Since the late 70s, much research activity has taken place on the class of dynamic vehicle routing problems DVRP, with the time period after year 2000 witnessing a real explosion in related papers. Our paper sheds more light into work in this area over more than 3 decades by developing a taxonomy of DVRP papers according to 11 criteria. These are 1 type of problem, 2 logistical context, 3 transportation mode, 4 objective function, 5 fleet size, 6 time constraints, 7 vehicle capacity constraints, 8 the ability to reject customers, 9 the nature of the dynamic element, 10 the nature of the stochasticity if any, and 11 the solution method. We comment on technological vis-i-vis methodological advances for this class of problems and suggest directions for further research. The latter include alternative objective functions, vehicle speed as decision variable, more explicit linkages of methodology to technological advances and analysis of worst case or average case performance of heuristics. © 2015 Wiley Periodicals, Inc. NETWORKS, Vol. 671, 3-31 2016

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Dynamic vehicle routing problems: Three decades and counting

This paper presents a mixed-integer linear programming (MILP) reformulation of the thermal unit commitment (UC) problem. The proposed formulation is simultaneously tight and compact. The tighter characteristic reduces the search space and the more compact characteristic increases the searching speed with which solvers explore that reduced space. Therefore, as a natural consequence, the proposed formulation significantly reduces the computational burden in comparison with analogous MILP-based UC formulations. We provide computational results comparing the proposed formulation with two others which have been recognized as computationally efficient in the literature. The experiments were carried out on 40 different power system mixes and sizes, running from 28 to 1870 generating units.

Tight and Compact MILP Formulation for the Thermal Unit Commitment Problem

Branch-and-bound algorithms

The SCIP Optimization Suite provides a collection of software packages for
mathematical optimization centered around the constraint integer programming frame-
work SCIP. This paper discusses enhancements and extensions contained in version 7.0
of the SCIP Optimization Suite. The new version features the parallel presolving library
PaPILO as a new addition to the suite. PaPILO 1.0 simplifies mixed-integer linear op-
timization problems and can be used stand-alone or integrated into SCIP via a presolver
plugin. SCIP 7.0 provides additional support for decomposition algorithms. Besides im-
provements in the Benders’ decomposition solver of SCIP, user-defined decomposition
structures can be read, which are used by the automated Benders’ decomposition solver
and two primal heuristics. Additionally, SCIP 7.0 comes with a tree size estimation
that is used to predict the completion of the overall solving process and potentially
trigger restarts. Moreover, substantial performance improvements of the MIP core were
achieved by new developments in presolving, primal heuristics, branching rules, conflict
analysis, and symmetry handling. Last, not least, the report presents updates to other
components and extensions of the SCIP Optimization Suite, in particular, the LP solver
SoPlex and the mixed-integer semidefinite programming solver SCIP-SDP.

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The SCIP Optimization Suite 7.0

The design of strategies for branching in Mixed Integer Programming (MIP) is guided by cycles of parameter tuning and offline experimentation on an extremely heterogeneous testbed, using the average performance. Once devised, these strategies (and their parameter settings) are essentially input-agnostic. To address these issues, we propose a machine learning (ML) framework for variable branching in MIP. Our method observes the decisions made by Strong Branching (SB), a time-consuming strategy that produces small search trees, collecting features that characterize the candidate branching variables at each node of the tree. Based on the collected data, we learn an easy-to-evaluate surrogate function that mimics the SB strategy, by means of solving a learning-to-rank problem, common in ML. The learned ranking function is then used for branching. The learning is instance-specific, and is performed on-the-fly while executing a branch-and-bound search to solve the instance. Experiments on benchmark instances indicate that our method produces significantly smaller search trees than existing heuristics, and is competitive with a state-of-the-art commercial solver.

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Learning to branch in Mixed Integer Programming

This paper reports on the fifth version of theMixed Integer Programming Library. The miplib 2010 is the first miplib release that has been assembled by a large group from academia and from industry, all of whom work in integer programming. There was mutual consent that the concept of the library had to be expanded in order to fulfill the needs of the community. The new version comprises 361 instances sorted into several groups. This includes the main benchmark test set of 87 instances, which are all solvable by today’s codes, and also the challenge test set with 164 instances, many of which are currently unsolved. For the first time, we include scripts to run automated tests in a predefined way. Further, there is a solution checker to test the accuracy of provided solutions using exact arithmetic.

Daniel E. Steffy

Papers

MIPLIB 2010 - Mixed Integer Programming Library version 5