Over-constrained Problems Research Articles

Explanations for over-constrained problems using QuickXPlain with speculative executions

Explanations for over-constrained problems using QuickXPlain with speculative executions

Peeling Away Constraints: Horst Rittel's Method of Systematic Doubt and Its Application to Collective Creativity

Over-constrained design problems can be solved through a method of systematic doubt articulated by Horst Rittel in the 1970s. This method peels away constraints by negating phrases in a problem statement. The technique is amenable to parallelization, and thus might be used in collective creativity: crowds or communities could peel off constraints, and generate ideas in the modified design space, in parallel.

MiniBrass: Soft constraints for MiniZinc

Over-constrained problems are ubiquitous in real-world decision and optimization problems. Plenty of modeling formalisms for various problem domains involving soft constraints have been proposed, such as weighted, fuzzy, or probabilistic constraints. All of them were shown to be instances of algebraic structures. In terms of modeling languages, however, the field of soft constraints lags behind the state of the art in classical constraint optimization. We introduce MiniBrass, a versatile soft constraint modeling language building on the unifying algebraic framework of partially ordered valuation structures (PVS) that is implemented as an extension of MiniZinc and MiniSearch. We first demonstrate the adequacy of PVS to naturally augment partial orders with a combination operation as used in soft constraints. Moreover, we provide the most general construction of a c-semiring from an arbitrary PVS. Both arguments draw upon elements from category theory. MiniBrass turns these theoretical considerations into practice: It offers a generic extensible PVS type system, reusable implementations of specific soft constraint formalisms as PVS types, operators for complex PVS products, and morphisms to transform PVS. MiniBrass models are compiled into MiniZinc to benefit from the wide range of solvers supporting FlatZinc. We evaluated MiniBrass on 28 “softened” MiniZinc benchmark problems with six different solvers. The results demonstrate the feasibility of our approach.

Defining tools to address over-constrained geometric problems in Computer Aided Design

This paper proposes a new tool for decision support to address geometric over-constrained problems in Computer Aided Design (CAD). It concerns the declarative modeling of geometrical problems. The core of the coordinate free solver used to solve the Geometric Constraint Satisfaction Problem (GCSP) was developed previously by the authors. This research proposes a methodology based on Michelucci’s witness method to determine whether the structure of the problem is over-constrained. In this case, the authors propose a tool for assisting the designer in solving the over-constrained problem by ensuring the consistency of the specifications. An application of the methodology and tool is presented in an academic example.

A framework to model and manipulate constraints for over-constrained geographic applications

Geographic applications are often over-constrained because of the stakeholders' multiple requirements and the various spatial, alphanumeric and temporal constraints to be satisfied. In most cases, solving over-constrained problems is based on the relaxation of some constraints according to values of preferences. This article proposes the modelling and the management of constraints in order to provide a framework to integrate stakeholders in the expression and the relaxation of their constraints. Three families of constraints are defined: static vs. dynamic, intra-entity vs. inter-entities and intra-instance vs. inter-instances. Constraints are modelled from two points of view: system with the complexity in time of the different involved operators and user with stakeholders' preferences. The methodology of constraints relaxation is based on primitive, complex and derived operations. These operations allow a modification of the constraints in order to provide a relevant solution to a simulation. The developed system was applied to reduce the streaming/floods risks in the territory of Pays de Caux (Seine Maritime, France).

Global propagation of side constraints for solving over-constrained problems

This article deals with the resolution of over-constrained problems using constraint programming, which often imposes to add to the constraint network new side constraints. These side constraints control how the initial constraints of the model should be satisfied or violated, to obtain solutions that have a practical interest. They are specific to each application. In our experiments, we show the superiority of a framework where side constraints are encoded by global constraints on new domain variables, which are directly included into the model. The case-study is a cumulative scheduling problem with over-loads. The objective is to minimize the total amount of over-loads. We augment the Cumulative global constraint of the constraint programming solver Choco with sweep and task interval violation-based algorithms. We provide a theoretical and experimental comparison of the two main approaches for encoding over-constrained problems with side constraints.

