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We formulate binary optimization functions for single-vehicle routing, travelling salesperson and collision-free multi-vehicle routing with significant improvements in the number of variables over existing formulations. The provided…
Many important challenges in science and technology can be cast as optimization problems. When viewed in a statistical physics framework, these can be tackled by simulated annealing, where a gradual cooling procedure helps search for…
Solutions to the Traveling Salesperson Problem (TSP) have practical applications to processes in transportation, logistics, and automation, yet must be computed with minimal delay to satisfy the real-time nature of the underlying tasks.…
The problem of minimization of a quadratic functional depending on great number of binary variables is examined. 3 variants of minimization procedure are studied with the aid of computer simulation for spin-glass matrices. It is shown that…
In this article we address the problem of partitioning a carsharing business area into pricing zones. We formalize the problem mathematically and show that the resulting partitioning problem can be formulated as a binary integer programming…
Recently, there has been considerable interest in solving optimization problems by mapping these onto a binary representation, sparked mostly by the use of quantum annealing machines. Such binary representation is reminiscent of a discrete…
Annealing machines specialized for combinatorial optimization problems have been developed, and some companies offer services to use those machines. Such specialized machines can only handle binary variables, and their input format is the…
We propose a general-purpose method for finding high-quality solutions to hard optimization problems, inspired by self-organizing processes often found in nature. The method, called Extremal Optimization, successively eliminates extremely…
In this paper we consider discrete robot path planning problems on metric graphs. We propose a clustering method, Gamma-Clustering for the planning graph that significantly reduces the number of feasible solutions, yet retains a solution…
We present an algorithm for the asymmetric traveling salesman problem on instances which satisfy the triangle inequality. Like several existing algorithms, it achieves approximation ratio O(log n). Unlike previous algorithms, it uses…
With applications to many disciplines, the traveling salesman problem (TSP) is a classical computer science optimization problem with applications to industrial engineering, theoretical computer science, bioinformatics, and several other…
Capacity expansions as well as its reduction have been widely anticipated as important countermeasures for traffic congestion. Although capacity expansion had been traditionally well noticed as a congestion mitigation measure, but it was…
This paper proposes a framework that formulates a wide range of graph combinatorial optimization problems using permutation-based representations. These problems include the travelling salesman problem, maximum independent set, maximum cut,…
Combinatorial optimization plays an important role in real-world problem solving. In the big data era, the dimensionality of a combinatorial optimization problem is usually very large, which poses a significant challenge to existing…
The Traveling Salesman Problem is one of the most intensively studied combinatorial optimization problems due both to its range of real-world applications and its computational complexity. When combined with the Set Covering Problem, it…
The Traveling Salesman Problem (TSP) is one of the classic and hard problems in combinatorial optimization. We develop a new heuristic that uses a connection between Minimum Cost Flow Problems and the TSP to improve on a given suboptimal…
The Traveling Thief Problem is an NP-hard combination of the well known traveling salesman and knapsack packing problems. In this paper, we use symbolic regression to learn useful features of near-optimal packing plans, which we then use to…
Original equipment manufacturers (OEMs) manufacture, inventory and transport new vehicles to franchised dealers. These franchised dealers inventory and sell new vehicles to end users. OEMs rely on logistics companies with a special type of…
Factorization Machine (FM) is the most commonly used model to build a recommendation system since it can incorporate side information to improve performance. However, producing item suggestions for a given user with a trained FM is…
The multi-path Traveling Salesman Problem with stochastic travel costs arises in hybrid vehicle routing applications designed for Smart City and City Logistics, where multiple paths exist between each pair of locations. Travel times along…