Learning Solutions of Similar Linear Programming Problems using Boosting Trees

In many optimization problems, similar linear programming (LP) problems occur in the nodes of the branch and bound trees that are used to solve integer (mixed or pure, deterministic or stochastic) programming problems. Similar LP problems are also found in problem domains where the objective function and constraint coefficients vary due to uncertainties in the operating conditions. In this report, we present a regression technique for learning a set of functions that map the objective function and the constraints to the decision variables of such an LP system by modifying boosting trees, an algorithm we term the Boost-LP algorithm. Matrix transformations and geometric properties of boosting trees are utilized to provide theoretical performance guarantees on the predicted values. The standard form of the loss function is altered to reduce the possibility of generating infeasible LP solutions. Experimental results on three different problems, one each on scheduling, routing, and planning respectively, demonstrate the effectiveness of the Boost-LP algorithm in providing significant computational benefits over regular optimization solvers without generating solutions that deviate appreciably from the optimum values

SUNNY-CP : a Sequential CP Portfolio Solver

International audienceThe Constraint Programming (CP) paradigm allows to model and solve Constraint Satisfaction / Optimization Problems (CSPs / COPs). A CP Portfolio Solver is a particular constraint solver that takes advantage of a portfolio of different CP solvers in order to solve a given problem by properly exploiting Algorithm Selection techniques. In this work we present sunny-cp: a CP portfolio for solving both CSPs and COPs that turned out to be competitive also in the MiniZinc Challenge, the reference competition for CP solvers

Portfolio Approaches for Constraint Optimization Problems

International audienceWithin the Constraints Satisfiability Problems (CSP) context, a methodology that has proved to be particularly performant consists in using a portfolio of different constraint solvers. Nevertheless, comparatively few studies and investigations has been done in the world of Constraint Optimization Problems (COP). In this work, we provide a generalization to COP as well as an empirical evaluation of different state of the art existing CSP portfolio approaches properly adapted to deal with COP. Experimental results confirm the effectiveness of portfolios even in the optimization field, and could give rise to some interesting future research

Efficiently Solving Repeated Integer Linear Programming Problems by Learning Solutions of Similar Linear Programming Problems using Boosting Trees

It is challenging to obtain online solutions of large-scale integer linear programming (ILP) problems that occur frequently in slightly different forms during planning for autonomous systems. We refer to such ILP problems as repeated ILP problems. The branch-and-bound (BAB) algorithm is commonly used to solve ILP problems, and a significant amount of computation time is expended in solving numerous relaxed linear programming (LP) problems at the nodes of the BAB trees. We observe that the relaxed LP problems, both within a particular BAB tree and across multiple trees for repeated ILP problems, are similar to each other in the sense that they contain almost the same number of constraints, similar objective function and constraint coefficients, and an identical number of decision variables. We present a boosting tree-based regression technique for learning a set of functions that map the objective function and the constraints to the decision variables of such a system of similar LP problems; this enables us to efficiently infer approximately optimal solutions of the repeated ILP problems. We provide theoretical performance guarantees on the predicted values and demonstrate the effectiveness of the algorithm in four representative domains involving a library of benchmark ILP problems, aircraft carrier deck scheduling, vehicle routing, and vehicle control

Combinatorial optimization through statistical instance-based learning

Different successful heuristic approaches have been proposed for solving combinatorial optimization problems. Commonly, each of them is specialized to serve a different purpose or address specific difficulties. However, most combinatorial problems that model real world applications have a priori well known measurable properties. Embedded machine learning methods may aid towards the recognition and utilization of these properties for the achievement of satisfactory solutions, In this paper we present a heuristic methodology which employs the instance-based machine learning paradigm, This methodology can be adequately configured for several types of optimization problems which are known to have certain properties. Experimental results are discussed concerning two well known problems, namely the knapsack problem and the set partitioning problem. These results show that the proposed approach is able to find significantly better solutions compared to intuitive search methods based on heuristics which are usually applied to the specific problems

Combinatorial Optimization through Statistical Instance-Based Learning

Different successful heuristic approaches have been proposed for solving combinatorial optimization problems. Commonly, each of them is specialized to serve a different purpose or address specific difficulties. However, most combinatorial problems that model real world applications have a priori well known measurable properties. Embedded machine learning methods may aid towards the recognition and utilization of these properties for the achievement of satisfactory solutions. In this paper, we present a heuristic methodology which employs the instance-based machine learning paradigm. This methodology can be adequately configured for several types of optimization problems which are known to have certain properties. Experimental results are discussed concerning two well known problems, namely the knapsack problem and the set partitioning problem. These results show that the proposed approach is able to find significantly better solutions compared to intuitive search methods based on heuristics which are usually applied to the specific problems. 1