impacts. We examine current research trends and speculate on future directions in the field.

U2 - 10.1016/j.ejor.2025.06.012

DO - 10.1016/j.ejor.2025.06.012

M3 - Review article

JO - European Journal of Operational Research

JF - European Journal of Operational Research

SN - 0377-2217

ER -