Solution to travelling salesman problem by clusters and a modified multi-restart iterated local search metaheuristic

Adapting blockchain's proof-of-work mechanism for multiple traveling salesmen problem optimization

The blockchain network uses a Proof-of-Work (PoW) mechanism to validate transactions and keep the blockchain growth safe against tampering, but it is hugely energy-consuming with no benefit to the peer-to-peer network participants. In this paper, we proposed a blockchain network for distributing products to different locations based on the use of the Proof of Useful Work mechanism, in which miners use computing resources to optimize the traveling salesman problem (TSP) as an alternative to solving mathematical problems that represent the basis of the traditional PoW mechanism to get a new block. According to this proposed blockchain, it not only receives and securely stores the distribution locations but also improves the paths for salesmen when traveling between different locations during the transportation process. This strategy aims to take advantage of the miners' efforts to minimize the traveled distance by applying the clustering technique and computing the shortest path by Guided Local Search (GLS) for each cluster at the same time. According to the tested results on TSP-LIB instances, the used strategy works efficiently with an average of 0.08 compared to the rest of the meta-heuristics, and the proposed architecture reduced total distances with an average of 0.025%. In addition, the block generation time in the blockchain decreased by 11.11% compared to other works.

A clustering metaheuristic for large orienteering problems

The Orienteering Problem is a routing problem that commonly appears in mapping, transportation, distribution, and scheduling scenarios. The Orienteering Problem is a challenging NP-hard problem, such that obtaining optimal or near optimal solutions usually requires a significant amount of computation for large and even moderately large instances. As a result, existing algorithms cannot effectively be utilized for solving large Orienteering Problems in an online setting, which is often required in real-world applications where a plan has to be iteratively computed. For instance, a planner might need to adapt to changes in the scenario or in the environment (e.g., this is common in goods delivery, as well as in mobile robotic scenarios for coverage, monitoring, and surveillance). Motivated by these limitations, we propose a multi-stage clustering-based metaheuristic for tackling large Orienteering Problems in an effective, strategically controlled amount of computation time. The metaheuristic starts by decomposing the problem into smaller, independent sub-problems that are efficiently solved using an algorithm of choice, sequentially or in parallel. The obtained solutions are then merged to form a solution for the original problem, and then further optimized and processed to ensure feasibility. The metaheuristic aims to dramatically improve the computation time of a given Orienteering Problem algorithm without a significant decrease in the solution quality of that algorithm, especially for large Orienteering Problems. We have validated the effectiveness of the proposed metaheuristic design through a set of computational experiments. In particular, using a state-of-the-art heuristic and an exact algorithm, we have shown that it is significantly beneficial to use the Orienteering Problem algorithm plugged into our metaheuristic, as opposed to using it as a standalone algorithm. This was found to be especially true for large problems. As a result, large instances of Orienteering Problems can be effectively tackled within reasonable time bounds even for online application scenarios.

Many Paths to the Same Goal: Balancing Exploration and Exploitation during Probabilistic Route Planning

During self-guided behaviors, animals identify constraints of the problems they face and adaptively employ appropriate strategies (Marsh, 2002). In the case of foraging, animals must balance sensory-guided exploration of an environment with memory-guided exploitation of known resource locations. Here, we show that animals adaptively shift cognitive resources between sensory and memory systems during foraging to optimize route planning under uncertainty. We demonstrate this using a new, laboratory-based discovery method to define the strategies used to solve a difficult route optimization scenario, the probabilistic “traveling salesman” problem (Raman and Gill, 2017; Fuentes et al., 2018; Mukherjee et al., 2019). Using this system, we precisely manipulated the strength of prior information as well as the complexity of the problem. We find that rats are capable of efficiently solving this route-planning problem, even under conditions with unreliable prior information and a large space of possible solutions. Through analysis of animals’ trajectories, we show that they shift the balance between exploiting known locations and searching for new locations of rewards based on the predictability of reward locations. When compared with a Bayesian search, we found that animal performance is consistent with an approach that adaptively allocates cognitive resources between sensory processing and memory, enhancing sensory acuity and reducing memory load under conditions in which prior information is unreliable. Our findings establish new approaches to understand neural substrates of natural behavior as well as the rational development of biologically inspired approaches for complex real-world optimization.

Multi-start heuristic approaches for one-to-one pickup and delivery problems with shortest-path transport along real-life paths

The One-to-one Pickup and Delivery Problem with Shortest-path Transport along Real-life Paths (OPDPSTRP) is presented in this paper. It is a variation of the One-to-one Pickup and Delivery Problem (OPDP), which is common in daily life, such as the Passenger Train Operation Plans (PTOP) and partial Taxi-sharing Problem. Unlike the classical OPDP, in the OPDPSTRP, (1) each demand must be transported along the shortest path according to passengers/shippers requirements, and (2) each vehicle should travel along a real-life path. First, six route structure rules are proposed for the OPDPSTRP, and a kind of Mixed-Integer Programming (MIP) models is formulated for it. Second, A Variable Neighborhood Descent (VND), a Variable Neighborhood Research (VNS), a Multi-Start VND (MS_VND) and a Multi-Start VNS (MS_VNS) with five neighborhood operators has been developed to solve the problem. Finally, The Gurobi solver, the VND, the VNS, the MS_VND and the MS_VNS have been compared with each other by 84 random instances partitioned in small size connected graphs, medium size connected graphs and large size connected graphs. From the test results we found that solutions generated by these approaches are often comparable with those found by the Gurobi solver, and the solutions found by these approaches are better than the solutions found by the Gurobi solver when solving instances with larger numbers of demands. In almost all instances, the MS_VND significantly outperforms the VND and the VNS in terms of solution quality, and outperforms the MS_VNS both in terms of solution quality and CPU time. In the instances with large numbers of demands, the MS_VND is still able to generate good feasible solutions in a reasonable CPU time, which is of vital practical significance for real-life instances.