General swap-based multiple neighborhood tabu search for the maximum independent set problem

Given a graph G=(V,E)G=(V,E), the Maximum Independent Set problem (MIS) aims to determine a subset S⊆VS⊆V of maximum cardinality such that no two vertices of S are adjacent. This paper presents a general Swap-Based Tabu Search (SBTS) for solving the MIS. SBTS integrates distinguished features including a general and unified (k,1)-swap operator, four constrained neighborhoods and specific rules for neighborhood exploration. Extensive evaluations on two popular benchmarks (DIMACS and BHOSLIB) of 120 instances show that SBTS attains the best-known results for all the instances. To our knowledge, such a performance was not reported in the literature for a single heuristic. The best-known results on 11 additional instances from code theory are also attained

An Efficient Local Search for Partial Latin Square Extension Problem

A partial Latin square (PLS) is a partial assignment of n symbols to an nxn grid such that, in each row and in each column, each symbol appears at most once. The partial Latin square extension problem is an NP-hard problem that asks for a largest extension of a given PLS. In this paper we propose an efficient local search for this problem. We focus on the local search such that the neighborhood is defined by (p,q)-swap, i.e., removing exactly p symbols and then assigning symbols to at most q empty cells. For p in {1,2,3}, our neighborhood search algorithm finds an improved solution or concludes that no such solution exists in O(n^{p+1}) time. We also propose a novel swap operation, Trellis-swap, which is a generalization of (1,q)-swap and (2,q)-swap. Our Trellis-neighborhood search algorithm takes O(n^{3.5}) time to do the same thing. Using these neighborhood search algorithms, we design a prototype iterated local search algorithm and show its effectiveness in comparison with state-of-the-art optimization solvers such as IBM ILOG CPLEX and LocalSolver.Comment: 17 pages, 2 figure

MBA Student Sectioning

Maastricht University is offering a MBA program for people that have a bachelor degree and at least 5 years of working experience. Within the MBA program, students work in groups of 5 during a two year cycle. This thesis is about the formation of the student groups. The MBA program contains 60 students. Every year, two intake moments take place that usually allow 15 new students to enter. All 60 students follow the same course at the same time, implying that the order in which a student follows the courses depends only on the moment at which he/she starts the program. Every two periods, The university creates new student groups according to a set of hard and soft constraints, such that well-diversified groups are formed. Therefore, the student-with-student history, gender, nationality, and level of expertise of each student is taken into account. Hence a mapping from a set of students to groups is created that takes into account the corresponding constraints. The university chooses a group leader for each group. Two general solution methods are applied to the MBA sectioning problem. The first method uses the simplex algorithm to solve the problem. Therefore an integer linear program formulation of the problem was needed, and used as an input for an efficient ILP solver. The second approach starts with an initial feasible solution and improves upon this feasible solution using different improvement algorithms. The quality of each feasible solution depends on the calculated objective function value that measures the level of satisfaction of the different constraints. Different initial solution and improvement algorithms are discussed that help to obtain a feasible solution with an objective function value that is as low as possible. The implemented improvement algorithms are the Descent Improvement algorithm, Tabu Search, Simulated Annealing, and the Bipartite Weighted Matching Improvement algorithm. The first three algorithms make individual students swap between existing group formations. The Bipartite Weighted Matching Improvement algorithm iteratively selects a student from each group, and finds local optimal solutions for a bipartite matching problem in order to improve the overall objective value of the whole problem. In order to test the algorithms, one has to make sure that the instance on which the algorithms are tested mimics a real life example. Therefore, a simulation program is established that mimics the two year cycle and produces such an instance. Empirical results show that the best improvement algorithm considered is the Bipartite Weighted Matching Improvement algorithm. This algorithm, combined with an initial solution algorithm, is now being implemented into the current computer system of Maastricht University

Algebraic Algorithm Design and Local Search

Formal, mathematically-based techniques promise to play an expanding role in the development and maintenance of the software on which our technological society depends. Algebraic techniques have been applied successfully to algorithm synthesis by the use of algorithm theories and design tactics, an approach pioneered in the Kestrel Interactive Development System (KIDS). An algorithm theory formally characterizes the essential components of a family of algorithms. A design tactic is a specialized procedure for recognizing in a problem specification the structures identified in an algorithm theory and then synthesizing a program. Design tactics are hard to write, however, and much of the knowledge they use is encoded procedurally in idiosyncratic ways. Algebraic methods promise a way to represent algorithm design knowledge declaratively and uniformly. We describe a general method for performing algorithm design that is more purely algebraic than that of KIDS. This method is then applied to local search. Local search is a large and diverse class of algorithms applicable to a wide range of problems; it is both intrinsically important and representative of algorithm design as a whole. A general theory of local search is formalized to describe the basic properties common to all local search algorithms, and applied to several variants of hill climbing and simulated annealing. The general theory is then specialized to describe some more advanced local search techniques, namely tabu search and the Kernighan-Lin heuristic

Feature-based tuning of simulated annealing applied to the curriculum-based course timetabling problem

We consider the university course timetabling problem, which is one of the most studied problems in educational timetabling. In particular, we focus our attention on the formulation known as the curriculum-based course timetabling problem, which has been tackled by many researchers and for which there are many available benchmarks. The contribution of this paper is twofold. First, we propose an effective and robust single-stage simulated annealing method for solving the problem. Secondly, we design and apply an extensive and statistically-principled methodology for the parameter tuning procedure. The outcome of this analysis is a methodology for modeling the relationship between search method parameters and instance features that allows us to set the parameters for unseen instances on the basis of a simple inspection of the instance itself. Using this methodology, our algorithm, despite its apparent simplicity, has been able to achieve high quality results on a set of popular benchmarks. A final contribution of the paper is a novel set of real-world instances, which could be used as a benchmark for future comparison

A hybrid shifting bottleneck-tabu search heuristic for the job shop total weighted tardiness problem

In this paper, we study the job shop scheduling problem with the objective of minimizing the total weighted tardiness. We propose a hybrid shifting bottleneck - tabu search (SB-TS) algorithm by replacing the reoptimization step in the shifting bottleneck (SB) algorithm by a tabu search (TS). In terms of the shifting bottleneck heuristic, the proposed tabu search optimizes the total weighted tardiness for partial schedules in which some machines are currently assumed to have infinite capacity. In the context of tabu search, the shifting bottleneck heuristic features a long-term memory which helps to diversify the local search. We exploit this synergy to develop a state-of-the-art algorithm for the job shop total weighted tardiness problem (JS-TWT). The computational effectiveness of the algorithm is demonstrated on standard benchmark instances from the literature

A Tabu Search algorithm for the vehicle routing problem with discrete split deliveries and pickups

The Vehicle Routing Problem with Discrete Split Deliveries and Pickups is a variant of the Vehicle Routing Problem with Split Deliveries and Pickups, in which customers’ demands are discrete in terms of batches (or orders). It exists in the practice of logistics distribution and consists of designing a least cost set of routes to serve a given set of customers while respecting constraints on the vehicles’ capacities. In this paper, its features are analyzed. A mathematical model and Tabu Search algorithm with specially designed batch combination and item creation operation are proposed. The batch combination operation is designed to avoid unnecessary travel costs, while the item creation operation effectively speeds up the search and enhances the algorithmic search ability. Computational results are provided and compared with other methods in the literature, which indicate that in most cases the proposed algorithm can find better solutions than those in the literature