Discrete particle swarm optimization for the team orienteering problem

Orienteering problem is a well researched routing problem which is a generalization of the traveling salesman problem. Team orienteering problem (TOP) is the extended version of the orienteering problem with more than one member in the team. In this paper the first known discrete particle swarm optimization (DPSO) algorithm has been developed for 2, 3 and 4-member TOP. In the DPSO meta-heuristic novel methods have been introduced for the initial particle generation process. Reduced variable neighborhood search and 2-opt were applied as the local search tools. The efficacy of the algorithm was tested using seven commonly used benchmark problem sets ranging in size from 21 to 102 nodes. The results of the DPSO algorithm were compared against seven other heuristic algorithms that have been developed for TOP. It was concluded that the developed DPSO algorithm for the TOP is competitive and robust across the benchmark problem sets.     

The Team Orienteering Problem with Time Windows: An LP-based Granular Variable Neighborhood Search

The Team Orienteering Problem (TOP) is a known NP-hard problem that typically arises in vehicle routing and production scheduling contexts. In this paper we introduce a new solution method to solve the TOP with hard Time Window constraints (TOPTW). We propose a Variable Neighborhood Search (VNS) procedure based on the idea of exploring, most of the time, granular instead of complete neighborhoods in order to improve the algorithm’s efficiency without loosing effectiveness. The method provides a general way to deal with granularity for those routing problems based on profits and complicated by time constraints. Extensive computational results are reported on standard benchmark instances. Performance of the proposed algorithm is compared to optimal solution values, when available, or to best known solution values obtained by state-of-the-art algorithms. The method comes out to be, on average, quite effective allowing to improve the best know values for 25 test instances.     

A memetic algorithm for the team orienteering problem

The team orienteering problem (TOP) is a generalization of the orienteering problem. A limited number of vehicles is available to visit customers from a potential set. Each vehicle has a predefined running-time limit, and each customer has a fixed associated profit. The aim of the TOP is to maximize the total collected profit. In this paper we propose a simple hybrid genetic algorithm using new algorithms dedicated to the specific scope of the TOP: an Optimal Split procedure for chromosome evaluation and local search techniques for mutation. We have called this hybrid method a memetic algorithm for the TOP. Computational experiments conducted on standard benchmark instances clearly show our method to be highly competitive with existing ones, yielding new improved solutions in at least 5 instances.     

Improved approximation for non-preemptive single machine flow-time scheduling with an availability constraint

We study the problem of scheduling n non-preemptable jobs on a single machine which is not available for processing during a given time period. The objective is to minimize the sum of the job completion times. The best known approximation algorithm for this NP-hard problem has a relative worst-case error bound of 17.6%. We present a parametric O(nlog n)-algorithm H with which better worst-case error bounds can be obtained. The best error bound calculated for the algorithm in the paper is 7.4%. In a computational experiment, we test the algorithm with the performance guarantee set to 10.2%. It turns out that randomly generated instances with up to 1000 jobs can be solved with a mean (maximum) error of 0.31% (3.18%) and a mean (maximum) computation time of 0.8 (9.7) seconds.     

Hybridized evolutionary local search algorithm for the team orienteering problem with time windows

The orienteering problem (OP) consists in finding an elementary path over a subset of vertices. Each vertex is associated with a profit that is collected on the visitor’s first visit. The objective is to maximize the collected profit with respect to a limit on the path’s length. The team orienteering problem (TOP) is an extension of the OP where a fixed number m of paths must be determined. This paper presents an effective hybrid metaheuristic to solve both the OP and the TOP with time windows. The method combines the greedy randomized adaptive search procedure (GRASP) with the evolutionary local search (ELS). ELS generates multiple distinct child solutions using a mutation mechanism. Each child solution is further improved by a local search procedure. GRASP provides multiple starting solutions to the ELS. The method is able to improve several best known results on available benchmark instances.     

A guided local search metaheuristic for the team orienteering problem

In the team orienteering problem (TOP) a set of locations is given, each with a score. The goal is to determine a fixed number of routes, limited in length, that visit some locations and maximise the sum of the collected scores. This paper describes an algorithm that combines different local search heuristics to solve the TOP. Guided local search (GLS) is used to improve two of the proposed heuristics. An extra heuristic is added to regularly diversify the search in order to explore more areas of the solution space. The algorithm is compared with the best known heuristics of the literature and applied on a large problem set. The obtained results are almost of the same quality as the results of these heuristics but the computational time is reduced significantly. Applying GLS to solve the TOP appears to be a very promising technique. Furthermore, the usefulness of exploring more areas of the solution space is clearly demonstrated.     

Decomposition and local search based methods for the traveling umpire problem

The Traveling Umpire Problem (TUP) is a challenging combinatorial optimization problem based on scheduling umpires for Major League Baseball. The TUP aims at assigning umpire crews to the games of a fixed tournament, minimizing the travel distance of the umpires. The present paper introduces two complementary heuristic solution approaches for the TUP. A new method called enhanced iterative deepening search with leaf node improvements (IDLI) generates schedules in several stages by subsequently considering parts of the problem. The second approach is a custom iterated local search algorithm (ILS) with a step counting hill climbing acceptance criterion. IDLI generates new best solutions for many small and medium sized benchmark instances. ILS produces significant improvements for the largest benchmark instances. In addition, the article introduces a new decomposition methodology for generating lower bounds, which improves all known lower bounds for the benchmark instances.     

A reduction approach for solving the rectangle packing area minimization problem

In the rectangle packing area minimization problem (RPAMP) we are given a set of rectangles with known dimensions. We have to determine an arrangement of all rectangles, without overlapping, inside an enveloping rectangle of minimum area. The paper presents a generic approach for solving the RPAMP that is based on two algorithms, one for the 2D Knapsack Problem (KP), and the other for the 2D Strip Packing Problem (SPP). In this way, solving an instance of the RPAMP is reduced to solving multiple SPP and KP instances. A fast constructive heuristic is used as SPP algorithm while the KP algorithm is instantiated by a tree search method and a genetic algorithm alternatively. All these SPP and KP methods have been published previously. Finally, the best variants of the resulting RPAMP heuristics are combined within one procedure. The guillotine cutting condition is always observed as an additional constraint. The approach was tested on 15 well-known RPAMP instances (above all MCNC and GSRC instances) and new best solutions were obtained for 10 instances. The computational effort remains acceptable. Moreover, 24 new benchmark instances are introduced and promising results are reported.     

A reactive tabu search for the vehicle routing problem

The classical vehicle routing problem (VRP) involves determining a fleet of homogeneous size vehicles and designing an associated set of routes that minimizes the total cost. Our tabu search (TS) algorithm to solve the VRP is based on reactive tabu search (RTS) with a new escape mechanism, which manipulates different neighbourhood schemes in a very sophisticated way in order to get a balanced intensification and diversification continuously during the search process. We compare our algorithm with the best methods in the literature using different data sets and report results including new best known solutions for several well-known benchmark problems.     

Curriculum-based course timetabling with SAT and MaxSAT

This paper describes our work on applying novel techniques based on propositional satisfiability (SAT) solvers and optimizers to the Curriculum-based Course Timetabling problem. Out of 32 standard benchmark instances derived from the Second International Timetabling Competition held in 2007, our techniques yield the best known solutions for 21 of them (19 of them being optimal), improving the previously best known solutions for 9. In addition, we obtain 18 new lower bounds for this benchmark set by applying a new full (Weighted) Partial MaxSAT approach of the Curriculum-based Course Timetabling problem.