A Variable Depth Search Algorithm for Binary Constraint Satisfaction Problems

The constraint satisfaction problem (CSP) is a popular used paradigm to model a wide spectrum of optimization problems in artificial intelligence. This paper presents a fast metaheuristic for solving binary constraint satisfaction problems. The method can be classified as a variable depth search metaheuristic combining a greedy local search using a self-adaptive weighting strategy on the constraint weights. Several metaheuristics have been developed in the past using various penalty weight mechanisms on the constraints.What distinguishes the proposed metaheuristic fromthose developed in the past is the update of k variables during each iteration when moving from one assignment of values to another. The benchmark is based on hard random constraint satisfaction problems enjoying several features that make them of a great theoretical and practical interest.The results show that the proposed metaheuristic is capable of solving hard unsolved problems that still remain a challenge for both complete and incomplete methods. In addition, the proposed metaheuristic is remarkably faster than all existing solvers when tested on previously solved instances. Finally, its distinctive feature contrary to other metaheuristics is the absence of parameter tuning making it highly suitable in practical scenarios

Combinatorial optimization and metaheuristics

Today, combinatorial optimization is one of the youngest and most active areas of discrete mathematics. It is a branch of optimization in applied mathematics and computer science, related to operational research, algorithm theory and computational complexity theory. It sits at the intersection of several fields, including artificial intelligence, mathematics and software engineering. Its increasing interest arises for the fact that a large number of scientific and industrial problems can be formulated as abstract combinatorial optimization problems, through graphs and/or (integer) linear programs. Some of these problems have polynomial-time (“efficient”) algorithms, while most of them are NP-hard, i.e. it is not proved that they can be solved in polynomial-time. Mainly, it means that it is not possible to guarantee that an exact solution to the problem can be found and one has to settle for an approximate solution with known performance guarantees. Indeed, the goal of approximate methods is to find “quickly” (reasonable run-times), with “high” probability, provable “good” solutions (low error from the real optimal solution). In the last 20 years, a new kind of algorithm commonly called metaheuristics have emerged in this class, which basically try to combine heuristics in high level frameworks aimed at efficiently and effectively exploring the search space. This report briefly outlines the components, concepts, advantages and disadvantages of different metaheuristic approaches from a conceptual point of view, in order to analyze their similarities and differences. The two very significant forces of intensification and diversification, that mainly determine the behavior of a metaheuristic, will be pointed out. The report concludes by exploring the importance of hybridization and integration methods

Integrating iterative crossover capability in orthogonal neighborhoods for scheduling resource-constrained projects

An effective hybrid evolutionary search method is presented which integrates a genetic algorithm with a local search. Whereas its genetic algorithm improves the solutions obtained by its local search, its local search component utilizes a synergy between two neighborhood schemes in diversifying the pool used by the genetic algorithm. Through the integration of these two searches, the crossover operators further enhance the solutions that are initially local optimal for both neighborhood schemes; and the employed local search provides fresh solutions for the pool whenever needed. The joint endeavor of its local search mechanism and its genetic algorithm component has made the method both robust and effective. The local search component examines unvisited regions of search space and consequently diversifies the search; and the genetic algorithm component recombines essential pieces of information existing in several high-quality solutions and intensifies the search. It is through striking such a balance between diversification and intensification that the method exploits the structure of search space and produces superb solutions. The method has been implemented as a procedure for the resource-constrained project scheduling problem. The computational experiments on 2,040 benchmark instances indicate that the procedure is very effective

Using Distributed Agents to Create University Course Timetables Addressing Essential & Desirable Constraints and Fair Allocation of Resources

In this study, the University Course Timetabling Problem (UCTP) has been investigated. This is a form of Constraint Satisfaction Problem (CSP) and belongs to the NP-complete class. The nature of a such problem is highly descriptive, a solution therefore involves combining many aspects of the problem. Although various timetabling algorithms have been continuously developed for nearly half a century, a gap still exists between the theoretical and practical aspects of university timetabling. This research is aimed to narrow the gap. We created an agent-based model for solving the university course timetabling problem, where this model not only considers a set of essential constraints upon the teaching activities, but also a set of desirable constraints that correspond to real-world needs. The model also seeks to provide fair allocation of resources. The capabilities of agents are harnessed for the activities of decision making, collaboration, coordination and negotiation by embedding them within the protocol designs. The resulting set of university course timetables involve the participation of every element in the system, with each agent taking responsibility for organising of its own course timetable, cooperating together to resolve problems. There are two types of agents in the model; these are Year-Programme Agent and Rooms Agent. In this study, we have used four different principles for organising the interaction between the agents: First-In-First-Out & Sequential (FIFOSeq), First-In-First-Out & Interleaved (FIFOInt), Round-Robin & Sequential (RRSeq) and Round-Robin & Interleaved (RRInt). The problem formulation and data instances of the third track of the Second International Timetabling Competition (ITC-2007) have been used as benchmarks for validating these implemented timetables. The validated results not only compare the four principles with each other; but also compare them with other timetabling techniques used for ITC-2007. The four different principles were able to successfully schedule all lectures in different periods, with no instances of two lectures occupying the same room at the same time. The lectures belonging to the same curriculum or taught by the same teacher do not conflict. Every lecture has been assigned a teacher before scheduling. The capacity of every assigned room is greater than, or equal to, the number of students in that course. The lectures of each course have been spread across the minimum number of working days with more than 98 percent success, and for more than 75 percent of the lectures under the same curriculum, it has been possible to avoid isolated deliveries. We conclude that the RRInt principle gives the most consistent likelihood of ensuring that each YPA in the system gets the best and fairest chance to obtain its resources

Heuristic algorithms for a vehicle routing problem with simultaneous delivery and pickup and time windows in home health care

International audienceThis paper addresses a vehicle scheduling problem encountered in home health care logistics. It concerns the delivery of drugs and medical devices from the home care company's pharmacy to patients' homes, delivery of special drugs from a hospital to patients, pickup of bio samples and unused drugs and medical devices from patients. The problem can be considered as a special vehicle routing problem with simultaneous delivery and pickup and time windows, with four types of demands: delivery from depot to patient, delivery from a hospital to patient, pickup from a patient to depot and pickup from a patient to a medical lab. Each patient is visited by one vehicle and each vehicle visits each node at most once. Patients are associated with time windows and vehicles with capacity. Two mixed-integer programming models are proposed. We then propose a Genetic Algorithm (GA) and a Tabu Search (TS) method. The GA is based on a permutation chromosome, a split procedure and local search. The TS is based on route assignment attributes of patients, an augmented cost function, route re-optimization, and attribute-based aspiration levels. These approaches are tested on test instances derived from existing VRPTW benchmarks