Discrete Optimization with Decision Diagrams

Abstract

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Multiobjective Optimization by Decision Diagrams

“…SupposeX ⊆ B 4 is given by the following set of solutions We refer the reader to the work by Bergman et al [5] for BDD compilation procedures for general optimization problems. …”

“…In this section we propose a technique which generalizes previous works on singleobjective optimization problems using BDDs [5]. Namely, suppose a MODO M has one objective function (i.e., p = 1) with…”

“…The objective coefficients were generated as they were for the MKP. The reduced BDDs for the MSPP and MSCP were compiled according to Bergman et al [7,5]. Table 2 presents the average cardinalities of the nondominated sets and the average solution times.…”

“…The utilization of decision diagrams in optimization is recent and focusses on the use of BDDs for a variety of purposes [5]. In this research stream, top-down compilation methods for set covering problems [7,6] and set packing problems [6,4] have been investigated, along with methods for creating BDDs for knapsack problems [2].…”

Decomposition Based on Decision Diagrams

“…In recent years, DDs have also been applied to encode the solution set of discrete optimization problems, serving for a variety purposes such as cut generation in mixed-integer linear programming [5], to enhance propagation in constraint programming [3], and in novel general branch-and-bound procedures for combinatorial optimization problems [8].…”