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In this paper, we present a new linear programming (LP) formulation of the Traveling Salesman Problem (TSP). The proposed model has O(n^8) variables and O(n^7) constraints, where n is the number of cities. Our numerical experimentation…
This paper addresses the Traveling Salesman Problem with Drone (TSP-D), in which a truck and drone are used to deliver parcels to customers. The objective of this problem is to either minimize the total operational cost (min-cost TSP-D) or…
This paper aims to develop a learning method for a special class of traveling salesman problems (TSP), namely, the pickup-and-delivery TSP (PDTSP), which finds the shortest tour along a sequence of one-to-one pickup-and-delivery nodes.…
The Flexible Job Shop Scheduling Problem (FJSP) is a combinatorial problem that continues to be studied extensively due to its practical implications in manufacturing systems and emerging new variants, in order to model and optimize more…
Severe weather events can cause extensive damage to electrical distribution networks, requiring a multi-day restoration effort. Optimizing the dispatch of repair crews minimizes the severe socio-economic consequences of such events.…
In the new wave of artificial intelligence, deep learning is impacting various industries. As a closely related area, optimization algorithms greatly contribute to the development of deep learning. But the reverse applications are still…
Traveling Salesman Problem (TSP) is a decision-making problem that is essential for a number of practical applications. Today, this problem is solved on digital computers exploiting Boolean-type architecture by checking one by one a number…
This work addresses the uniform parallel machine scheduling problem within an optimistic bilevel optimization framework. The leader seeks to minimize the weighted number of tardy jobs, while the follower aims to minimize the total…
The Multiple Traveling Salesman Problem (mTSP) extends the Traveling Salesman Problem to m tours that start and end at a common depot and jointly visit all customers exactly once. In the min-max variant, the objective is to minimize the…
In this paper, we present formulations and an exact method to solve the Time Dependent Traveling Salesman Problem with Time Window (TD-TSPTW) under a generic travel cost function where waiting is allowed. A particular case in which the…
In the Traveling Salesman Problem (TSP), a salesman wants to visit a set of cities and return home. There is a cost $c_{ij}$ of traveling from city $i$ to city $j$, which is the same in either direction for the Symmetric TSP. The objective…
The Traveling Thief Problem (TTP) is a multi-component optimization problem that captures the interplay between routing and packing decisions by combining the classical Traveling Salesperson Problem (TSP) and the Knapsack Problem (KP). The…
A new characterization of Hamiltonian graphs using f-cutset matrix is proposed. Based on this new characterization, a new exact polynomial time algorithm for the traveling salesman problem (TSP) is developed. We then define the so-called…
We present a benchmark set for Traveling salesman problem (TSP) with characteristics that are different from the existing benchmark sets. In particular, we focus on small instances which prove to be challenging for one or more…
In this paper, we revisit the application of Genetic Algorithm (GA) to the Traveling Salesperson Problem (TSP) and introduce a family of novel crossover operators that outperform the previous state of the art. The novel crossover operators…
Large Language Models (LLMs) have shown notable potential in code generation for optimization algorithms, unlocking exciting new opportunities. This paper examines how LLMs, rather than creating algorithms from scratch, can improve existing…
In this paper, we propose a method to solve a bi-objective variant of the well-studied Traveling Thief Problem (TTP). The TTP is a multi-component problem that combines two classic combinatorial problems: Traveling Salesman Problem (TSP)…
We present a physics inspired heuristic method for solving combinatorial optimization problems. Our approach is specifically motivated by the desire to avoid trapping in metastable local minima- a common occurrence in hard problems with…
We present a scalable, high-performance algorithm that deterministically solves large-scale instances of the Traveling Salesman problem (in its asymmetric version, ATSP) to optimality using commercially available computing hardware. By…
Ant Colony Algorithm (ACA) and Genetic Local Search (GLS) are two optimization algorithms that have been successfully applied to the Traveling Salesman Problem (TSP). In this paper we define new crossover operator then redefine ACAs ants as…