Solving temporal over-constrained problems using fuzzy techniques

The satellite-scheduling problem represents an interesting field to test non-conventional temporal solvers because scheduling-problems are inherently over-constrained and, moreover, the tasks may b...

Exact Max-SAT solvers for over-constrained problems

We present a new generic problem solving approach for over-constrained problems based on Max-SAT. We first define a Boolean clausal form formalism, called soft CNF formulas, that deals with blocks of clauses instead of individual clauses, and that allows one to declare each block either as hard (i.e., must be satisfied by any solution) or soft (i.e., can be violated by some solution). We then present two Max-SAT solvers that find a truth assignment that satisfies all the hard blocks of clauses and the maximum number of soft blocks of clauses. Our solvers are branch and bound algorithms equipped with original lazy data structures, powerful inference techniques, good quality lower bounds, and original variable selection heuristics. Finally, we report an experimental investigation on a representative sample of instances (random 2-SAT, Max-CSP, graph coloring, pigeon hole and quasigroup completion) which provides experimental evidence that our approach is very competitive compared with the state-of-the-art approaches developed in the CSP and SAT communities.

Solving Hierarchical Constraints over Finite Domains with Local Search

Many real world problems have requirements and constraints which conflict with each other. One approach for dealing with such over-constrained problems is with constraint hierarchies. In the constraint hierarchy framework, constraints are classified into ranks, and appropriate solutions are selected using a comparator which takes into account the constraints and their ranks. In this paper, we present a local search solution to solving hierarchical constraint problems over finite domains (HCPs). This is an extension of local search for over-constrained integer programs WSAT(OIP) to constraint hierarchies and general finite domain constraints. The motivation for this work arose from solving large airport gate allocation problems. We show how gate allocation problems can be formulated as HCPs using typical gate allocation constraints. Using the gate allocation benchmarks, we investigate how constraint heirarchy selection strategies and the problem formulation using two models: a 0–1 linear constraint hierarchy model and a nonlinear finite domain constraint hierarchy model.

Current Approaches for Solving Over-Constrained Problems

We summarize existing approaches to model and solve overconstrained problems. These problems are usually formulated as combinatorial optimization problems, and different specific and generic formalisms are discussed, including the special case of multi-objective optimization. Regarding solving methods, both systematic and local search approaches are considered. Finally we review a number of case studies on overconstrained problems taken from the specialized literature.

Partition-Based Lower Bound for Max-CSP

In this paper we address Max-CSP, a constraint optimization problem typically solved using a branch and bound scheme. It is well known that the efficiency of branch and bound greatly depends on the quality of the available lower bound. Previous approaches aggregate to the lower bound individual contributions of unassigned variables. In this paper, we augment this approach by adding global contributions of disjoint subsets of unassigned variables, which requires a partition of the set of unassigned variables. Using this idea, we introduce the i>partition-based lower bound. It improves previous approaches based on individual contributions in the sense that our method can be i>added up to previous bounds, possibly increasing their value. We demonstrate our method presenting two new algorithms, PFC-PRDAC and PFC-MPRDAC, which are the natural successors of PFC-RDAC and PFC-MRDAC augmented with our approach. We provide experimental evidence for the superiority of the new algorithms on random problems and real instances of weighted over-constrained problems.

MMC – a new numerical approach to the kinematics of complex manipulators

A numerical approach (MMC-model; MMC – mean of multiple computations) is proposed for solving the kinematics of manipulators of nearly arbitrary configuration. It is applicable to serial, parallel and hybrid-chain-manipulators (HCMs). Even changing configurations of the manipulator are possible, because the structural analysis of the current manipulator configuration is done automatically. This approach does not make a strict distinction between the direct and inverse kinematics, but solves both tasks as well as mixed control tasks in a single model. With a slight modification over-constrained problems can also be solved. These properties make the model especially suitable for the simulation of reconfigurable HCMs. The advantages of the MMC-model arise from splitting the structural analysis into two parts. The first, linear part performs the topological analysis without any constraints. Only this part performs the numerical approximation. The second, generally non-linear part adds the constraints and thus allows versatile control of the movement without changing the equations of the approximation procedure in the first part. After a general description of the model we present a hexapod walking system as a complex application of a HCM.

