Meinolf Sellmann

InsideOpt · Network Optimization

Reinforcement learning (RL) has seen increasing success at solving a variety of combinatorial optimization problems. These techniques have generally been applied to deterministic optimization problems with few side constraints, such as the traveling salesperson problem (TSP) or capacitated vehicle routing problem (CVRP). With this in mind, the rece...

Algorithm configuration has emerged as an essential technology for the improvement of high-performance solvers. We present new algorithmic ideas to improve state-of-the-art solver configurators automatically by tuning. Particularly, we introduce 1. a forward-simulation method to improve parallel performance, 2. an improvement to the configuration p...

This paper reports on the first international competition on AI for the traveling salesman problem (TSP) at the International Joint Conference on Artificial Intelligence 2021 (IJCAI-21). The TSP is one of the classical combinatorial optimization problems, with many variants inspired by real-world applications. This first competition asked the parti...

We consider black-box optimization in which only an extremely limited number of function evaluations, on the order of around 100, are affordable and the function evaluations must be performed in even fewer batches of a limited number of parallel trials. This is a typical scenario when optimizing variable settings that are very costly to evaluate, f...

We present a dynamic branching scheme for set partitioning problems. The idea is to trace features of the underlying MIP model and to base search decisions on the features of the current subproblem to be solved. We show how such a system can be trained efficiently by introducing minimal learning bias that traditional model-based machine learning ap...

We present PyDGGA, a Python tool that implements a distributed version of the automatic algorithm configurator GGA, which is a specialized genetic algorithm to find high quality parameters for solvers and algorithms. PyDGGA implements GGA using an event-driven architecture and runs a simulation of future generations of the genetic algorithm to maxi...

We consider black-box optimization in which only an extremely limited number of function evaluations, on the order of around 100, are affordable and the function evaluations must be performed in even fewer batches of a limited number of parallel trials. This is a typical scenario when optimizing variable settings that are very costly to evaluate, f...

We consider the dynamic classifier selection (DCS) problem: Given an ensemble of classifiers, we are to choose which classifier to use depending on the particular input vector that we get to classify. The problem is a special case of the general algorithm selection problem where we have multiple different algorithms we can employ to process a given...

We consider the dialectic search paradigm for box-constrained, non-linear optimization with heterogeneous variable types. In particular, we devise an implementation that can handle any computable objective function, including non-linear, non-convex, non-differentiable, non-continuous, non-separable and multi-modal functions. The variable types we c...

We present a new methodology for assessing when data-based predictive models can be trusted. Particularly, we propose to learn a model from experimentation that determines, for a given labeled data set and a learning technique, when the model generated by the respective technique on the given data can be trusted to perform within specified accuracy...

We propose a new framework for decision making under uncertainty to overcome the main drawbacks of current technology: modeling complexity, scenario generation, and scaling limitations. We consider three NP-hard optimization problems: the Stochastic Knapsack Problem (SKP), the Stochastic Shortest Path Problem (SSPP), and the Resource Constrained Pr...

We propose a new framework for decision making under uncertainty to overcome the main drawbacks of current technology: modeling complexity, scenario generation, and scaling limitations. We consider three NP-hard optimization problems: the Stochastic Knapsack Problem (SKP), the Stochastic Shortest Path Problem (SSPP), and the Resource Constrained Pr...

We consider the task of aggregating scores provided by experts that each have scored only a subset of all objects to be rated. Since experts only see a subset of all objects, they lack global information on the overall quality of all objects, as well as the global range in quality. Inherently, the only reliable information we get from experts is th...

Local search metaheuristics have been developed as a general tool for solving hard combinatorial search problems. However, in practice, metaheuristics very rarely work straight out of the box. An expert is frequently needed to experiment with an approach and tweak parameters, remodel the problem, and adjust search concepts to achieve a reasonably e...

