Koji Nonobe

Formulation and Tabu Search Algorithm for the Resource Constrained Project Scheduling Problem

The resource constrained project scheduling problem (RCPSP) can formulate many scheduling problems including jobshop and flowshop scheduling problems. In this paper, we extend the definition of RCPSP further so that various complicated constraints and objective functions arising in practice can be handled; for example, each activity can be processed in one of the selectable modes, the available amounts of renewable resources may vary depending on the periods, setup activities can be dealt with, and complex objective functions can be handled. Then, we develop a tabu search based heuristic algorithm, which contains elaborations in representing solutions and in constructing neighborhood. Our code was tested for many benchmarks of RCPSP, and also for some problems from real applications. For a number of RCPSP instances, we found better solutions than the best ones found so far. These computational results indicate the effectiveness and usefulness of our approach.

A tabu search approach to the constraint satisfaction problem as a general problem solver

Many combinatorial problems, including a variety of combinatorial optimization problems, can be naturally formulated as a constraint satisfaction problem (CSP). We develop in this paper a tabu search-based algorithm for the CSP as a foundation for a general problem solver. In addition to the basic components of tabu search, we develop a number of elaborations, such as an automatic control mechanism for the tabu tenure, modification of the penalty function to handle objective functions, and enlargement of the neighborhood by allowing swap operations. Computational results with our algorithm are reported for various problems selected from a wide range of applications, i.e., graph coloring, generalized assignment, set covering, timetabling and nurse scheduling. Our results appear to be competitive with those of existing algorithms specially developed for the respective problem domains.

Exact algorithms for the two-dimensional strip packing problem with and without rotations

We propose exact algorithms for the 2-dimensional strip packing problem (2SP) with and without 90 degrees rotations. We first focus on the perfect packing problem (PP), which is a special case of 2SP, wherein all given rectangles are required to be packed without wasted space, and design branch-and-bound algorithms introducing several branching rules and bounding operations. A combination of these rules yields an algorithm that is especially efficient for feasible instances of PP. We then propose several methods of applying the PP algorithms to 2SP. Our algorithms succeed in efficiently solving benchmark instances of PP with up to 500 rectangles and those of 2SP with up to 200 rectangles. They are often faster than existing exact algorithms specially tailored for problems without rotations.

An iterated local search algorithm for the vehicle routing problem with convex time penalty functions

We propose an iterated local search algorithm for the vehicle routing problem with time window constraints. We treat the time window constraint for each customer as a penalty function, and assume that it is convex and piecewise linear. Given an order of customers each vehicle to visit, dynamic programming (DP) is used to determine the optimal start time to serve the customers so that the total time penalty is minimized. This DP algorithm is then incorporated in the iterated local search algorithm to efficiently evaluate solutions in various neighborhoods. The amortized time complexity of evaluating a solution in the neighborhoods is a logarithmic order of the input size (i.e., the total number of linear pieces that define the penalty functions). Computational comparisons on benchmark instances with up to 1000 customers show that the proposed method is quite effective, especially for large instances.

An improved tabu search method for the weighted constraint satisfaction problem

Abstract Aiming at developing a general problem solver for combinatorial optimization problems, we consider in this paper the weighted constraint satisfaction problem (WCSP), which, given a number of constraints and their weights of importance, asks to minimize the total weight of unsatisfied constraints. We propose a tabu search algorithm for WCSP with the features that it uses an evaluation function, defined in terms of the modified weights of constraints, for guiding the search, and that it incorporates an automatic control mechanism of the weights in the evaluation function. Using this code, we solved a number of problems including those from real applications such as generalized assignment, set covering, parallel shop scheduling, timetabling and nurse scheduling. Many problems that arise in cellular manufacturing can also be formulated as WCSP, including the problems of cell formation and tool selection. Our computational results indicate that the control mechanism of weights makes our tabu search more powerful, and our algorithm is practically usable.

