It is a long time that the Simulated Annealing (SA) procedure has been introduced as a model-free optimization for solving NP-hard problems. Improvements from the standard SA in the recent decade mostly concentrate on combining its original algorithm with some heuristic methods. These modifications are rarely happened to the initial condition selection methods from which the annealing schedules...

This paper introduces a time efficient deep learning-based solution to the traveling salesman problem with window (TSPTW). Our goal is reduce total tour length traveled by -*the agent without violating any limitations. will aid in decreasing required supply type of service, as well lowering emissions produced automobiles, allowing our planet recover from air pollution emissions. The proposed mo...

It is a long time that the Simulated Annealing (SA) procedure is introduced as a model-free optimization for solving NP-hard problems. Improvements from the standard SA in the recent decade mostly concentrate on combining its original algorithm with some heuristic methods. These modifications are rarely happened to the initial condition selection methods from which the annealing schedules start...

It is a long time that the Simulated Annealing (SA) procedure is introduced as a model-free optimization for solving NP-hard problems. Improvements from the standard SA in the recent decade mostly concentrate on combining its original algorithm with some heuristic methods. These modifications are rarely happened to the initial condition selection methods from which the annealing schedules start...

The optimal cooling schedule for simulated annealing is formulated to derive a differential equation for the time-dependent temperature T(t). Based on this equation, the long-term behavior of T(t), entropy production, and the Kullback-Leibler entropy are studied. For some simple examples, such as a many-level system and the small scale traveling salesman problem, the explicit time dependence of...

We consider a single-machine scheduling problem which arises as a subproblem in a job-shop environment where the jobs have to be transported between the machines by a single transport robot. The robot scheduling problem may be regarded as a generalization of the traveling salesman problem with time windows, where additionally generalized precedence constraints have to be respected. The objectiv...

Traveling Salesman Problem (TSP) is a generic name that includes diverse practical models. Motivated by applications, a new model of TSP is examined — a synthesis of classical TSP and classical Transportation Problem. Algorithms based on Integer Programming cutting-plane methods and Branch and Bound Techniques are obvious. Mathematics Subject Classification 2000: 91A05, 91A06, 91A10, 91A44, 90C...

In the Attractive Traveling Salesman Problem the vertex set is partitioned into facility vertices and customer vertices. A maximum profit tour must be constructed on a subset of the facility vertices. Profit is computed through an attraction function: every visited facility vertex attracts a portion of the profit from the customer vertices based on the distance between the facility and customer...

In the online traveling salesman problem requests for visits to cities (points in a metric space) arrive online while the salesman is traveling. The salesman moves at no more than unit speed and starts and ends his work at a designated origin. The objective is to find a routing for the salesman which finishes as early as possible. Performance of algorithms is measured through their competitive ...

In this paper, we present a polynomial-sized linear programming formulation of the Traveling Salesman Problem (TSP). The proposed linear program is a network flow-based model. Numerical implementation issues and results are discussed. KeyWords: Linear Programming; Network Optimization; Integer Programming; Traveling Salesman Problem; Combinatorial Optimization; Scheduling; Sequencing.