We revisit algorithm selection for declarative programming solvers. We introduce two main ideas to improve cost-sensitive hierarchical clustering: First, to augment the portfolio builder with a self-configuration component. And second, we propose that the algorithm selector assesses the confidence level of its own prediction, so that a more defensi...

Building on the recent success of bet-and-run approaches for restarted local search solvers, we introduce the idea of learning online adaptive restart strategies. Universal restart strategies deploy a fixed schedule that runs with utter disregard of the characteristics that each individual run exhibits. Whether a run looks promising or abysmal, it...

Metaheuristics have been developed to provide general purpose approaches for solving hard combinatorial problems. While these frameworks often serve as the starting point for the development of problem-specific search procedures, they very rarely work efficiently in their default state. We combine the ideas of reactive search, which adjusts key par...

Metaheuristics have been developed to provide general purpose approaches for solving hard combinatorial problems. While these frameworks often serve as the starting point for the development of problem-specific search procedures, they very rarely work efficiently in their default state. We combine the ideas of reactive search, which adjusts key par...

A brief overview of algorithms that improve other algorithms and their role in cognitive computing.

This book constitutes the thoroughly refereed post-conference proceedings of the 10th International Conference on Learning and Optimization, LION 10, which was held on Ischia, Italy, in May/June 2016. The 14 full papers presented together with 9 short papers and 2 GENOPT papers were carefully reviewed and selected from 47 submissions. The papers ad...

We develop a new approach for a pre-disaster planning problem which consists in computing an optimal investment plan to strengthen a transportation network, given that a future disaster probabilistically destroys links in the network. We show how the problem can be formulated as a non-linear integer program and devise an AI algorithm to solve it. I...

Our objective is to boost the state-of-the-art performance in MaxSAT solving. To this end, we employ the instance-specific algorithm configurator ISAC, and improve it with the latest in portfolio technology. Experimental results on SAT show that this combination marks a significant step forward in our ability to tune algorithms instance-specificall...

We consider the problem of parallelizing restarted backtrack search. With few notable exceptions, most commercial and academic constraint programming solvers do not learn no-goods during search. Depending on the branching heuristics used, this means that there are little to no side-effects between restarts, making them an excellent target for paral...

Our objective is to boost the state-of-the-art performance in MaxSATsolving. To this end, we employ the instance-specific algorithmconfigurator ISAC, and improve it with the latest inportfolio technology. Experimental results on SAT show that thiscombination marks a significant step forward in our ability to tunealgorithms instance-specifically. We...

Different solution approaches for combinatorial problems often exhibit incomparable performance that depends on the concrete problem instance to be solved. Algorithm portfolios aim to combine the strengths of multiple algorithmic approaches by training a classifier that selects or schedules solvers dependent on the given instance. We de-vise a new...

Algorithm portfolios try to combine the strength of individual algorithms to tackle a problem instance at hand with the most suitable technique. In the context of SAT the effectiveness of such approaches is often demonstrated at the SAT Competitions. In this paper we show that a competitive algorithm portfolio can be designed in an extremely simple...

Sequential algorithm portfolios for satisfiability testing (SAT), such as SATzilla and 3S, have enjoyed much success in the last decade. By leveraging the differing strengths of individual SAT solvers, portfolios employing older solvers have often fared as well or better than newly designed ones, in several categories of the annual SAT Competitions...

In [3], SAT conflict analysis graphs were used to learn additional clauses, which we refer to as back-clauses. These clauses may be viewed as enabling the powerful notion of "probing": Back-clauses make inferences that would normally have to be deduced by setting a variable deliberately the other way and observing that unit propagation leads to a c...

Instance-specific algorithm configuration generalizes both instance-oblivious algorithm tuning as well as algorithm portfolio generation. ISAC is a recently proposed non-model-based approach for tuning solver parameters de-pendent on the specific instance that needs to be solved. While ISAC has been compared with instance-oblivious algorithm tuning...

