An evolution strategy approach to the team orienteering problem with time windows

doi:10.1016/j.cie.2019.106109

Computers & Industrial Engineering

Volume 139, January 2020, 106109

https://doi.org/10.1016/j.cie.2019.106109 Get rights and content

Highlights

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A new constructive heuristic and an evolution strategy approach are presented.
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Solutions are generated by the self-adaptive ruin and recreate heuristic.
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Efficient and effective random local search is developed.
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A goodness of scores method is proposed for truncation of offspring population.
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7 new best-known solutions are obtained by the evolution strategy approach.

Abstract

The team orienteering problem with time windows (TOPTW) is a highly constrained NP-hard problem having many practical applications in vehicle routing and production scheduling. The TOPTW is an extended variant of the Orienteering Problem (OP), where each node has a predefined time window during which the service has to be started. The aim is to maximize the total collected score by visiting a set of nodes with a limited number of tours since the given distance budget is limited. We propose an evolution strategy (ES) together with an effective constructive heuristic for solving the TOPTW. The main feature of the ES is to generate an offspring solution through ruin and recreate (RR) heuristic, where a number of nodes are removed from the incumbent solution and then, they are reinserted into tours until a complete solution is obtained. The ES is hybridized with an efficient random local search to enhance solution quality. For survivor selection, we use a goodness of scores approach to determine and diversify the population for the next generation. Parameters of the ES are determined through the design of experiment approach to tune them. The computational results show that the constructive heuristic is slightly better than existing heuristics in the literature. Furthermore, the detailed computation results on the benchmark suite from the literature confirm the effectiveness of the evolution strategy. Ultimately, the evolution strategy obtains new best-known solutions for 7 benchmark problem instances.

Section snippets

Introduction and literature review

As a sports discipline, orienteering can be defined as follows. Given a set of control points with associated profits together with the start and end points, the orienteering problem (OP) aims to obtain a tour between the start and endpoints so as to maximize the total profit collected; subject to a given distance budget. Since distance is limited, a tour cannot include all points. The first public orienteering competition was held in 1897 in Norway; however, the practice in the army is earlier

The constructive heuristic

Constructive heuristics aim to develop good solutions/individuals by starting from an empty solution and iteratively adding solution components to the current partial solution. Since the TOPTW is a constrained optimization problem, a constructive heuristic must ensure that the solution is feasible when new components are added to the partial solution. Constructive heuristics generally use a problem-specific cost function to select the next candidate node to insert into the partial solution. One

Evolution strategy approach

Evolution strategy (ES) is a metaheuristic optimization algorithm developed by Rechenberg, 1971, Schwefel, 1975. ES is typically applied to real parameter optimization problems and it uses mutation for offspring generation. The mutation is performed by adding a random value drawn from a normal distribution. Parameter tuning is an important issue when using evolutionary algorithms, including ES. The idea of evolving parameters within the individuals, self-adaption, is considered as a standard

Computational experiments

The proposed constructive heuristic and evolutionary strategy are coded in C++ and experiments are carried out on a computer having a 2.66 GHz Intel Core2 Quad Q9400 CPU and 3GBs of main memory. Two benchmark sets are used in experiments. There are 144 problem instances in total in these two benchmark sets. The first set is designed by Montemanni and Gambardella (2009) based on their OPTW instances, which in turn are based on Solomon (1987) vehicle routing with time windows test instances and

Conclusion

A novel KT constructive heuristic and a self-adaptive evolution strategy for solving the TOPTW are presented in this paper. Three individuals in the initial population are constructed using KT, LS1 and VI heuristics. Then, the rest of the population is constructed by perturbations of these three heuristics in such a way that randomly chosen two neighborhood structures are applied to these three solutions. Offspring are generated by the ruin and recreate algorithm, where ruin size is adaptively

Acknowledgement

M. Fatih Tasgetiren acknowledges the HUST Project in Wuhan, China. He is partially supported by the National Natural Science Foundation of China with Grant No. 51435009.

