Michela Milano

Cost-Based Domain Filtering

Constraint propagation is aimed at removing from variable domains combinations of values which cannot appear in any consistent solution. Pruning derives from feasibility reasoning. When coping with optimization problems, pruning can be performed also on the basis of costs, i.e., optimality reasoning. Propagation can be aimed at removing combination of values which cannot lead to solutions whose cost is better then the best one found so far. For this purpose, we embed in global constraints optimization components representing suitable relaxations of the constraint itself. These components provide efficient Operations Research algorithms computing the optimal solution of the relaxed problem and a gradient function representing the estimated cost of each variable-value assignment. We exploit these pieces of information for pruning and for guiding the search. We have applied these techniques to a couple of ILOG Solver global constraints (a constraint of difference and a path constraint) and tested the approach on a variety of combinatorial optimization problems such as Timetabling, Travelling Salesman Problems and Scheduling Problems with setup. Comparisons with pure Constraint Programming approaches and related literature clearly show the benefits of the proposed approach. By using cost-based filtering in global constraints, we can optimally solve problems that are one order of magnitude greater than those solved by pure CP approaches, and we outperform other hybrid approaches integrating OR techniques in Constraint Programming.

A Hybrid Exact Algorithm for the TSPTW

TheTraveling Salesman Problem with Time Windows (TSPTW) is the problem of finding a minimum-cost path visiting a set of cities exactly once, where each city must be visited within a specific time window. We propose a hybrid approach for solving the TSPTW that merges Constraint Programming propagation algorithms for the feasibility viewpoint (find a path), and Operations Research techniques for coping with the optimization perspective (find the best path). We show with extensive computational results that the synergy between Operations Research optimization techniques embedded in global constraints, and Constraint Programming constraint solving techniques, makes the resulting framework effective in the TSPTW context also if these results are compared with state-of-the-art algorithms from the literature.

Communication-aware allocation and scheduling framework for stream-oriented multi-processor systems-on-chip

This paper proposes a complete allocation and scheduling framework, where an MPSoC virtual platform is used to accurately derive input parameters, validate abstract models of system components and assess constraint satisfaction and objective function optimization. The optimizer implements an efficient and exact approach to allocation and scheduling based on problem decomposition. The allocation subproblem is solved through integer programming while the scheduling one through constraint programming. The two solvers can interact by means of no-good generation, thus building an iterative procedure which has been proven to converge to the optimal solution. Experimental results show significant speedups w.r.t. pure IP and CP exact solution strategies as well as high accuracy with respect to cycle accurate functional simulation. A case study further demonstrates the practical viability of our framework for real-life systems and applications

MAGMA: a multiagent architecture for metaheuristics

In this work, we introduce a multiagent architecture called the MultiAGent Metaheuristic Architecture (MAGMA) conceived as a conceptual and practical framework for metaheuristic algorithms. Metaheuristics can be seen as the result of the interaction among different kinds of agents: The basic architecture contains three levels, each hosting one or more agents. Level-0 agents build solutions, level-1 agents improve solutions, and level-2 agents provide the high level strategy. In this framework, classical metaheuristic algorithms can be smoothly accommodated and extended. The basic three level architecture can be enhanced with the introduction of a fourth level of agents (level-3 agents) coordinating lower level agents. With this additional level, MAGMA can also describe, in a uniform way, cooperative search and, in general, any combination of metaheuristics. We describe the entire architecture, the structure of agents in each level in terms of tuples, and the structure of their coordination as a labeled transition system. We propose this perspective with the aim to achieve a better and clearer understanding of metaheuristics, obtain hybrid algorithms, suggest guidelines for a software engineering-oriented implementation and for didactic purposes. Some specializations of the general architecture will be provided in order to show that existing metaheuristics [e.g., greedy randomized adaptive procedure (GRASP), ant colony optimization (ACO), iterated local search (ILS), memetic algorithms (MAs)] can be easily described in our framework. We describe cooperative search and large neighborhood search (LNS) in the proposed framework exploiting level-3 agents. We show also that a simple hybrid algorithm, called guided restart ILS, can be easily conceived as a combination of existing components in our framework.

Allocation and scheduling for MPSoCs via decomposition and no-good generation

This paper describes an efficient, complete approach for solving a complex allocation and scheduling problem for Multi-Processor System-on-Chip (MPSoC). Given a throughput constraint for a target application characterized as a task graph annotated with computation, communication and storage requirements, we compute an allocation and schedule which minimizes communication cost first, and then the makespan given the minimal communication cost. Our approach is based on problem decomposition where the allocation is solved through an Integer Programming solver, while the scheduling through a Constraint Programming solver. The two solvers are interleaved and their interaction regulated by no-good generation. Experimental results show speedups of orders of magnitude w.r.t. pure IP and CP solution strategies.

