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

Hybrid algorithms for independent batch scheduling in grids

Grid computing has emerged as a wide area distributed paradigm for solving large-scale problems in science, engineering, etc. and is known as the family of eScience grid-enabled applications. Computing planning of incoming jobs efficiently with available machines in the grid system is the main requirement for optimised system performance. One version of the problem is that of independent batch scheduling, in which jobs are assumed to be independent and are scheduled in batches aimed at minimising the makespan and flowtime. Given the hardness of the problem, heuristics are used to find high quality solutions for practical purposes of designing efficient grid schedulers. Recently, considerable efforts were spent in implementing and evaluating not only stand-alone heuristics and meta-heuristics, but also their hybridisation into even higher level algorithms. In this paper, we present a study on the performance of two popular algorithms for the problem, namely Genetic Algorithms (GAs) and Tabu Search (TS) and two hybridisations involving them, namely, the GA (TS) and GA-TS, which differ in the way the main control and cooperation among GA and TS are implemented. The hierarchic and simultaneous optimisation modes are considered for the bi-objective scheduling problem. Evaluation is done using different grid scenarios generated by a grid simulator. The computational results showed that the hybrid algorithm outperforms both the GA and TS for the makespan parameter, but not for the flowtime parameter.Peer ReviewedPostprint (author's final draft

A Tabu Search algorithm for ground station scheduling problem

(c) 2014 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.Mission planning plays an important role in satellite control systems. Satellites are not autonomously operated in many cases but are controlled by tele-commands transmitted from ground stations. Therefore, mission scheduling is crucial to efficient satellite control systems, especially with increase of number of satellites and more complex missions to be planned. In a general setting, the satellite mission scheduling consists in allocating tasks such as observation, communication, etc. to resources (spacecrafts (SCs), satellites, ground stations). One common version of this problem is that of ground station scheduling, in which the aim is to compute an optimal planning of communications between satellites and operations teams of Ground Station (GS). Because the communication between SCs and GSs can be done during specific window times, this problem can also be seen as a window time scheduling problem. The required communication time is usually quite smaller than the window of visibility of SCs to GSs, however, clashes are produced, making the problem highly constrained. In this paper we present a Tabu Search (TS) algorithm for the problem, while considering several objective functions, namely, windows fitness, clashes fitness, time requirement fitness, and resource usage fitness. The proposed algorithm is evaluated by a set of problem instances of varying size and complexity generated with the STK simulation toolkit. The computational results showed the efficacy of TS for solving the problem on all considered objectives.Peer ReviewedPostprint (author's final draft

Hybrid ant colony system algorithm for static and dynamic job scheduling in grid computing

Grid computing is a distributed system with heterogeneous infrastructures. Resource management system (RMS) is one of the most important components which has great influence on the grid computing performance. The main part of RMS is the scheduler algorithm which has the responsibility to map submitted tasks to available resources. The complexity of scheduling problem is considered as a nondeterministic polynomial complete (NP-complete) problem and therefore, an intelligent algorithm is required to achieve better scheduling solution. One of the prominent intelligent algorithms is ant colony system (ACS) which is implemented widely to solve various types of scheduling problems. However, ACS suffers from stagnation problem in medium and large size grid computing system. ACS is based on exploitation and exploration mechanisms where the exploitation is sufficient but the exploration has a deficiency. The exploration in ACS is based on a random approach without any strategy. This study proposed four hybrid algorithms between ACS, Genetic Algorithm (GA), and Tabu Search (TS) algorithms to enhance the ACS performance. The algorithms are ACS(GA), ACS+GA, ACS(TS), and ACS+TS. These proposed hybrid algorithms will enhance ACS in terms of exploration mechanism and solution refinement by implementing low and high levels hybridization of ACS, GA, and TS algorithms. The proposed algorithms were evaluated against twelve metaheuristic algorithms in static (expected time to compute model) and dynamic (distribution pattern) grid computing environments. A simulator called ExSim was developed to mimic the static and dynamic nature of the grid computing. Experimental results show that the proposed algorithms outperform ACS in terms of best makespan values. Performance of ACS(GA), ACS+GA, ACS(TS), and ACS+TS are better than ACS by 0.35%, 2.03%, 4.65% and 6.99% respectively for static environment. For dynamic environment, performance of ACS(GA), ACS+GA, ACS+TS, and ACS(TS) are better than ACS by 0.01%, 0.56%, 1.16%, and 1.26% respectively. The proposed algorithms can be used to schedule tasks in grid computing with better performance in terms of makespan

Hybridization as Cooperative Parallelism for the Quadratic Assignment Problem

International audienceThe Quadratic Assignment Problem is at the core of several real-life applications. Finding an optimal assignment is computationally very difficult, for many useful instances. The best results are obtained with hybrid heuristics, which result in complex solvers. We propose an alternate solution where hybridization is obtain by means of parallelism and cooperation between simple single-heuristic solvers. We present experimental evidence that this approach is very efficient and can effectively solve a wide variety of hard problems, often surpassing state-of-the-art systems