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Citation Excerpt :
The ES is generally used for continuous optimization, but it has also been applied to discrete optimization problems. For example, the ES has recently been successfully applied for solving the team orienteering problem with time windows (Karabulut and Tasgetiren, 2020) and the multiple traveling salesmen problem (Karabulut et al., 2021). In this paper, we extend the ES to the DPFSP-SDST with problem-specific adjustments based on these successful applications.
This paper considers a distributed permutation flowshop scheduling problem with sequence-dependent setup times (DPFSP-SDST) to minimize the maximum completion time among the factories. The global economy has enabled large companies to have distributed production centers to become widespread, and effective production scheduling between these centers plays a vital role in the competitiveness of companies. To provide effective scheduling for the DPFSP-SDST, we propose a new mixed-integer linear programming (MILP) model and a new constraint programming (CP) model, which is presented for the first time in literature to the best of our knowledge. As the CP has become a solid competitor to the MILP in the literature, this study aims to exploit the effectiveness of CP to solve such a complex DPFSP-SDST. Since the problem is NP-hard, we also offer an evolution strategy (ES_en) algorithm that employs a self-adaptive scheme to obtain high-quality solutions in a short time. A ruin-and-recreate procedure is also embedded into the developed ES_en. We calibrate the parameters of the proposed ES_en using a design of experiment approach. We also compare the proposed ES_en algorithm's performance with three state-of-the-art metaheuristic algorithms from the literature, i.e., the IG2S (a variant of an iterated greedy algorithm with NEH2_en initialization), IGR (another variant of an iterated greedy algorithm with a restart scheme), and discrete artificial bee colony (DABC) algorithm. A detailed computational experiment is carried out to evaluate the performance of the mathematical models (MILP and CP) and the heuristic algorithms (ES_en, IG2S, IGR, and DABC). A comprehensive benchmark set is generated for the DPFSP-SDST from the well-known PFSP instances from the literature, considering various combinations of jobs, machines, factories, and SDST settings, resulting in 2880 benchmark instances. For 216 out of 240 small-size instances, optimal results are reported by solving the proposed MILP and CP models, whereas time-limited model results are reported for the rest. The computational results show that the CP model outperforms the MILP model in terms of the solution time for small-size instances. Initially, the performance of the heuristic algorithms is verified concerning the optimal results on small-size instances. Then, the performance of the heuristic algorithms is evaluated for large instances. ES_en algorithm significantly outperforms the IG2S, IGR, and DABC algorithms for solving large instances. The computational results show that the proposed ES_en algorithm is robust and provides good-quality solutions for the DPFSP-SDST in a short computational time.

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An evolution strategy approach to the team orienteering problem with time windows

Highlights

Abstract

Section snippets

Introduction and literature review

The constructive heuristic

Evolution strategy approach

Computational experiments

Conclusion

Acknowledgement

European Journal of Operational Research

European Journal of Operational Research

Computers & Industrial Engineering

Computers & Industrial Engineering

Applied Soft Computing

European Journal of Operational Research

Computers & Industrial Engineering

European Journal of Operational Research

European Journal of Operational Research

European Journal of Operational Research

Computers & Operations Research

Computers & Operations Research

Expert Systems with Applications

Journal of Computational Physics

European Journal of Operational Research

Computers & Operations Research

Computers & Operations Research

Computers & Operations Research

Computers and Operations Research

European Journal of Operational Research

European Journal of Operational Research

Computers & Industrial Engineering

Evolution strategies – A comprehensive introduction

Natural Computing

A memetic algorithm for the team orienteering problem

4OR

Algorithms and solutions to multi-level vehicle routing problems

A tabu search heuristic for periodic and multi-depot vehicle routing problems

Networks

Introduction to evolutionary computing

Efficient cluster-based heuristics for the team orienteering problem with time windows

Asia-Pacific Journal of Operational Research

The orienteering problem

Naval Research Logistics