Embedding Relaxations in Global Constraints for Solving TSP and TSPTW

Constraint Programming (CP) has been successfully applied to several combinatorial optimization problems. One of its advantages is the availability of complex global constraints performing efficient propagation and interacting with each other through shared variables. However, CP techniques have shown their limitations in dealing with optimization problems since the link between the objective function and problem decision variables is often quite loose and does not produce an effective propagation. We propose to integrate optimization components in global constraints, aimed at optimally solving a relaxation corresponding to the constraint itself. The optimal solution of the relaxation provides pieces of information which can be exploited in order to perform pruning on the basis of cost-based reasoning. In fact, we exploit reduction rules based on lower bound and reduced costs calculation to remove those branches which cannot improve the best solution found so far. The interest of integrating efficient well-known Operations Research (OR) algorithms into CP is mainly due to the smooth interaction between CP domain reduction and information provided by the relaxation acting on variable domains which can be seen as a communication channel among different techniques. We have applied this technique to symmetric and asymmetric Traveling Salesman Problem (TSP) instances both because the TSP is an interesting problem arising in many real-life applications, and because pure CP techniques lead to disappointing results for this problem. We have tested the proposed optimization constraints using ILOG solver. Computational results on benchmarks available from literature, and comparison with related approaches are described in the paper. The proposed method on pure TSPs improves the performances of CP solvers, but is still far from the OR state of the art techniques for solving the problem. However, due to the flexibility of the CP framework, we could easily use the same technique on TSP with Time Windows, a time constrained variant of the TSP. For this type of problem, we achieve results that are comparable with state of the art OR results.     

Mixed Global Constraints and Inference in Hybrid CLP–IP Solvers

The complementing strengths of Constraint (Logic) Programming (CLP) and Mixed Integer Programming (IP) have recently received significant attention. Although various optimization and constraint programming packages at a first glance seem to support mixed models, the modeling and solution techniques encapsulated are still rudimentary. Apart from exchanging bounds for variables and objective, little is known of what constitutes a good hybrid model and how a hybrid solver can utilize the complementary strengths of inference and relaxations. This paper adds to the field by identifying constraints as the essential link between CLP and IP and introduces an algorithm for bidirectional inference through these constraints. Together with new search strategies for hybrid solvers and cut-generating mixed global constraints, solution speed is improved over both traditional IP codes and newer mixed solvers.     

区间非线性路径约束的动态优化问题求解

本文研究路径约束中含有区间参数形式的动态优化问题,提出了一种新的非线性路径约束的确定化描述形式,和采用惩罚函数法的求解算法。对于转化后的极大极小优化命题,论文提出采用Lagrangian多项式加权和的方法得到有限维的确定性优化求解形式。该算法可有效地描述和求解不确定参数动态优化问题。     

不等式约束的非线性规划混合遗传算法

针对带不等式约束的非线性规划问题,提出了一个混合遗传算法。该算法分为全局探测和局部开采两个阶段,全局探测阶段是通过在有潜力的小生境内嵌入单纯形搜索,快速确定有前景的区域;而局部开采阶段则是在最有前景的区域进行单纯形搜索。该算法增强了局部搜索能力并同时保持种群的多样性,有效地解决了遗传算法的过早收敛和局部搜索能力弱的问题。典型非线性规划算例验证了混合算法的效率、精度和可靠性。     

Scheduling under Labour Resource Constraints

In this paper we introducean optimisation problem extracted from an industrial application:the scheduling problem under labour constraints. After givinga short summary of the origins of this problem and its mathematicalformulation, the different methods used for solving it (at leastpartially) are briefly described. In the last part, we presenta set of 25 instances of different sizes for benchmark purposes.So far, only 5 of these test instances have been solved to optimality,the others remaining open.     

Cost-Based Arc Consistency for Global Cardinality Constraints

A global cardinality constraint (gcc) is specified in terms of a set of variables X={x ₁,...,x _p} which take their values in a subset of V={v ₁,...,v _d}. It constrains the number of times each value v _iV is assigned to a variable in X to be in an interval [l _i,u _i]. A gcc with costs (costgcc) is a generalization of a gcc in which a cost is associated with each value of each variable. Then, each solution of the underlying gcc is associated with a global cost equal to the sum of the costs associated with the assigned values of the solution. A costgcc constrains the global cost to be less than a given value. Cardinality constraints with costs have proved very useful in many real-life problems, such as traveling salesman problems, scheduling, rostering, or resource allocation. For instance, they are useful for expressing preferences or for defining constraints such as a constraint on the sum of all different variables. In this paper, we present an efficient way of implementing arc consistency for a costgcc. We also study the incremental behavior of the proposed algorithm.     