We present a dynamic branching scheme for set partitioning problems. The idea is to trace features of the underlying MIP model and to base search decisions on the features of the current subproblem to be solved. We show how such a system can be trained efficiently by introducing minimal learning bias that traditional model-based machine learning ap...

Combining differing solution approaches by means of solver portfolios has proven as a highly effective technique for boosting solver performance. We consider the problem of generating parallel SAT solver portfolios. Our approach is based on a recently introduced sequential SAT solver portfolio that excelled at the last SAT competition. We show how...

We present a simple modification to the idea of impact-based search which has proven highly effective for several applications. Impacts measure the average reduction in search space due to propagation after a variable assignment has been committed. Rather than considering the mean reduction only, we consider the idea of incorporating the variance i...

We formulate a general framework for pseudo-Boolean multi-valued nogood-learning, generalizing conflict analysis performed by modern SAT solvers and its recent extension for disjunctions of multi-valued variables. This framework can handle more general constraints as well as different domain representations, such as interval domains which are commo...

When tackling a computationally challenging combinatorial problem, one often observes that some solution approaches work well on some instances, while other approaches work better on other instances. This observation has given rise to the idea of building algorithm portfolios [5]. Leyton-Brown et al. [1], for instance, proposed to select one of the...

We formulate a general framework for pseudo-Boolean multi-valued nogood-learning, generalizing conflict analysis performed by modern SAT solvers and its recent extension for disjunctions of multi-valued variables. This framework can handle more general constraints as well as different domain representations, such as interval domains which are commo...

Algorithm portfolios aim to increase the robustness of our ability to solve problems efficiently. While recently proposed algorithm selection methods come ever closer to identifying the most appropriate solver given an input instance, they are bound to make wrong and, at times, costly decisions. Solver scheduling has been proposed to boost the perf...

We present a new complete multi-valued SAT solver, based on current state-of-the-art SAT technology. It features watched literal propagation and conflict driven clause learning. We combine this technology with state-of-the-art CP methods for branching and introduce quantitative supports which augment the watched literal scheme with a watched domain...

We present a highly efficient incremental algorithm for propagating bounded knapsack constraints. Our algorithm is based on the sublinear filtering algorithm for binary knapsack constraints by Katriel et al. and achieves similar speed-ups of one to two orders of magnitude when compared with its linear-time counterpart. We also show that the represe...

With the introduction of the Regular Membership Constraint, a new line of research has opened where constraints are based on formal languages. This paper is taking the next step, namely to investigate constraints based on grammars higher up in the Chomsky hierarchy. We devise a time- and space-efficient incremental arc-consistency algorithm for con...

We present a new method to compute upper bounds of the number of solutions of binary integer programming (BIP) problems. Given a BIP, we create a dynamic programming (DP) table for a redundant knapsack constraint which is obtained by surrogate relaxation. We then consider a Lagrangian relaxation of the original problem to obtain an initial weight b...

We propose a framework which we call stochastic off-line programming (SOP). The idea is to embed the development of combinatorial algorithms in an off-line learning environment which helps the developer choose heuristic advisors that guide the search for satisfying or optimal solutions. In particular, we consider the case where the developer has se...

We present a new method for instance-specific algorithm configuration (ISAC). It is based on the integration of the algorithm configuration system GGA and the recently proposed stochastic off- line programming paradigm. ISAC is provided a solver with cate- gorical, ordinal, and/or continuous parameters, a training benchmark set of input instances f...

We present a highly efficient incremental algorithm for propagating bounded knapsack constraints. Our algorithm is based on the sublinear filtering algorithm for binary knapsack constraints by Katriel et at. and achieves similar speed-ups of one to two orders of magnitude when compared with its linear-time counterpart. We also show that the represe...

In recent years, symmetry breaking for constraint satisfaction problems (CSPs) has attracted considerable attention. Various general schemes have been proposed to eliminate symmetries. In general, these schemes may,take exponential space or time to eliminate all the symmetries. We identify several classes of CSPs that encompass,many practical probl...

