This paper is concerned with a variant of the traveling salesman problem (TSP) called the maximum scatter traveling salesman problem (MSTSP). The goal of MSTSP is to find a Hamiltonian cycle that maximizes the minimum length edge of the cycle. ...

• This paper is concerned with the maximum scatter traveling salesman problem (MSTSP).
• Two evolutionary approaches are proposed for solving this problem.
• First approach is a steady-state genetic algorithm, while the latter is a ...

Let X be an n-element point set in the k-dimensional unit cube ${[0,1]}^k$ where $k\ge 2$. According to an old result of Bollobás and Meir (Oper Res Lett 11:19–21, 1992) , there exists a cycle (tour) $x_1,x_2,\dots ,x_n$ through the n points, such that ${\left({\sum }_{i=1}^n,{|x_i-x_{i+1}|}^{\mathrm{...}}\right)}^{\mathrm{}}{}_{}$$$${}_{}$${}_{\mathrm{}}{}_{\mathrm{}}$$\mathrm{}$$\mathrm{}$${\mathrm{}\mathrm{}}^{}$${\left({}_{\mathrm{}}^{},{{}_{}{}_{\mathrm{}}}^{}\right)}^{\mathrm{}}{\mathrm{}}^{\mathrm{}}\sqrt{}$${}_{\mathrm{}}\mathrm{}$${}_{}\mathrm{}{\left(\frac{\mathrm{}}{\mathrm{}}\right)}^{\mathrm{}}\sqrt{}$$\mathrm{}$${}_{}{\mathrm{}}^{\mathrm{}}\sqrt{}$$\mathrm{}$${}_{}\mathrm{}\sqrt{\mathrm{}}{\left(\frac{\mathrm{}}{\mathrm{}}\right)}^{\mathrm{}}\sqrt{}$${}_{}\mathrm{}\sqrt{}\mathrm{}{}_{}\mathrm{}$${}_{\mathrm{}}{\mathrm{}}^{\mathrm{}\mathrm{}}$$\mathrm{}$

This article is concerned with a recently introduced variant of the generalized traveling salesman problem (GTSP) called the family traveling salesman problem (FTSP). Given a set of nodes partitioned into multiple clusters termed as families, the ...

Aiming at the problem that Ant Colony Optimization (ACO) is subject primarily to the parameters, we propose a hybrid algorithm SOA-ACO-2Opt to optimize the ACO parameter combination through Seagull Optimization Algorithm (SOA) to strengthen ACO’s ...

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• A hybrid algorithm SOA-ACO-2Opt is proposed to solve TSP.
• A multi-population mechanism is used to reduce redundant computation and avoid early convergence.
• The desired-path-based avoidance strategy is efficient and of low ...

Traveling Salesman Problem (TSP) and Traveling Repairman Problem (TRP) have been studied due to their real-world applications. While the TSP minimizes the total time to travel to all customers, the TRP minimizes the total waiting time between a ...

• Develop the first formulations for both TSPPD and TRPPD and solving by MIP-Solver.
• Propose a combining the MFEA framework and Tabu Search to solve TSPPD and TRPPD.
• Experiments show that proposed MFEA-TS obtains near-optimal ...

Several studies have attempted to solve traveling salesman problems (TSPs) using various deep learning techniques. Among them, Transformer-based models show state-of-the-art performance even for large-scale Traveling Salesman Problems (TSPs). ...

In recent years, there has been a notable surge in research on machine learning techniques for combinatorial optimization. It has been shown that learning-based methods outperform traditional heuristics and mathematical solvers on the Traveling ...

The use of deep reinforcement learning (DRL) techniques to solve classical combinatorial optimization problems like the Traveling Salesman Problem (TSP) has garnered considerable attention due to its advantage of flexible and fast model-based ...

For the artificial bee colony algorithm (ABC), it is easy to fall into local optimum and has lower convergence accuracy when solving the traveling salesman problem. For addressing this demerit further, a discrete artificial bee colony algorithm ...

• Traveling salesman problem is parallelized by clustering its nodes.
• Clustering is fulfilled iteratively by two-group partitioning of every cluster.
• No further clustering is needed if an open-loop problem is sufficiently small.
• ...

A method of heuristically solving large traveling salesman problems is suggested, where a dramatic computational speedup is guaranteed. A specific genetic algorithm is the solver. The initial problem is broken into a set of open-loop subproblems ...

Combinatorial optimization problem (COP) is an NP-hard problem for which finding an optimal solution is difficult, especially as the problem size increases. The Traveling Salesman Problem (TSP), one of the COPs that can be formulated over a graph,...

This paper addresses the traveling salesman problem with job-times (TSPJ). TSPJ considers two sets of equal size, a set of tasks and a set of vertices, where a traveler must visit each vertex exactly once, return to the starting vertex, and ...

• A multioperator genetic algorithm for the traveling salesman problem with job-times.
• The algorithm works with three crossover and five mutation operators.
• Synergistic effect between the multioperator approach and effective ...

This paper deals with an $\mathcal{N}\mathcal{P}$-hard problem called the colored balanced traveling salesman problem (CBTSP), which is a variation of colored traveling salesman problem (CTSP) which in turn is a variation of multiple traveling salesman problem. To ...

The traveling salesman problem with time windows (TSPTW) has wide practical applications in transportation and scheduling operations. We study the TSPTW in the deterministic case as well as under travel time uncertainty. We consider the three ...

Deep reinforcement learning (RL) has proved to be a competitive heuristic for solving small-sized instances of traveling salesman problems (TSP), but its performance on larger-sized instances is insufficient. Since training on large instances is ...

We study the problem of learning the preferences of drivers and planners in the context of last mile delivery. Given a data set containing historical decisions and delivery locations, the goal is to capture the implicit preferences of the ...

• Expert routing preferences are learned from past solutions in last mile delivery.
• Two-stage approach to learn routing preferences in the traveling salesman problem.
• Structured output prediction is used to improve route prediction ...

The Close-Enough Traveling Salesman Problem (CETSP) is a variant of the well-known Traveling Salesman Problem (TSP). Unlike the TSP, each target in the CETSP has a disk neighborhood, and the target is considered visited when any point in its ...

• The Close-Enough Traveling Salesman Problem is a general model for applications.
• We propose a hybrid evolutionary algorithm for solving this challenging problem.
• The algorithm combines a dedicated crossover and a powerful local ...

• We propose a novel tool for selecting a distribution center for aid distribution.
• We combine knowledge from different fields for a hybrid decision-making approach.
• We provide a promising solution for timely decisions in ...

The distribution of humanitarian aid is a vital issue for humanity's future. In recent years, the management of humanitarian crises has become more crucial than it was a decade ago. Due to the volatility and urgency that characterize such ...

This paper addresses the Family Traveling Salesman Problem (FTSP), a variant of the Traveling Salesman Problem that group nodes into families. The goal is to select the best route by visiting only a subset of nodes from each family. We developed ...

• We propose exact and heuristic methods to solve the Family Traveling Salesman Problem.
• We design a parallel branch&cut algorithm with an efficient local search procedure.
• A BRKGA-QL method was adapted with different decoders and ...

The balanced traveling salesman problem (BTSP) is a variant of the traveling salesman problem, in which one seeks a tour that minimizes the difference between the largest and smallest edge costs in the tour. The BTSP, which is obviously NP-hard, ...