People

This paper proposes a new tool for decision support to address geometric over-constrained problems in Computer Aided Design (CAD). It concerns the declarative modeling of geometrical problems. The core of the coordinate free solver used to solve the Geometric Constraint Satisfaction Problem (GCSP) was developed previously by the authors. This research proposes a methodology based on Michelucci’s witness method to determine whether the structure of the problem is over-constrained. In this case, the authors propose a tool for assisting the designer in solving the over-constrained problem by ensuring the consistency of the specifications. An application of the methodology and tool is presented in an academic example.

Solving Over-Constrained Satellite Remote-Sensing Scheduling Problems

Abstract The high demand for satellite imagery and the relative scarcity of commercial imaging satellites combine to produce scheduling problems in which one or more of the resources is over constrained. Over-constrained scheduling problems can be problematic for constraint programming methods because of the overhead associated with propagating constraints and because of the time spent backtracking over a large number of tasks that are very unlikely to be scheduled. For this reason, we have developed and evaluated a hybrid scheduling method that we call priority segmentation. Priority segmentation breaks the problem up into sub-problems based on the priority of the tasks, finds an optimal solution to each sub-problem, and then combines the sub-problem solutions. We present preliminary results evaluating this approach for different sub-problem sizes on randomly generated satellite imaging problems. Our preliminary results indicate that priority segmentation produces solutions that are an improvement over a greedy solution when the problems are highly over constrained. When the problems are only slightly over constrained, the amount of improvement over greedy is very small. Although this approach has provided satisfactory results for our customers' highly over-constrained problems, we are pursuing alternative methods that provide better performance; both in terms of expected solution quality and computational requirements.

Approximate algorithms for generalized maximum utility problems

. Some constraint satisfaction problems are over-constrained, i.e. it is impossible to find a solution that would satisfy all the constraints. In such situations one often assigns some weights (utilities) to constraints and looks for solutions that maximize the sum of the weights of satisfied constraints. The problem of finding such solutions is referred to as the maximum utility problem (MUP). Sometimes one allows weights to depend on values of variables involved in the constraints, i.e. the utility of each constraint is a function of the corresponding variables. This generalized version of MUP, GMUP, provides a powerful framework for expressing preferences on solutions of over-constrained problems. This paper presents a number of very effective approximate algorithms for solving both MUPs and GMUPs. The algorithms presented are local search procedures that are guided by the expected value (in a probabilistic sense) of the utility of a solution that can be achieved by expanding the current (partial) solution randomly. Results of numerous tests demonstrate the high performance of this approach: the algorithms are very fast and the quality of the generated solutions is high.

A Novel Search Technique for Solving Over-Constrained Problems

In many applications, such as decision support, negotiation, planning, scheduling, etc., one needs to express requirements that can be only partially satisfied. In order to express such requirements, we propose a technique called forward-tracking. Intuitively, forward-tracking is a kind of dual of chronological back-tracking: if a program globally fails to find a solution, then a new execution is started from a program point and a state 'forward' in the computation tree. This search technique is applied to the specific paradigm of constraint logic programming, obtaining a powerful extension that preserves all the useful properties of the original scheme. We report on the successful practical application of forward-tracking to the evolutionary training of (constrained) neural networks, and discuss other interesting applications.

The Houria Constraint Solver

The Houria constraint solver is an efficient incremental algorithm that uses local propagation to maintain sets of required and preferential constraints. Houria represents constraints between variables by sets of short procedures (methods) and incrementally resatisftes the set of constraints when individual constraints are added and removed. The criterion of comparison used in Houria is more powerful than that of some other solvers. Houria is used to construct a graph of methods by planning and executing all these methods to found a best solution. The solution found by Houria satisfies more constraints than the one produced by some other solvers and that for the same over-constrained problems while respecting the hierarchy.