Roland Braune

Benefits of plugin-based heuristic optimization software systems

Plugin-based software systems are the next step of evolution in application development. By supporting fine grained modularity not only on the source code but also on the post-compilation level, plugin frameworks help to handle complexity, simplify application configuration and deployment, and enable users or third parties to easily enhance existing applications with self-developed modules without having access to the whole source code. In spite of these benefits, plugin-based software systems are seldom found in the area of heuristic optimization. Some reasons for this drawback are discussed, several benefits of a plugin-based heuristic optimization software system are highlighted and some ideas are shown, how a heuristic optimization meta-model as the basis of a thorough plugin infrastructure for heuristic optimization could be defined.

An exact approach for single machine subproblems in shifting bottleneck procedures for job shops with total weighted tardiness objective

In this paper, we propose an exact solution method for single machine scheduling problems typically arising from bottleneck-based decomposition of weighted tardiness job shops. The encountered subproblems are characterized by delayed precedence constraints, multiple local due dates per operation and an objective function that is given by a weighted sum of maximum tardiness values. The key concept for solving these subproblems to optimality is a dominance rule whose underlying concepts have been newly developed to cope with the given structural properties. Furthermore, a simple lower bound and a dedicated constraint programming technique are presented. The efficiency of the proposed method is demonstrated by means of single machine problems collected during a run of a shifting bottleneck procedure for job shops in different size and due date tightness configurations.

Enhancing local search algorithms for job shops with min-sum objectives by approximate move evaluation

Exact move evaluation in local search-based job shop scheduling is known to be time consuming, especially for medium and large size instances. Therefore, approximation functions providing quick estimates for the cost induced by a move are often used in order to accelerate the search process. This paper describes the generalization of an existing cost estimation function for insertion moves towards min-sum objectives, such as total weighted tardiness, total weighted completion time and total weighted number of late jobs. Besides the transfer of the concept itself, shortcomings of the original approach are identified and eliminated and an enhanced approximation scheme is presented. The final estimation function is able to provide a considerably increased accuracy for the considered min-sum objectives compared to the existing approach. The advantage of the new function emerges most clearly when it is embedded into a tabu search algorithm, as verified based on benchmark instances from literature involving up to 100 jobs and 20 machines.

Optimization methods for large-scale production scheduling problems

In this paper we present a computational study of optimization methods for production scheduling problems which can be described by a job shop model. Contrary to most existing publications in this field our research focuses on the performance of these methods with respect to large-scale problem instances. The examined methods rely on a graph model as a solution representation and have originally been designed for problems of small size. We apply them to a set of semi-randomly generated problem instances whose properties have been transferred from common (smaller) benchmarks. The experiments are based on tardiness minimization and the results are evaluated in relation to a priority rule based heuristic.

Lower bounds for single machine subproblems occurring in weighted tardiness oriented shifting bottleneck procedures

In this paper, we propose lower bounds for single machine scheduling problems which occur during a run of a shifting bottleneck procedure for total weighted tardiness job shops. The specific structure of this kind of problem and its objective function in particular prevent an immediate transfer or an adaption of existing lower bounds from “conventional” single machine problems with tardiness related objectives. Hence it has been necessary to develop bounding approaches which are to some extent conceptually new. Potential application scenarios range from exact subproblem solution methods or machine prioritization criteria in a shifting bottleneck procedure to branch-and-bound algorithms for job shops with total weighted tardiness objective. In order to provide a significant evaluation of the proposed lower bounds regarding their effectiveness and efficiency, we tested them based on problem instances which actually have been generated in a shifting bottleneck procedure applied to benchmark job shop problems.

A Computational Study of Lower Bounding Schemes for Total Weighted Tardiness Job Shops

In this paper, we perform a computational study of lower bounding schemes for job shop scheduling problems under special consideration of total weighted tardiness costs. Due to the characteristics of this objective function, lower bounds are much more difficult to derive than for the classical makespan. On the other hand, the practical relevance of tardiness related costs makes it even more important to have corresponding bounds available, especially for rating the results of approximate optimization approaches. Apart from the quality of the bounds, i.e. the tightness with respective to an existing optimal solution or upper bound, a further important focus of our investigations is the required computation time, since this is a determining criterion for the applicability. Computational results are reported based on selected benchmark problems.

Bandit-based Monte-Carlo planning for the single-machine total weighted tardiness scheduling problem

The balance of exploration and exploitation is the essence of any successful meta-heuristic. The Multi-armed Bandit Problem represents a simple form of this general dilemma. This paper describes two heuristic optimization methods that use a simple yet efficient allocation strategy for the bandit problem called UCB1 to control the optimization process. The algorithms are applied to the well known Single Machine Total Weighted Tardiness Problem and the results compared to the results of other successful meta-heuristics for this scheduling problem.

Metaheuristics Based on Solution Construction

In section 3.1.1 we saw how randomization can make constructive search methods better than pure greedy methods, because the danger of being too eager is dampened a little. We called this approach randomized adaptive search. Now we want to explain a metaheuristic which is based on this idea. It is called Greedy Randomized Adaptive Search Procedure (GRASP, cf [70, 170]). As it is a constructive search method, it starts with an empty solution and adds solution elements to a partial solution until it is complete. It may be argued, this is exactly the way a greedy construction method works, but there are subtle differences, which are pointed out now. Greedy methods do not perform search, they construct a single solution in an iterative fashion by evaluating all remaining solution elements and according to their performance add them to the partial solution. Elements are added as long as the solution is improved. If this is not the case anymore, the construction is stopped and the final solution is returned. Hence greedy methods do not perform search.

Lower bounds for a bin packing problem with linear usage cost

Abstract In this paper, we address a one-dimensional bin packing problem with bin-specific usage cost. The cost coefficients have a direct linear relationship to the bin index, favoring packings with higher loads in “earlier” bins. We show how lower bounding schemes known from standard bin packing can be adapted to fit this objective function and conduct a worst-case performance analysis. The contribution also covers a conceptually new lower bound for the problem at hand. Computational experience based on randomly generated instances and benchmark libraries provides strong evidence for high quality bounds achievable with low computational effort. This observation is further underpinned by a successful embedding of the lower bounds into a branch-and-bound approach as a computational framework. Clear advantages over a state-of-the-art mixed-integer programming formulation can be obtained for particular problem settings.

Metaheuristics in Vehicle Routing

The metaheuristics previously explained are now applied to a transportation problem. In modern economy goods are sourced worldwide an transportation and the organization of transportation has gained more and more attention. Transportation not only causes cost but also increases traffic, environment pollution, noise, and inefficient transportation organization may cause a decrease of the service level. There are plenty of reasons to do optimization of vehicle routes. Transportation optimization is a frequently studied problem in the context of logistics. It not only arises in collection and distribution of goods but also in service applications like taxi driving, package delivery, school bus routing, repairman routing, and so on (cf. [74]).