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Combinatorial optimization and metaheuristics
Today, combinatorial optimization is one of the youngest and most active areas of discrete mathematics. It is a branch of optimization in applied mathematics and computer science, related to operational research, algorithm theory and computational complexity theory. It sits at the intersection of several fields, including artificial intelligence, mathematics and software engineering. Its increasing interest arises for the fact that a large number of scientific and industrial problems can be formulated as abstract combinatorial optimization problems, through graphs and/or (integer) linear programs. Some of these problems have polynomial-time (“efficient”) algorithms, while most of them are NP-hard, i.e. it is not proved that they can be solved in polynomial-time. Mainly, it means that it is not possible to guarantee that an exact solution to the problem can be found and one has to settle for an approximate solution with known performance guarantees. Indeed, the goal of approximate methods is to find “quickly” (reasonable run-times), with “high” probability, provable “good” solutions (low error from the real optimal solution). In the last 20 years, a new kind of algorithm commonly called metaheuristics have emerged in this class, which basically try to combine heuristics in high level frameworks aimed at efficiently and effectively exploring the search space. This report briefly outlines the components, concepts, advantages and disadvantages of different metaheuristic approaches from a conceptual point of view, in order to analyze their similarities and differences. The two very significant forces of intensification and diversification, that mainly determine the behavior of a metaheuristic, will be pointed out. The report concludes by exploring the importance of hybridization and integration methods
Reinforcement learning based local search for grouping problems: A case study on graph coloring
Grouping problems aim to partition a set of items into multiple mutually
disjoint subsets according to some specific criterion and constraints. Grouping
problems cover a large class of important combinatorial optimization problems
that are generally computationally difficult. In this paper, we propose a
general solution approach for grouping problems, i.e., reinforcement learning
based local search (RLS), which combines reinforcement learning techniques with
descent-based local search. The viability of the proposed approach is verified
on a well-known representative grouping problem (graph coloring) where a very
simple descent-based coloring algorithm is applied. Experimental studies on
popular DIMACS and COLOR02 benchmark graphs indicate that RLS achieves
competitive performances compared to a number of well-known coloring
algorithms
A Study on the Optimization of Chain Supermarkets’ Distribution Route Based on the Quantum-Inspired Evolutionary Algorithm
The chain supermarket has become a major part of China’s retail industry, and the optimization of chain supermarkets’ distribution route is an important issue that needs to be considered for the distribution center, because for a chain supermarket it affects the logistics cost and the competition in the market directly. In this paper, analyzing the current distribution situation of chain supermarkets both at home and abroad and studying the quantum-inspired evolutionary algorithm (QEA), we set up the mathematical model of chain supermarkets’ distribution route and solve the optimized distribution route throughout QEA. At last, we take Hongqi Chain Supermarket in Chengdu as an example to perform the experiment and compare QEA with the genetic algorithm (GA) in the fields of the convergence, the optimal solution, the search ability, and so on. The experiment results show that the distribution route optimized by QEA behaves better than that by GA, and QEA has stronger global search ability for both a small-scale chain supermarket and a large-scale chain supermarket. Moreover, the success rate of QEA in searching routes is higher than that of GA
Digital Ecosystems: Ecosystem-Oriented Architectures
We view Digital Ecosystems to be the digital counterparts of biological
ecosystems. Here, we are concerned with the creation of these Digital
Ecosystems, exploiting the self-organising properties of biological ecosystems
to evolve high-level software applications. Therefore, we created the Digital
Ecosystem, a novel optimisation technique inspired by biological ecosystems,
where the optimisation works at two levels: a first optimisation, migration of
agents which are distributed in a decentralised peer-to-peer network, operating
continuously in time; this process feeds a second optimisation based on
evolutionary computing that operates locally on single peers and is aimed at
finding solutions to satisfy locally relevant constraints. The Digital
Ecosystem was then measured experimentally through simulations, with measures
originating from theoretical ecology, evaluating its likeness to biological
ecosystems. This included its responsiveness to requests for applications from
the user base, as a measure of the ecological succession (ecosystem maturity).
Overall, we have advanced the understanding of Digital Ecosystems, creating
Ecosystem-Oriented Architectures where the word ecosystem is more than just a
metaphor.Comment: 39 pages, 26 figures, journa
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