Beam search heuristics for the single machine scheduling problem with linear earliness and quadratic tardiness costs

In this paper, we consider the single machine scheduling problem with linear earliness and quadratic tardiness costs, and no machine idle time. We present heuristic algorithms based on the beam search technique. These algorithms include classic beam search procedures, as well as the filtered and recovering variants. Several dispatching rules are considered as evaluation functions, in order to analyse the effect of different rules on the effectiveness of the beam search algorithms. The computational results show that using better rules indeed improves the performance of the beam search heuristics. The detailed, filtered and recovering beam search procedures outperform the best existing heuristic. The best results are given by the recovering and detailed variants, which provide objective function values that are quite close to the optimum. For small to medium size instances, either of these procedures can be used. For larger instances, however, the detailed beam search algorithm requires excessive computation times, and the recovering beam search procedure then becomes the heuristic of choice.scheduling, single machine, linear earliness, quadratic tardiness, beam search, heuristics

Local Branching Relaxation Heuristics for Integer Linear Programs

Large Neighborhood Search (LNS) is a popular heuristic algorithm for solving combinatorial optimization problems (COP). It starts with an initial solution to the problem and iteratively improves it by searching a large neighborhood around the current best solution. LNS relies on heuristics to select neighborhoods to search in. In this paper, we focus on designing effective and efficient heuristics in LNS for integer linear programs (ILP) since a wide range of COPs can be represented as ILPs. Local Branching (LB) is a heuristic that selects the neighborhood that leads to the largest improvement over the current solution in each iteration of LNS. LB is often slow since it needs to solve an ILP of the same size as input. Our proposed heuristics, LB-RELAX and its variants, use the linear programming relaxation of LB to select neighborhoods. Empirically, LB-RELAX and its variants compute as effective neighborhoods as LB but run faster. They achieve state-of-the-art anytime performance on several ILP benchmarks

Heuristics for optimum binary search trees and minimum weight triangulation problems

AbstractIn this paper we establish new bounds on the problem of constructing optimum binary search trees with zero-key access probabilities (with applications e.g. to point location problems). We present a linear-time heuristic for constructing such search trees so that their cost is within a factor of 1 + ε from the optimum cost, where ε is an arbitrary small positive constant. Furthermore, by using an interesting amortization argument, we give a simple and practical, linear-time implementation of a known greedy heuristics for such trees.The above results are obtained in a more general setting, namely in the context of minimum length triangulations of so-called semi-circular polygons. They are carried over to binary search trees by proving a duality between optimum (m − 1)-way search trees and minimum weight partitions of infinitely-flat semi-circular polygons into m-gons. With this duality we can also obtain better heuristics for minimum length partitions of polygons by using known algorithms for optimum search trees

Heuristics for the dynamic facility layout problem with unequal area departments

The facility layout problem (FLP) is a well researched problem of finding positions of departments on a plant floor such that departments do not overlap and some objective(s) is (are) optimized. In this dissertation, the FLP with unequal area rectangular shaped departments is considered, when material flows between departments change during the planning horizon. This problem is known as the dynamic FLP. The change in material flows between pairs of departments in consecutive periods may require rearrangements of departments during the planning horizon in order to keep material handling costs low. The objective of our problem is to minimize the sum of the material handling and rearrangement costs. Because of the combinatorial structure of the problem, only small sized problems can be solved in reasonable time using exact techniques. As a result, construction and improvement heuristics are developed for the proposed problem. The construction algorithms are boundary search heuristics as well as a dual simplex method, and the improvement heuristics are tabu search and memetic heuristics with boundary search and dual simplex (linear programming model) techniques. The heuristics were tested on a generated data set as well as some instances from the literature. In summary, the memetic heuristic with the boundary search technique out-performed the other techniques with respect to solution quality

Decision-making Tools and Memetic Algorithms in Management and Linear Programming Problems

Operational Research uses a set of tools based on scientific research principles to achieve rational and meaningful management decisions. This article tries to give solution to a highly complex Linear Programming problem by using Simplex method, Solver and a hybrid prototype which combines the theories of Genetic Algorithms with a new local search heuristic technique. Hybridization of these two techniques is becoming known as Memetic Algorithm. Additionally, this article tries to present different techniques to support management decision-making, with the intention of being used increasingly in the business environment sustaining, thus, decisions by mathematics or artificial intelligence and not only by experience.quantitative management; quantitative methods; decision-making; linear programming; operational research; heuristics; hybrid methods; memetic algorithms.

Higher-Dimensional Potential Heuristics for Optimal Classical Planning

Potential heuristics for state-space search are defined as weighted sums over simple state features. Atomic features consider the value of a single state variable in a factored state representation, while binary features consider joint assignments to two state variables. Previous work showed that the set of all admissible and consistent potential heuristics using atomic features can be characterized by a compact set of linear constraints. We generalize this result to binary features and prove a hardness result for features of higher dimension. Furthermore, we prove a tractability result based on the treewidth of a new graphical structure we call the context-dependency graph. Finally, we study the relationship of potential heuristics to transition cost partitioning. Experimental results show that binary potential heuristics are significantly more informative than the previously considered atomic ones

Computational methods for finding long simple cycles in complex networks

© 2017 Elsevier B.V. Detection of long simple cycles in real-world complex networks finds many applications in layout algorithms, information flow modelling, as well as in bioinformatics. In this paper, we propose two computational methods for finding long cycles in real-world networks. The first method is an exact approach based on our own integer linear programming formulation of the problem and a data mining pipeline. This pipeline ensures that the problem is solved as a sequence of integer linear programs. The second method is a multi-start local search heuristic, which combines an initial construction of a long cycle using depth-first search with four different perturbation operators. Our experimental results are presented for social network samples, graphs studied in the network science field, graphs from DIMACS series, and protein-protein interaction networks. These results show that our formulation leads to a significantly more efficient exact approach to solve the problem than a previous formulation. For 14 out of 22 networks, we have found the optimal solutions. The potential of heuristics in this problem is also demonstrated, especially in the context of large-scale problem instances