Heuristic methods for routing and scheduling

A locomotive assignment is one of the subproblems in railway scheduling domain. In this report present general mathematical model of this specific subproblem and describe how methods known from other problems domain like traveling salesman problem, operation research and constraint programming can be used to solve it. We concentrate especially on method known as {\it k--interchange} for traveling salesman problem with time windows and give an outline how it can be adopted to locomotive assignment problem. Further, while turning from one trip to another a locomotive must often be reallocated from one station to another. This can be performed in two ways. A locomotive can be driven from one place to another not performing any specific trip and exclusively using track resource, i.e. performs so called deadhead transport, or can be attached to any other transport and passively drown to another station, i.e. perform so called passive transport. Because the cost of passive transport is much lower then cost of a deadhead it is advantageous to, if possible, replace any deadhead by passive transport. In this report we describe a method of converting deadheads into passive transports, describe conversion algorithm, its implementation and report computational result of the algorithm. Finally, we give directions for future research in locomotive planning problem domain

Dynamic scheduling. State of the art report.

Most of the research literature concerning scheduling concentrates on the static problems, i.e. problems where all input data is known and does not vary over the time. However, the real world scheduling problems are very seldom static. Events like machine failures or work overloads are, in some situations, impossible to predict. Dynamic scheduling is a research field which take into consideration uncertainty and dynamic changes in the scheduling problem. This paper gives an overview of the state of the art in the field of dynamic scheduling

Generating Stable Loading Patterns for Pallet Loading Problems

Abstract. This paper describes an integer programming model for generating stable loading patterns for the Pallet Loading Problem. The algorithm always gives optimal or near-optimal utilization of the pallet area and fulfills stability criteria for 98% of the test cases

Filtering methods for symmetric cardinality constraint

The symmetric cardinality constraint is described in terms of variables X = {x_1,...,x_k} which take values in the subset of values V={v_1,...,v_n}. It constraints the number of times a value can be assigned to a variable in X to be in an interval [l_{x_i},c_{x_i}] and at the same time it restricts the number of values in V which any variable can take to an interval [l_{v_j},c_{v_j}]. In this paper we introduce the symmetric cardinality constraint and define set constraint satisfaction problem as a framework for dealing with this type of constraints. Moreover, we present effective filtering methods for the symmetric cardinality constraint

Designing Global Scheduling Constraints for Local Search: A Generic Approach

In this work we present a novel method to automate the computation of global constraints cost for local search. The method is based on the representation of a global constraints as graph properties on a binary constraint network. This formulation simplifies the implementation of global constraints in local search, and provides a cost that can be readily compared to one obtained for subproblems using binary constraints exclusively. The cost obtained can be efficiently updated during the search using incremental methods. The representation of a global constraint as outlined above can also be used for generation of suitable neighborhoods for the constraint. This is done using simple repair functions applied on the elementary constraints in the global constraint graph. We show the usability of our approach by presenting formulations of global constraints in non-overlapping and cumulative scheduling

Designing Global Scheduling Constraints for Local Search: A Generic Approach

In this work we present a novel method to automate the computation of global constraints cost for local search. The method is based on the representation of a global constraints as graph properties on a binary constraint network. This formulation simplifies the implementation of global constraints in local search, and provides a cost that can be readily compared to one obtained for subproblems using binary constraints exclusively. The cost obtained can be efficiently updated during the search using incremental methods. The representation of a global constraint as outlined above can also be used for generation of suitable neighborhoods for the constraint. This is done using simple repair functions applied on the elementary constraints in the global constraint graph. We show the usability of our approach by presenting formulations of global constraints in non-overlapping and cumulative scheduling

Maintaining Consistency of Dynamic Cardinality Constraints with Costs

This paper introduce a novel method for maintaining consistency of cardinality constraints in context of dynamic constraint satisfaction. The presente

Symmetric Cardinality Constraint with Costs

The symmetric cardinality constraint is described in terms of a set of variables X = {x1 , . . . , xk}, which take their values as subsets of V = {v1 , . . . , vn}. It constraints the cardinality of the set assigned to each variable to be in an interval [l x i , ux i ] and at the same time it restricts the number of occurrences of each value v j V in the sets assigned to variables in X to be in an other interval [l v j , uv j ]. In this paper we extend the symmetric cardinality constraint with a function which associate with each value of each variable a cost and constraints the global cost of the constraint to the sum of costs associated with assigned values. We also give an algorithm for computing the consistency of a symmetric cardinality constraint with costs and describe filtering methods for this constraint