$${\varvec{teaspoon}}$$ : solving the curriculum-based course timetabling problems with answer set programming

Annals of Operations Research - Answer Set Programming (ASP) is an approach to declarative problem solving, combining a rich yet simple modeling language with high performance solving capacities....     

Recent progress of local search in handling the time window constraints of the vehicle routing problem

Vehicle routing and scheduling problems have a wide range of applications and have been intensively studied in the past half century. The condition that enforces each vehicle to start service at each customer in the period specified by the customer is called the time window constraint. This paper reviews recent results on how to handle hard and soft time window constraints, putting emphasis on its different definitions and algorithms. With these diverse time windows, the problem becomes applicable to a wide range of real-world problems.     

The vehicle routing problem with flexible time windows and traveling times

We generalize the standard vehicle routing problem by allowing soft time window and soft traveling time constraints, where both constraints are treated as cost functions. With the proposed generalization, the problem becomes very general. In our algorithm, we use local search to determine the routes of vehicles. After fixing the route of each vehicle, we must determine the optimal start times of services at visited customers. We show that this subproblem is NP-hard when cost functions are general, but can be efficiently solved with dynamic programming when traveling time cost functions are convex even if time window cost functions are non-convex. We deal with the latter situation in the developed iterated local search algorithm. Finally we report computational results on benchmark instances, and confirm the benefits of the proposed generalization.     

Recent progress of local search in handling the time window constraints of the vehicle routing problem

Vehicle routing and scheduling problems have a wide range of applications and have been intensively studied in the past half century. The condition that enforces each vehicle to start service at each customer in the period specified by the customer is called the time window constraint. This paper reviews recent results on how to handle hard and soft time window constraints, putting emphasis on its different definitions and algorithms. With these diverse time windows, the problem becomes applicable to a wide range of real-world problems.     

Metal-nanoparticle-induced crystallization of amorphous Ge film using ferritin

The metal-induced lateral crystallization (MILC) of an amorphous Ge (a-Ge) thin film using Ni nanoparticles (NPs) was investigated. Ni-NPs were formed and evenly distributed onto a 30 nm thick a-Ge film by cage-shaped protein. After complete elimination of protein shell, crystal growth was performed at 400 °C. Raman spectra and electron backscatter diffraction (EBSD) studies revealed that a poly-Ge film with a maximum grain size approximately 1 μm was successfully formed. The Ni contamination in the poly-Ge film was reduced by more than one order of magnitude compared with that in the case of a conventional MILC process.     

An iterated local search algorithm for the time-dependent vehicle routing problem with time windows

We generalize the standard vehicle routing problem with time windows by allowing both traveling times and traveling costs to be time-dependent functions. In our algorithm, we use a local search to determine routes of the vehicles. When we evaluate a neighborhood solution, we must compute an optimal time schedule for each route. We show that this subproblem can be efficiently solved by dynamic programming, which is incorporated in the local search algorithm. The neighborhood of our local search consists of slight modifications of the standard neighborhoods called 2- opt^*, cross exchange and Or-opt. We propose an algorithm that evaluates solutions in these neighborhoods more efficiently than the ones computing the dynamic programming from scratch by utilizing the information from the past dynamic programming recursion used to evaluate the current solution. We further propose a filtering method that restricts the search space in the neighborhoods to avoid many solutions having no prospect of improvement. We then develop an iterated local search algorithm that incorporates all the above ingredients. Finally we report computational results of our iterated local search algorithm compared against existing methods, and confirm the effectiveness of the restriction of the neighborhoods and the benefits of the proposed generalization.     

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.     

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.     

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

We propose exact algorithms for the two-dimensional strip packing problem (2SP) with and without 90° 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.