Constructive Negation of Arithmetic Constraints Using Dataflow Graphs

A system which extracts a dataflow graph from sets of arithmetic constraints is described. This information is used to simplify constraints and to extract positive information from negations of constraints. The context for this work is a Prolog implementation where intervals are used to represent the underlying arithmetic variables. The system uses simple information about the existence of solutions of primitive constraints to derive the dataflow graph. This makes the system easily extensible to new primitives and domains. A practical implementation over both real and integer arithmetic is described and an extended example of its application given.     

Multiconsistency and Robustness with Global Constraints

We propose a natural generalization of arc-consistency, which we call multiconsistency: a value v in the domain of a variable x is k-multiconsistent with respect to a constraint C if there are at least k solutions to C in which x is assigned the value v. We present algorithms that determine which variable-value pairs are k-multiconsistent with respect to several well known global constraints. In addition, we show that finding super solutions is sometimes strictly harder than finding arbitrary solutions for these constraints and suggest multiconsistency as an alternative way to search for robust solutions.Supported by the Danish Research Agency (grant # 272-05-0081).Basic Research in Computer Science, funded by the Danish National Research Foundation.     

矩形毛坯排样中条带长度的约束处理

该文的排样问题是根据剪冲工艺的要求抽象出来的。剪冲工艺是指分两步将板材分割成毛坯:第一步用平剪床将板材切成条带;第二步采用剪或冲的方式,将条带切成毛坯。所考虑的工艺约束包括最小条带长度约束和最大条带长度约束,排样方式中条带的长度,必须在最小和最大条带长度约束值之间。该文对基本的动态规划算法加以改造,使之能够处理最小和最大条带长度约束,并在C++环境下,开发出同尺寸矩形毛坯排样系统UR。利用这个软件,进行了大量的例题测试,得出对生产实践具有指导意义的结论。     

Applying Ad-hoc Global Constraints with the {\tt case} Constraint to Still-Life

The Still-Life problem is challenging for CP techniques because the basic constraints of the game of Life are loose and give poor propagation for Still-Life. In this paper, we show how ad hoc global constraints can be customized to construct various models to provide much stronger propagation with CP solvers. Since we use custom ad hoc constraints of high arity where the number of tuples to define the constraint are large, the actual constraint representation becomes important to avoid excessive space consumption. We demonstrate how to use BDDs to construct good representations for the constraint which is critical for efficiency. Our results seem comparable to hybrid CP/IP models even though we are only using propagation albeit on ad hoc global constraints. This paper shows an extensive example of how to systematically build models using different kinds of ad hoc constraints. It also demonstrates the solving potential of ad hoc global constraints.     

Handling Global Constraints in Compiler Strategy

To achieve high-performance on processors featuring ILP, most compilers apply locally a set of heuristics. This leads to a potentially high-performance on separate code fragments. Unfortunately, most optimizations also increase code size, which may lead to a global net performance loss. In this paper, we propose a Global Constraints-Driven Strategy (GCDS) for guiding code optimization. When using GCDS, the final code optimization decision is taken according to global criteria rather than local criteria. For instance, such criteria might be performance, code size, instruction cache behavior, etc. The performance/code size trade-off is a particularly important problem for embedded systems. We show how GCDS can be used to master code size while optimizing performance.     

Semiring-Based CSPs and Valued CSPs: Frameworks, Properties, and Comparison

In this paper we describe and compare two frameworks for constraint solving where classical CSPs, fuzzy CSPs, weighted CSPs, partial constraint satisfaction, and others can be easily cast. One is based on a semiring, and the other one on a totally ordered commutative monoid. While comparing the two approaches, we show how to pass from one to the other one, and we discuss when this is possible. The two frameworks have been independently introduced in ijcai95,jacm and schiex-ijcai95.     

