Breakout Local Search for the Travelling Salesman Problem

The travelling salesman problem (TSP), a famous NP-hard combinatorial optimisation problem (COP), consists of finding a minimum length tour that visits n cities exactly once and comes back to the starting city. This paper presents a resolution of the TSP using the breakout local search metaheuristic algorithm (BLS), which is based on the iterated local search (ILS) framework and improves it by introducing some fundamental features of several well-established metaheuristics such as tabu search (TS) and variable neighbourhood search (VNS). BLS moves from a local optimum of a neighbourhood to another by applying perturbation jumps whose type and number are determined adaptively. It has already been applied to many COP and gives good results. This innovative hybridisation resolved well 41 instances from the commonly used benchmark library TSPLIB. The high quality of experimental results shows the competitiveness of the proposed algorithm compared to other algorithms based on local search

О Классификации Приближенных Методов Комбинаторной Оптимизации

В работе предлагается классификация приближенных методов комбинаторной оптимизации, которая обобщает и дополняет существующие подходы

Global optimization of spin Hamiltonians with gain-dissipative systems.

Recently, several platforms were proposed and demonstrated a proof-of-principle for finding the global minimum of the spin Hamiltonians such as the Ising and XY models using gain-dissipative quantum and classical systems. The implementation of dynamical adjustment of the gain and coupling strengths has been established as a vital feedback mechanism for analog Hamiltonian physical systems that aim to simulate spin Hamiltonians. Based on the principle of operation of such simulators we develop a novel class of gain-dissipative algorithms for global optimisation of NP-hard problems and show its performance in comparison with the classical global optimisation algorithms. These systems can be used to study the ground state and statistical properties of spin systems and as a direct benchmark for the performance testing of the gain-dissipative physical simulators. Our theoretical and numerical estimations suggest that for large problem sizes the analog simulator when built might outperform the classical computer computations by several orders of magnitude under certain assumptions about the simulator operation

Revisiting the Evolution and Application of Assignment Problem: A Brief Overview

The assignment problem (AP) is incredibly challenging that can model many real-life problems. This paper provides a limited review of the recent developments that have appeared in the literature, meaning of assignment problem as well as solving techniques and will provide a review on   a lot of research studies on different types of assignment problem taking place in present day real life situation in order to capture the variations in different types of assignment techniques. Keywords: Assignment problem, Quadratic Assignment, Vehicle Routing, Exact Algorithm, Bound, Heuristic etc

Elitist Schema Overlays: A Multi-Parent Genetic Operator

Genetic Algorithms are programs inspired by natural evolution used to solve difficult problems in Mathematics and Computer Science. The theoretical foundations of Genetic Algorithms, the schema theorem and the building-block hypothesis, state that the success of Genetic Algorithms stems from the propagation of fit genetic subsequences. Multi-parent operators were shown to increase the performance of Genetic Algorithms by increasing the disruptivity of genetic operations. Disruptive genetic operators help prevent suboptimal genetic sequences from propagating into future generations, which leads to an improved fitness for the population over time. In this paper we explore the use of a novel multi-parent genetic operator, the elitist schema overlay, which propagates the matching segments in the genetic sequences of the elite subpopulation to bias the global search towards the best known solutions. We investigate the parameters that drive the behavior of elitist schema overlays to determine the most successful model, and we compare this to successful multi-parent and traditional genetic operators from the literature

Exploratory Combinatorial Optimization with Reinforcement Learning

Many real-world problems can be reduced to combinatorial optimization on a graph, where the subset or ordering of vertices that maximize some objective function must be found. With such tasks often NP-hard and analytically intractable, reinforcement learning (RL) has shown promise as a framework with which efficient heuristic methods to tackle these problems can be learned. Previous works construct the solution subset incrementally, adding one element at a time, however, the irreversible nature of this approach prevents the agent from revising its earlier decisions, which may be necessary given the complexity of the optimization task. We instead propose that the agent should seek to continuously improve the solution by learning to explore at test time. Our approach of exploratory combinatorial optimization (ECO-DQN) is, in principle, applicable to any combinatorial problem that can be defined on a graph. Experimentally, we show our method to produce state-of-the-art RL performance on the Maximum Cut problem. Moreover, because ECO-DQN can start from any arbitrary configuration, it can be combined with other search methods to further improve performance, which we demonstrate using a simple random search.Comment: In Proceedings of the 34th National Conference on Artificial Intelligence, AAAI 202