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

Genetic algorithm approach to find the best input variable partitioning

Conference PaperThis paper presents a variable partition algorithm which combines the quasi-reduced ordered multiple-terminal multiple-valued decision diagrams and genetic algorithms (GAs). The algorithm is better than the previous techniques which find a good functional decomposition by non-exhaustive search and expands the range of searching for the best decomposition providing the optimal subtable multiplicity. The possible solutions are evaluated using the gain of decomposition for a multiple-output multiple-valued logic function. The distinct feature of GA is the possible solutions being coded by real numbers. Here the simplex-based crossover is proposed to use for the recombination stage of GA. It permits to increase the GA coverag

An Efficient Approach towards Network Routing using Genetic Algorithm

The network field has been very popular in recent times and has aroused much of the attention of researchers. The network must keep working with the varying infrastructure and must adapt to rapid topology changes. Graphical representation of the networks with a series of edges varying over time can help in analysis and study. This paper presents a novel adaptive and dynamic network routing algorithm based on a Regenerate Genetic Algorithm (RGA) with the analysis of network delays. With the help of RGA at least a very good path, if not the shortest one, can be found starting from the origin and leading to a destination. Many algorithms are devised to solve the shortest path (SP) problem for example Dijkstra algorithm which can solve polynomial SP problems. These are equally effective in wired as well as wireless networks with fixed infrastructure. But the same algorithms offer exponential computational complexity in dealing with the real-time communication for rapidly changing network topologies. The proposed genetic algorithm (GA) provides more efficient and dynamic solutions despite changes in network topology, network change, link or node deletion from the network, and the network volume (with numerous routes)

A bi-objective genetic algorithm approach to risk mitigation in project scheduling

A problem of risk mitigation in project scheduling is formulated as a bi-objective optimization problem, where the expected makespan and the expected total cost are both to be minimized. The expected total cost is the sum of four cost components: overhead cost, activity execution cost, cost of reducing risks and penalty cost for tardiness. Risks for activities are predefined. For each risk at an activity, various levels are defined, which correspond to the results of different preventive measures. Only those risks with a probable impact on the duration of the related activity are considered here. Impacts of risks are not only accounted for through the expected makespan but are also translated into cost and thus have an impact on the expected total cost. An MIP model and a heuristic solution approach based on genetic algorithms (GAs) is proposed. The experiments conducted indicate that GAs provide a fast and effective solution approach to the problem. For smaller problems, the results obtained by the GA are very good. For larger problems, there is room for improvement

An efficient genetic algorithm for large-scale transmit power control of dense and robust wireless networks in harsh industrial environments

The industrial wireless local area network (IWLAN) is increasingly dense, due to not only the penetration of wireless applications to shop floors and warehouses, but also the rising need of redundancy for robust wireless coverage. Instead of simply powering on all access points (APs), there is an unavoidable need to dynamically control the transmit power of APs on a large scale, in order to minimize interference and adapt the coverage to the latest shadowing effects of dominant obstacles in an industrial indoor environment. To fulfill this need, this paper formulates a transmit power control (TPC) model that enables both powering on/off APs and transmit power calibration of each AP that is powered on. This TPC model uses an empirical one-slope path loss model considering three-dimensional obstacle shadowing effects, to enable accurate yet simple coverage prediction. An efficient genetic algorithm (GA), named GATPC, is designed to solve this TPC model even on a large scale. To this end, it leverages repair mechanism-based population initialization, crossover and mutation, parallelism as well as dedicated speedup measures. The GATPC was experimentally validated in a small-scale IWLAN that is deployed a real industrial indoor environment. It was further numerically demonstrated and benchmarked on both small- and large-scales, regarding the effectiveness and the scalability of TPC. Moreover, sensitivity analysis was performed to reveal the produced interference and the qualification rate of GATPC in function of varying target coverage percentage as well as number and placement direction of dominant obstacles. (C) 2018 Elsevier B.V. All rights reserved