Car sequencing with constraint-based ACO

Hybrid methods for solving combinatorial optimization problems have become increasingly popular recently. The present paper is concerned with hybrids of ant colony optimization and constraint programming which are typically useful for problems with hard constraints. However, the original algorithm suffered from large CPU time requirements. It was shown that such an integration can be made efficient via a further hybridization with beam search resulting in CP-Beam-ACO. The original work suggested this in the context of job scheduling. We show here that this algorithm type is also effective on another problem class, namely the car sequencing. We consider an optimization version, where we aim to optimize the utilization rates across the sequence. Car sequencing is a notoriously difficult problem, because it is difficult to obtain good bounds via relaxations. We show that stochastic sampling provides superior results to well known lower bounds for this problem when combined with CP-Beam-ACO

The Maximum Happy Induced Subgraph Problem: Bounds and Algorithms

In this paper we consider a combinatorial optimisation problem that takes as input a graph in which some of the vertices have been preassigned to colours. The aim is to then identify the largest induced subgraph in which all remaining vertices are able to assume the same colour as all of their neighbours. This problem shares similarities with the graph colouring problem, vertex cut problems, and the maximum happy vertices problem. It is NP-hard in general. In this paper we derive a number of upper and lower bounds and also show how certain problem instances can be broken up into smaller subproblems. We also propose one exact and two heuristic algorithms for this problem and use these to investigate the factors that make some problem instances more difficult to solve than others

Mining Negative Rules using GRD

Abstract. GRD is an algorithm for k-most interesting rule discovery. In contrast to association rule discovery, GRD does not require the use of a minimum support constraint. Rather, the user must specify a measure of interestingness and the number of rules sought (k). This paper reports efficient techniques to extend GRD to support mining of negative rules. Keywords: Rule Discovery, Negative Rules.

Strip packing with hybrid ACO: Placement order is learnable

This paper investigates the use of hybrid meta-heuristics based on ant colony optimization (ACO) for the strip packing problem. Here, a fixed set of rectangular items of fixed sizes have to be placed on a strip of fixed width and infinite height without overlaps and with the objective to minimize the height used. We analyze a commonly used basic placement heuristic (BLF) by itself and in a number of hybrid combinations with ACO. We compare versions that learn item order only, item rotation only, both independently, and rotations conditionally upon placement order. Our analysis shows that integrating a learning meta-heuristic provides a significant performance advantage over using the basic placement heuristic by itself. The experiments confirm that even just learning a placement order alone can provide significant performance improvements. Interestingly, learning item rotations provides at best a marginal advantage. The best hybrid algorithm presented in this paper significantly outperforms previously reported strip packing meta-heuristics

Finding happiness: an analysis of the maximum happy vertices problem

The maximum happy vertices problem involves determining a vertex colouring of a graph such that the number of vertices assigned to the same colour as all of their neighbours is maximised. This problem is trivial if no vertices are precoloured, though in general it is NP-hard. In this paper we derive a number of upper and lower bounds on the number of happy vertices that are achievable in a graph and then demonstrate how certain problem instances can be broken up into smaller subproblems. Four different algorithms are also used to investigate the factors that make some problem instances more difficult to solve than others. In general, we find that the most difficult problems are those with relatively few edges and/or a small number of precoloured vertices. Ideas for future research are also discussed

Constraint-based ACO for a shared resource constrained scheduling problem

We consider a scheduling problem arising in the mining industry. Ore from several mining sites must be transferred to ports to be loaded on ships in a timely manner. In doing so, several constraints must be met which involve transporting the ore and deadlines. These deadlines are two-fold: there is a preferred deadline by which the ships should be loaded and there is a final deadline by which time the ships must be loaded. Corresponding to the two types of deadlines, each task is associated with a soft and hard due time. The objective is to minimize the cumulative tardiness, measured using the soft due times, across all tasks. This problem can be formulated as a resource constrained job scheduling problem where several tasks must be scheduled on multiple machines satisfying precedence and resource constraints and an objective to minimize total weighted tardiness. For this problem we present hybrids of ant colony optimization, Beam search and constraint programming. These algorithms have previously shown to be effective on similar tightly-constrained combinatorial optimization problems. We show that the hybrid involving all three algorithms provides the best solutions, particularly with respect to feasibility. We also investigate alternative estimates for guiding the Beam search component of our algorithms and show that stochastic sampling is the most effective

Car sequencing with constraint-based ACO

Hybrid methods for solving combinatorial optimization problems have become increasingly popular recently. The present paper is concerned with hybrids of ant colony optimization and constraint programming which are typically useful for problems with hard constraints. However, the original algorithm suffered from large CPU time requirements. It was shown that such an integration can be made efficient via a further hybridization with beam search resulting in CP-Beam-ACO. The original work suggested this in the context of job scheduling. We show here that this algorithm type is also effective on another problem class, namely the car sequencing. We consider an optimization version, where we aim to optimize the utilization rates across the sequence. Car sequencing is a notoriously difficult problem, because it is difficult to obtain good bounds via relaxations. We show that stochastic sampling provides superior results to well known lower bounds for this problem when combined with CP-Beam-ACO