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The non-smooth and bi-objective team orienteering problem with soft constraints

- Estrada-Moreno, Alejandro, Ferrer, Albert, Juan, Angel, Panadero, Javier, Bagirov, Adil

  • Authors: Estrada-Moreno, Alejandro , Ferrer, Albert , Juan, Angel , Panadero, Javier , Bagirov, Adil
  • Date: 2020
  • Type: Text , Journal article
  • Relation: Mathematics Vol. 8, no. 9 (2020), p.
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  • Description: In the classical team orienteering problem (TOP), a fixed fleet of vehicles is employed, each of them with a limited driving range. The manager has to decide about the subset of customers to visit, as well as the visiting order (routes). Each customer offers a different reward, which is gathered the first time that it is visited. The goal is then to maximize the total reward collected without exceeding the driving range constraint. This paper analyzes a more realistic version of the TOP in which the driving range limitation is considered as a soft constraint: every time that this range is exceeded, a penalty cost is triggered. This cost is modeled as a piece-wise function, which depends on factors such as the distance of the vehicle to the destination depot. As a result, the traditional reward-maximization objective becomes a non-smooth function. In addition, a second objective, regarding the design of balanced routing plans, is considered as well. A mathematical model for this non-smooth and bi-objective TOP is provided, and a biased-randomized algorithm is proposed as a solving approach. © 2020 by the authors.
  • Description: This work has been partially supported by the Spanish Ministry of Economy and Competitiveness & FEDER (SEV-2015-0563), the Spanish Ministry of Science (PID2019-111100RB-C21, RED2018-102642-T), and the Erasmus+ Program (2019-I-ES01-KA103-062602).

A constraint handling technique for constrained multi-objective genetic algorithm

- Long, Qiang

  • Authors: Long, Qiang
  • Date: 2014
  • Type: Text , Journal article
  • Relation: Swarm and Evolutionary Computation Vol. 15, no. (2014), p. 66-79
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  • Description: A new constraint handling technique for multi-objective genetic algorithm is proposed in this paper. There are two important issues in multi-objective genetic algorithm, closeness of the obtained solutions to the real Pareto frontier and diversity of the obtained solutions. If considering a constrained multi-objective programming problem, one needs to take account of feasibility of solutions. Thus, in this new constraint handling technique, we systematically take closeness, diversity and feasibility as three objectives in a multi-objective subproblem. And solutions in each iteration are sorted by optimal sequence method based on those three objectives. Then, the solutions inherited to the next generation are selected based on its optimal order. Numerical tests show that the solutions obtained by this method are not only feasible, but also close to the real Pareto front and have good diversity. © 2013 Elsevier B.V. © 2014 Elsevier Inc.

A prioritized objective actor-critic method for deep reinforcement learning

- Nguyen, Ngoc, Nguyen, Thanh, Vamplew, Peter, Dazeley, Richard, Nahavandi, Saeid

  • Authors: Nguyen, Ngoc , Nguyen, Thanh , Vamplew, Peter , Dazeley, Richard , Nahavandi, Saeid
  • Date: 2021
  • Type: Text , Journal article
  • Relation: Neural Computing and Applications Vol. 33, no. 16 (2021), p. 10335-10349
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  • Description: An increasing number of complex problems have naturally posed significant challenges in decision-making theory and reinforcement learning practices. These problems often involve multiple conflicting reward signals that inherently cause agents’ poor exploration in seeking a specific goal. In extreme cases, the agent gets stuck in a sub-optimal solution and starts behaving harmfully. To overcome such obstacles, we introduce two actor-critic deep reinforcement learning methods, namely Multi-Critic Single Policy (MCSP) and Single Critic Multi-Policy (SCMP), which can adjust agent behaviors to efficiently achieve a designated goal by adopting a weighted-sum scalarization of different objective functions. In particular, MCSP creates a human-centric policy that corresponds to a predefined priority weight of different objectives. Whereas, SCMP is capable of generating a mixed policy based on a set of priority weights, i.e., the generated policy uses the knowledge of different policies (each policy corresponds to a priority weight) to dynamically prioritize objectives in real time. We examine our methods by using the Asynchronous Advantage Actor-Critic (A3C) algorithm to utilize the multithreading mechanism for dynamically balancing training intensity of different policies into a single network. Finally, simulation results show that MCSP and SCMP significantly outperform A3C with respect to the mean of total rewards in two complex problems: Food Collector and Seaquest. © 2021, The Author(s), under exclusive licence to Springer-Verlag London Ltd. part of Springer Nature.
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