Finding a representative nondominated set for multi-objective mixed integer programs

Representative Solutions for Bi-Objective Optimisation

“…There is a number of works aiming to filter the Pareto front by selecting only a few Pareto optimal solutions and obtain a "good" representation (Eusébio, Figueira, and Ehrgott 2014;Vaz et al 2015;Schwind et al 2016;Raith and Sedeño-Noda 2017;Masin and Bukchin 2008;Ceyhan, Köksalan, and Lokman 2019). How well a Pareto front is represented by means of a few solutions depends on the context.…”

Distribution based representative sets for multi-objective integer programs

“…Faulkenberg and Wiecek (2010) review quality measures to assess the discrete representations of the nondominated sets and classify them into three groups as suggested by Sayın (2000). Sylva and Crema (2007), Masin and Bukchin (2008) and Ceyhan et al (2019) develop algorithms that generate a representative set for MOIPs. These algorithms allow the decision maker (DM) can stop the algorithm when the desired cardinality or coverage level is achieved.…”

“…The algorithms developed by Sylva and Crema (2007) and Masin and Bukchin (2008) solve a more-constrained model at each iteration in order to generate a new representative point. Ceyhan et al (2019) utilize a decomposition and search method in representative generation and provide a substantial improvement over these algorithms. Ceyhan et al (2019) also develop a holistic approach, Surface projection algorithm (SPA), that is designed to generate a high-quality representative set when the number of representative points is known a priori.…”

“…Ceyhan et al (2019) utilize a decomposition and search method in representative generation and provide a substantial improvement over these algorithms. Ceyhan et al (2019) also develop a holistic approach, Surface projection algorithm (SPA), that is designed to generate a high-quality representative set when the number of representative points is known a priori. Bektaş (2018)'s algorithm also generates a subset of the nondominated set but he does not measure the quality of the representation.…”

“…The coverage gap value, α R , corresponds to the distance of the worst represented point to its representative. At the coverage gap calculations, unlike Sayın (2000), we use a Tchebycheff-based distance function to quantify the representation error, max 1≤i≤m (z i − y i ) as in Sylva and Crema (2007), Masin and Bukchin (2008) and Ceyhan et al (2019). That is, the difference between the objective values contributes to the representation error only when the nondominated point is superior to its representative point on that objective, z i > y i for any i = 1, .…”