Inference in constraint programming is usually based on the deductions generated by individual constraints which are then communicatedto other constraintsthroughdomain filtering. Frequentlywe findthat thisis a toocoarse-grained form of communication since constraints could exchange more powerful forms of deductions that could help reduce thesearche...

The length-lex representation for set variables orders all subsets of a given universe of values according to cardinality and lexicography. To achieve length-lex bounds consistency for Knapsack constraints it has been proposed to decompose the constraint into two sum constraints. We provide theoretical and practical evidence which shows that decomp...

A problem that is inherent to the development and efficient use of solvers is that of tuning parameters. The CP community has a long history of ad- dressing this task automatically. We propose a robust, inherently parallel genetic algorithm for the problem of configuring solvers automatically. In order to cope with the high costs of evaluating the...

We introduce Hegel and Fichte’s dialectic as a search meta-heuristic for constraint satisfaction and optimization. Dialectic is an appealing mental concept for local search as it tightly integrates and yet clearly marks off of one another the two most important aspects of local search algorithms, search space exploration and exploitation. We believ...

The AllDifferent constraint was one of the first global constraints [17] and it enforces the conjunction of one binary constraint, the not-equal constraint, for every pair of variables. By looking at the set of all pairwise not-equal relations at the same time, AllDifferent offers greater filtering power. The natural question arises whether we can...

We reconsider the idea of structural symmetry breaking for constraint satisfaction problems (CSPs). We show that the dynamic dominance checks used in symmetry breaking by dominance-detection search for CSPs with piecewise variable and value symmetries have a static counterpart: there exists a set of constraints that can be posted at the root node a...

We introduce the automatic recording constraint (ARC) that can be used to model and solve scheduling problems where tasks may not overlap in time and the tasks linearly exhaust some resource. Since achieving generalized arc-consistency for the ARC is NP-hard, we develop a filtering algorithm that achieves approximated consistency only. Numerical re...

We propose exact hybrid methods based on integer linear programming (ILP) and constraint programming (CP) for an integrated employee timetabling and job-shop scheduling problem. Each method we investigate uses a CP formulation associated with an LP relaxation. ...

Context-free grammar constraints enforce that a sequence of variables forms a word in a language defined by a context-free grammar. T he constraint has received a lot of attention in the last few years as it repr esents an effective and highly expressive modeling entity. Its application has been studied in the field of Constraint Programming, Mixed...

There has been considerable interest in the identification of structural properties of combinatorial problems that lead, directly or in-directly, to the development of efficient algorithms for solving them. One such concept is that of a backdoor set—a set of variables such that once they are instantiated, the remaining problem simplifies to a tract...

We propose a framework which we call stochastic off-line programming (SOP). The idea is to embed the development of combinatorial algorithms in an off-line learning environment which helps the developer choose heuristic advisors that guide the search for satisfying or optimal solutions. In particular, we consider the case where the developer has se...

Recently, a new domain store for set-variables has been proposed which totally orders all values in the domain of a set-variable based on cardinality and lexicography. Traditionally, knapsack constraints have been studied with respect to the required and possible set domain representation. For this domain-store efficient filtering algorithms achiev...

There exist various methods to break symmetries. The two that concern us in this paper are static symmetry breaking where we add static constraints to the problem (see e.g. [1,3]) and symmetry breaking by dominance detection (SBDD) where we filter values based on a symmetric dominance analysis when comparing the current searchnode with those that w...

We devise a theoretical model for dichotomic search algo- rithms for constrained optimization. We show that, within our model, a certain way of choosing the breaking point minimizes both expected as well as worst case performance in a skewed binary search. Further- more, we show that our protocol is optimal in the expected and in the worst case. Ex...