Solving the irregular strip packing problem via guided local search for overlap minimization

The irregular strip-packing problem (ISP) requires a given set of non-convex polygons to be placed without overlap within a rectangular container having a fixed width and a variable length, which is to be minimized. As a core sub-problem to solve ISP, we consider an overlap minimization problem (OMP) whose objective is to place all polygons into a container with given width and length so that the total amount of overlap between polygons is made as small as possible. We propose to use directional penetration depths to measure the amount of overlap between a pair of polygons, and present an efficient algorithm to find a position with the minimum overlap for each polygon when it is translated in a specified direction. Based on this, we develop a local search algorithm for OMP that translates a polygon in horizontal and vertical directions alternately. Then we incorporate it in our algorithm for OMP, which is a variant of the guided local search algorithm. Computational results show that our algorithm improves the best-known values of some well-known benchmark instances.

Web-based tools to sustain the motivation of students in distance education

In distance education, students in a remote classroom tend not to sustain their motivation, mainly because of a lack of intensity due to non-physical presence of a lecturer. To address this issue, two software tools were developed for teachers and students, respectively. The tool for teachers is called eRoster. On the teachers PC, the eRoster can display not only the students name but also the students attributes - id, future career, interest, club, faculty, and entrance time. Then, the teacher by name can call on the appropriate student whose attribute is related to the topics of the lecture. The tool for students is a so-called clicker and enables students to be more completely engaged in the interactivity of active learning. The developed system facilitates individually owned multi-devices of the students like PCs, cell phones, iPod Touches, and other PDAs as data entry systems.

A Metaheuristic Approach to the Resource Constrained Project Scheduling with Variable Activity Durations and Convex Cost Functions

We introduce a generalized model of the resource constrained project scheduling problem (RCPSP). It features that (i) the duration of an activity is not constant, but can vary in a specified range, and (ii) the objective is to minimize a convex function of time-lag costs, where a time-lag cost is charged according to the difference between the start/completion times of activities. These features achieve the flexibility of the model. It is known that, in the RCPSP, resource constraints can be replaced by some precedence constraints appropriately defined between the activities that require a common scarce resource. If we remove resource constraints by precedence constraints, our problem can be formulated as the dual problem of a minimum cost flow problem, and thus can be solved efficiently. Exploiting this property, we design a heuristic algorithm based on local search. We conducted computational experiments with benchmark instances to minimize the weighted earliness-tardiness costs, as well as instances in which activity-crashing or relaxation of temporal constraints are allowed. These results indicate the usefulness of our generalized RCPSP model and the proposed algorithm.

A set covering approach for the pickup and delivery problem with general constraints on each route

We consider a generalization of the pickup and delivery problem with time windows by allowing general constraints on each route, and propose a heuristic algorithm based on the set covering approach, in which all requests are required to be covered by a set of feasible routes. Our algorithm first generates a set of feasible routes, and repeats reconstructing of the set by using information from a Lagrangian relaxation of the set covering problem corresponding to the set. The algorithm then solves the resulting set covering problem instance to find a good feasible solution for the original problem. We conduct computational experiments for instances with various constraints and confirm the flexibility and robustness of our algorithm.

Efficient branch-and-bound algorithms for weighted MAX-2-SAT

MAX-2-SAT is one of the representative combinatorial problems and is known to be NP-hard. Given a set of m clauses on n propositional variables, where each clause contains at most two literals and is weighted by a positive real, MAX-2-SAT asks to find a truth assignment that maximizes the total weight of satisfied clauses. In this paper, we propose branch-and-bound exact algorithms for MAX-2-SAT utilizing three kinds of lower bounds. All lower bounds are based on a directed graph that represents conflicts among clauses, and two of them use a set covering representation of MAX-2-SAT. Computational comparisons on benchmark instances disclose that these algorithms are highly effective in reducing the number of search tree nodes as well as the computation time.