基于约束的调度研究和实现

运用约束程序设计(CP)思想和技术来调度正成为一个新兴的研究领域。文章首先对CP和调度的相关领域知识进行了简要介绍;然后按照CP所倡导的问题建模和问题求解相分离的思想,建立起一般理论调度问题的约束模型,并设计实现了一个基于约束的调度求解算法CBS-1;并对一些典型问题进行了实验,实验结果表明算法提高了约束调度求解的效率和通用性。     

Value Constraints in the CLP Scheme

We define value constraints, a method for incorporating constraint propagation into logic programming. It is a subscheme of the CLP scheme and is applicable wherever one has an efficient method for representing sets of possible values. As examples we present: small finite sets, sets of ground instances of a term, and intervals of reals with floating-point numbers as bounds. Value constraints are defined by distinguishing two storage management strategies in the CLP scheme. In value constraints the infer step of the CLP scheme is implemented by Waltz filtering. We give a semantics for value constraints in terms of set algebra that gives algebraic characterizations of local and global consistency. The existing extremal fixpoint characterization of chaotic iteration is shown to be applicable to prove convergence of Waltz filtering.     

Parametric Sequence Alignment with Constraints

Approximate matching techniques based on string alignment are important tools for investigating similarities between strings, such as those representing DNA and protein sequences. We propose a constraint based approach for parametric sequence alignment which allows for more general string alignment queries where the alignment cost can itself be parameterized as a query with some initial constraints. Thus, the costs need not be fixed in a parametric alignment query unlike the case in normal alignment. The basic dynamic programming string edit distance algorithm is generalized to a naive algorithm which uses inequalities to represent the alignment score. The naive algorithm is rather costly and the remainder of the paper develops an improvement which prunes alternatives where it can and approximates the alternatives otherwise. This reduces the number of inequalities significantly and strengthens the constraint representation with equalities. We present some preliminary results using parametric alignment on some general alignment queries.     

Dynamic PSO method for nonlinear constrained programming problems

A new approach is presented to solve the nonlinear constrained programming problems. Firstly, the nonlinear constrained programming problem is transformed into a bi-ohjective optimization problem. Based on the reasonable design of the searching operation and different parameters, a new dynamic particle swarm optimization algorithm （TS-MC） is proposed. The numerical experiments show that the proposed algorithm is effective in dealing with the nonlinear constrained programming problems.     

The progressive party problem: Integer linear programming and constraint programming compared

Many discrete optimization problems can be formulated as either integer linear programming problems or constraint satisfaction problems. Although ILP methods appear to be more powerful, sometimes constraint programming can solve these problems more quickly. This paper describes a problem in which the difference in performance between the two approaches was particularly marked, since a solution could not be found using ILP.The problem arose in the context of organizing a progressive party at a yachting rally. Some yachts were to be designated hosts; the crews of the remaining yachts would then visit the hosts for six successive half-hour periods. A guest crew could not revisit the same host, and two guest crews could not meet more than once. Additional constraints were imposed by the capacities of the host yachts and the crew sizes of the guests.Integer linear programming formulations which included all the constraints resulted in very large models, and despite trying several different strategies, all attempts to find a solution failed. Constraint programming was tried instead and solved the problem very quickly, with a little manual assistance. Reasons for the success of constraint programming in this problem are identified and discussed.     

分布式约束优化方法研究进展

多agent系统作为分布式人工智能研究领域的重要分支,已被广泛应用于多个领域中复杂系统的建模.而分布式约束优化作为一种多agent系统求解的关键技术,已成为约束推理研究的热点.首先对其适用性进行分析,并基于对已有算法的研究,总结出采用该方法解决问题的基本流程,在此基础上,从解的质量保证、求解策略等角度对算法进行了完整的分类;其次,根据算法分类结果以及执行机制,对大量经典以及近年来的分布式约束优化算法进行了深入分析,并从通信、求解质量、求解效率等方面对典型算法进行了实验对比;最后,结合分布式约束优化技术的求解优势给出了分布式约束优化问题的实际应用特征,总结了目前存在的一些问题,并对下一步工作进行了展望.     

Constraint Solving and Programming: What Next?

In this paper we advocate for more flexible and user-friendly constraint solving environments, as well as for constraint programming languages which have great expressive power while maintaining a formal semantics based on few crucial concepts. We cite some of our work in these directions and we hint at subjects of our future research.     

约束求解与优化技术的结合

提出了将混合约束问题转化为混合整数规划问题的方法.用约束求解方法及混合整数规划方法共同求解混合约束问题可以令二者相互借鉴,从而促进二者求解技术的进一步发展.同时,由混合约束问题转化而来的混合整数规划问题也可作为求解混合整数规划问题的测试问题（benchmarks）.