We correct a result that we recently published in this conference series on the polytope of Binary Constraint Problems (BCPs). We had claimed that the so-called "support formulation" would characterize the convex hull of all feasible solutions to tree-structured BCPs. We show that this claim is not accurate by providing a small counter example. We...

Theoretical models for the evaluation of quickly improving search strategies, like limited discrepancy search, are based on specific assum ptions re- garding the probability that a value selection heuristic makes a correct pre diction. We provide an extensive empirical evaluation of value selection heuristics for knapsack problems. We investigate h...

With the introduction of constraints based on finite automata a new line of research has opened where constraints are based on formal languages. Recently, constraints based on grammars higher up in the Chomsky hierarchy were intro- duced. We devise a time- and space-efficient incremental arc-consistency algorithm for context-free grammars. Partic-...

Spatial heterogeneity in fields may affect the outcome of experiments. The conventional randomized allocation of treatments to plots may cause bias and variable precision in the presence of trends (including periodicity) and spatial autocorrelation. Agricultural scientists appear to mostly use conventional experimental designs that are susceptible...

Many real world problems, e.g. personnel scheduling and transportation planning, can be modeled naturally as Constrained Shortest Path Problems (CSPPs), i.e., as Shortest Path Problems with additional constraints. A well studied problem in this class is the Resource Constrained Shortest Path Problem. Reduction techniques are vital ingredients of so...

We show how to efficiently model binary constraint problems ( BCP) as integer programs. After considering tree-structured BCPs first, we show that a Sherali-Adams-like procedure results in a polynomial-size linear programming description of the convex hull of all integer feasible solut ions when the BCP that is given has bounded tree-width.

We develop an efficient incremental version of an existing cost-based filtering algorithm for the knapsack constraint. On a universe of n elements, m invocations of the algorithm require a total of O(n log n+mk log(n/k)) time, where k ≤ n depends on the specific knapsack instance. We show that the expected value of k is significantly smaller than n...

Symmetry breaking by dominance detection (SBDD) [4,6,1,12], has proven to excel on problems that contain large symmetry groups. The core task of SBDD is the dominance detection algorithm. The first automated dominance detection algorithms were based on group theory [7], while the first provably polynomial-time dominance checkers for specific types...

We reconsider the idea of structural symmetry breaking (SSB) for constraint satisfaction problems (CSPs). We show that the dynamic dominance checks used in symmetry breaking by dominance-detection search for CSPs with piecewise variable and value symmetries have a static counterpart: there exists a set of constraints that can be posted at the root...

By introducing the Regular Membership Constraint, Gilles Pesant pi- oneered the idea of basing constraints on formal languages. The paper presented here is highly motivated by this work, taking the obvious next step, namely to investigate constraints based on grammars higher up in the Chomsky hierarchy. We devise an arc-consistency algorithm for co...

We address the following dilemma: When making decisions in real life, we often face the problem that, while we have time to contemplate about a problem, we are not entirely sure what the exact parameters of our problem will be. And, on the other hand, as soon as the real world is revealed to us, we need to act quickly and have no more time to rethi...

We present a theoretical study on the idea of using mathematical programming relaxations for filtering binary constraint satisfaction problems. We introduce the consistent value polytope and give a linear programming description that is provably tighter than a recently studied formulation. We then provide an experimental study that shows that, desp...

A hybrid algorithm is devised to boost the performance of complete search on under-constrained problems. We suggest to use random variable selection in combination with restarts, augmented by a coarse-grained local search algorithm that learns favorable value heuristics over the course of several restarts. Numerical results show that this method ca...

In constraint optimization, global constraints play a decisive role. To develop an efficient optimization tool, we need to be able to assess whether we are still able to improve the objective function further. This observation has lead to the development of a special kind of global constraints, so-called optimization constraints [2,5]. Roughly spea...

Recently, new cost-based filtering algorithms for shorter-path con- straints have been developed. However, so far only the theoretical properties of shorter-path constraint filtering have been studied. We provide the first extensive experimental evaluation of the new algorithms in the context of the resource con- strained shortest path problem. We...

