A parallel approach to bi-objective integer programming

Abstract

The real world applications of optimisation algorithms often are only interested in the running time of an algorithm, which can frequently be significantly reduced through parallelisation. We present two methods of parallelising the recursive algorithm presented by Ozlen, Burton and MacRae [J. Optimization Theory and Applications; 160: [470][471][472][473][474][475][476][477][478][479][480][481][482] 2014]. Both new methods utilise two threads and improve running times. One of the new methods, the Meeting algorithm, halves running time to achieve near-perfect parallelisation, allowing users to solve bi-objective integer problems with more variables.

Multiobjective Integer Programming: Synergistic Parallel Approaches

“…This lemma is also given in [20], and the proof of this lemma follows trivially from Definition 3. The lemma says that if a thread is solving OIP n s (n − 1, (a s(n) )), and has found all solutions above this problem, then any other thread can also ignore any solution x for which f s(n) (x) > a s(n) .…”

“…Our code was compiled with GCC 4.9.0, and we used CPLEX 12.7.0 as our single objective IP solver, and settings for CPLEX were left at their default, except to limit the number of threads which CPLEX could internally spawn, and also enable deterministic parallelism in such cases where CPLEX would spawn multiple threads. We ran each algorithm over the 3-objective and 4-objective problems described in Section 4.2 (for 2-objective problems, our new algorithms reduce to the much simpler case with no synergy as given in [20], which also includes experimental results). The aim of this computational study is to compare the scalability of our new parallel algorithms to existing parallel algorithms from the literature.…”

“…Threads are given a unique approach to the problem (as determined by an element of the symmetric group S n ). This approach, but limited to the biobjective case where the theory is trivial and there is no synergy, is used in [20] where it just equally partitions the objective space. We present results which allow the real-time sharing of bounds to all other threads.…”

“…The implementation of this new algorithm is based on AIRA as used in [20]. The availability of the source code sped up the implementation process.…”

OOESAlgorithm.jl: a julia package for optimizing a linear function over the set of efficient solutions for biobjective mixed integer linear programming

“…However, unfortunately, this topic has been almost untouched in the literature of exact algorithms. The recent study conducted by Pettersson and Özlen () is one of the few papers (if not the only one) in this scope. The package allows users to choose between different single‐objective optimization solvers by just tuning a parameter. The default solvers include GLPK, CPLEX, Gurobi, Xpress, and SCIP, but it works for all other solvers supported by MathProgBase.jl as well. The package can be modified by users to return the entire nondominated frontier of a BOMILP.…”