An efficient and complete approach for throughput-maximal SDF allocation and scheduling on multi-core platforms

Our work focuses on allocating and scheduling a synchronous data-flow (SDF) graph onto a multi-core platform subject to a minimum throughput requirement. This problem has traditionally be tackled by incomplete approaches based on problem decomposition and local search, which could not guarantee optimality. Exact algorithms used to be considered reasonable only for small problem instances. We propose a complete algorithm based on Constraint Programming which solves the allocation and scheduling problem as a whole. We introduce a number of search acceleration techniques that significantly reduce run-time by aggressively pruning the search space without compromising optimality. The solver has been tested on a number of non-trivial instances and demonstrated promising run-times on SDFGs of practical size and one order of magnitude speed-up w.r.t. the fastest known complete approach.

Optimization-Oriented Global Constraints

In this paper, we propose a way of exploiting Operations Research techniques within global constraints for cost-based domain filtering. In Constraint Programming, constraint propagation is aimed at removing from variable domains combinations of values which are proven infeasible. Pruning derives from feasibility reasoning. When coping with optimization problems, pruning can be performed also on the basis of costs, i.e., optimality reasoning. Cost-based filtering removes combination of values which are proven sub-optimal. For this purpose, we encapsulate in global constraints optimization components representing suitable relaxations of the constraint itself. These components embed efficient Operations Research algorithms computing the optimal solution of the relaxed problem and a gradient function representing the estimated cost of each variable-value assignment. We exploit these pieces of information for pruning and for guiding the search. We have applied these techniques to a couple of ILOG Solver global constraints (a constraint of difference and a path constraint) and tested the approach on a variety of combinatorial optimization problems such as Timetabling, Travelling Salesman Problems and Scheduling Problems with sequence dependent setup times. Comparisons with pure Constraint Programming approaches and related literature clearly show the benefits of the proposed approach.

Integrating constraint logic programming and operations research techniques for the crew rostering problem

In this paper, we investigate the possibility of integrating Artificial Intelligence (AI) and Operations Research (OR) techniques for solving the Crew Rostering Problem (CRP). CRP calls for the optimal sequencing of a given set of duties into rosters satisfying a set of constraints. The optimality criterion requires the minimization of the number of crews needed to cover the duties. This kind of problem has been traditionally solved by OR techniques. In recent years, a new programming paradigm based on Logic Programming, named Constraint Logic Programming (CLP), has been successfully used for solving hard combinatorial optimization problems. CLP maintains all the advantages of logic programming such as declarativeness, non‐determinism and an incremental style of programming, while overcoming its limitations, mainly due to the inefficiency in exploring the search space. CLP achieves good results on hard combinatorial optimization problems which, however, are not comparable with those achieved by OR approaches. Therefore, we integrate both techniques in order to design an effective heuristic algorithm for CRP which fully exploits the advantages of the two methodologies: on the one hand, we maintain the declarativeness of CLP, its ease of representing knowledge and its rapid prototyping; on the other hand, we inherit from OR some efficient procedures based on a mathematical approach to the problem. Finally, we compare the results we achieved by means of the integration with those obtained by a pure OR approach, showing that AI and OR techniques for hard combinatorial optimization problems can be effectively integrated.

Integrating Operations Research in Constraint Programming

This paper presents Constraint Programming as a natural formalism for modelling problems, and as a flexible platform for solving them. CP has a range of techniques for handling constraints including several forms of propagation and tailored algorithms for global constraints. It also allows linear programming to be combined with propagation and novel and varied search techniques which can be easily expressed in CP. The paper describes how CP can be used to exploit linear programming within different kinds of hybrid algorithm. In particular it can enhance techniques such as Lagrangian relaxation, Benders decomposition and column generation.

Throughput Constraint for Synchronous Data Flow Graphs

Stream (data-flow) computing is considered an effective para-digm for parallel programming of high-end multi-core architectures for embedded applications (networking, multimedia, wireless communication). Our work addresses a key step in stream programming for embedded multicores, namely, the efficient mapping of a synchronous data-flow graph (SDFG) onto a multi-core platform subject to a minimum throughput requirement. This problem has been extensively studied in the past, and its complexity has lead researches to develop incomplete algorithms which cannot exclude false negatives. We developed a CP-based complete algorithm based on a new throughput-bounding constraint. The algorithm has been tested on a number of non-trivial SDFG mapping problems with promising results.