Symmetry breaking has been shown to be an im- portant method to speed up the search in con- straint satisfaction problems that contain symme- try. When breaking symmetry by dominance detec- tion, a computationally efficient symmetry break- ing scheme can be achieved if we can solve the dominance detection problem in polynomial time. We study the co...

We introduce a new approach for focusing constraint rea-soning using so-called streamlining constraints. Such constraints parti-tion the solution space to drive the search first towards a small and structured combinatorial subspace. The streamlining constraints capture regularities observed in a subset of the solutions to smaller problem in-stances...

CP-based Lagrangian Relaxation allows us to reason on local substructures while maintaining a global view on an entire optimization problem. While the idea of cost-based filtering with respect to systematically changing objective functions has been around for more than three years now, so far some important observations have not been explained. In...

The development of the theory and construction of combinatorial designs originated with the work of Euler on Latin squares. A Latin square on symbols is an matrix ( is the order of the Latin square), in which each symbol occurs precisely once in each row and in each column. Several interesting research questions posed by Euler with respect to Latin...

Knapsack constraints are a key modeling structure in dis- crete optimization and form the core of many real-life prob- lem formulations. Only recently, a cost-based filtering algo- rithm for Knapsack constraints was published that is based on some previously developed approximation algorithms for the Knapsack problem. In this paper, we provide an e...

Many real world problems, e.g. in personnel scheduling and transportation planning, can be modeled naturally as Constrained Shortest Path Problems (CSPPs), i.e., as Shortest Path Problems with additional constraints. A well studied problem in this class is the Resource Constrained Shortest Path Problem. Reduction techniques are vital ingredients of...

While global constraints give a broader view on the entire problem and therefore allow more effective constraint propagation, the development of efficient generalized arc-consistency (GAC) algorithms for global constraints is frequently prevented by the fact that the associated decision problems are NP-hard. A prominent example for this is the Knap...

We present a fully polynomial-time approximation scheme for a mul- ticommodity flow problem that yields lower bounds of the graph bisection prob- lem. We compare the approximation algorithm with Lagrangian relaxation based cost-decomposition approaches and linear programming software when embed- ded in an exact branch&bound approach for graph bisec...

For NP-hard constraint satisfaction problems the existence of a feasible solution cannot be decided eciently. Applying a tree search often results in the exploration of parts of the search space that do not contain feasible solutions at all. Redundant constraints can help to detect inconsistencies of partial assignments higher up in the search tree...

Whereas CP methods are strong with respect to the detection of local infeasibilities, OR approaches have powerful optimization abilities that ground on tight global bounds on the objective. An integration of propagation ideas from CP and Lagrangian relaxation techniques from OR combines the merits of both approaches. We introduce a general way of h...

We present a branch-and-bound approach for the Capacitated Net- work Design Problem. We focus on tightening strategies such as variable fixing and local cuts that can be applied in every search node. Different variable fix- ing algorithms based on Lagrangian relaxations are evaluated solitarily and in combined versions. Moreover, we develop cardina...

Historically, discrete minimization problems in constrained logical programming were modeled with the help of an isolated bounding constraint on the objective that is to be decreased. To overcome this frequently inefficient way of searching for improving solutions, the notion of optimization constraints was introduced. Optimization constraints can...

For NP-hard constraint satisfaction problems the existence of a feasible solution cannot be decided efficiently. Applying a tree search often results in the exploration of parts of the search space that do not contain feasible solutions at all. Redundant constraints can help to detect inconsistencies of partial assignments higher up in the search t...

We present cost based filtering methods for Knapsack Problems (KPs). Cost based filtering aims at fixing variables with respect to the objective function. It is an important technique when solving complex problems such as Quadratic Knapsack Problems, or KPs with additional constraints (Constrained Knapsack Problems (CKPs)). They evolve, e.g., when...