An Iterative Path-Breaking Approach with Mutation and Restart Strategies for the MAX-SAT Problem

Although Path-Relinking is an effective local search method for many combinatorial optimization problems, its application is not straightforward in solving the MAX-SAT, an optimization variant of the satisfiability problem (SAT) that has many real-world applications and has gained more and more attention in academy and industry. Indeed, it was not used in any recent competitive MAX-SAT algorithms in our knowledge. In this paper, we propose a new local search algorithm called IPBMR for the MAX-SAT, that remedies the drawbacks of the Path-Relinking method by using a careful combination of three components: a new strategy named Path-Breaking to avoid unpromising regions of the search space when generating trajectories between two elite solutions; a weak and a strong mutation strategies, together with restarts, to diversify the search; and stochastic path generating steps to avoid premature local optimum solutions. We then present experimental results to show that IPBMR outperforms two of the best state-of-the-art MAX-SAT solvers, and an empirical investigation to identify and explain the effect of the three components in IPBMR

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

Towards hybrid methods for solving hard combinatorial optimization problems

Tesis doctoral leída en la Escuela Politécnica Superior de la Universidad Autónoma de Madrid el 4 de septiembre de 200

Improving police efficiency to meet demand issues

Demand modelling and simulation techniques are used in many industrial practices in order to be able to effectively manage the utilization of available resources. The current economic climate has intensified activity within this field with particular interest being paid to any potential cost savings and other financial benefits that may be obtained. Further the creation of a realistic representation of the demands present within a system can lead to a better understanding of system behaviour; this then may facilitate the identification of elements that are likely to allow improvement to system performance through their perturbation. Within this thesis a model is constructed for the demands upon front line Police officers that are used in response to high importance calls to service from the public. Tabu search and genetic algorithms are optimizing search techniques developed and applied across a wide variety of fields. They are particularly well suited to combinatorial problems in which the ordering or arrangement of system elements has an impact upon the quality of solution as assessed by some quantifying objective function. In this thesis both of these methods are applied to the staff resource allocation problem as posed by Leicestershire Police with the strengths and weaknesses of each evaluated. Customized diversification and intensification approaches are applied to the tabu search methodology in order to improve performance through tailoring it to the specific optimization problem considered. Both search algorithms are shown to be well suited to the target problem and each result in the generation of solutions of similar quality.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Domain-independent local search for linear integer optimization

Integer and combinatorial optimization problems constitute a major challenge for algorithmics. They arise when a large number of discrete organizational decisions have to be made, subject to constraints and optimization criteria. This thesis describes and investigates new domain-independent local search strategies for linear integer optimization. We introduce WSAT(OIP), an integer local search method which operates on an algebraic problem representation. WSAT(OIP) generalizes Walksat, a successful local search procedure for propositional satisfiability (SAT), to more expressive constraint systems. For this purpose, we introduce over-constrained integer programs (OIPs), a constraint class which is closely related to integer programs. OIP allows for a natural generalization of the principles of SAT local search to integer optimization. Further, it will be shown that OIPs are a special case of integer linear programs and permit combinations with linear programming for bound computation, initialization by rounding, search space reduction, and feasibility testing. The representation is similar enough to integer programs to make use of existing algebraic modeling languages as front-end to a local search solver. To improve performance on realistic problems, WSAT(OIP) incorporates strategies from Tabu Search. We experimentally investigate WSAT(OIP) for a variety of realistic integer optimization problems from the domains of time tabling, sports scheduling, radar surveillance, course assignment, and capacitated production planning. The experimental design examines efficiency, scaling (with increasing problem size and constrainedness), and robustness. The results demonstrate that integer local search can outperform or compete with state-of-the-art integer programming (IP) branch-and-bound and constraint programming (CP) approaches to these problems in finding near-optimal solutions. Key findings of our empirical study include that integer local search is able to solve difficult constraint problems from time-tabling and sports scheduling when cast into a 0-1 representation, which are beyond the scope of IP branch-and-bound strategies and for which devising robust constraint programs is a non-trivial task. For several realistic optimization problems (0-1 integer and finite domain) we show that integer local search exhibits graceful runtime scaling with increasing problem size and constrainedness. It can therefore significantly outperform IP branch-and-bound strategies on large or tightly constrained problems in finding near-optimal solutions. The problems under consideration are mostly beyond the limitations of a previous general-purpose simulated annealing strategy for 0-1 integer programs.Ganzzahlige und kombinatorische Optimierungsprobleme stellen eine schwierige Herausforderung im Gebiet der Algorithmen dar. Sie treten auf, wenn eine große Anzahl diskreter organisatorischer Entscheidungen unter Berücksichtigung von Constraints und Optimierungskriterien zu treffen sind. Diese Arbeit beschreibt und untersucht neue, domänenunabhängige Strategien der lokalen Suche zur ganzzahligen linearen Optimierung. Wir beschreiben WSAT(OIP), eine Strategie "ganzzahliger lokaler Suche\u27;, die auf einer algebraischen Problemrepräsentation operiert. WSAT(OIP) verallgemeinert Walksat, eine erfolgreiche Prozedur lokaler Suche für das Erfüllbarkeitsproblem der Aussagenlogik (SAT), auf ausdrucksstärkere Constraint-Systeme. Für diesen Zweck führen wir die Klasse der "Over-constrained Integer Programs\u27;(OIPs) ein, eine Constraint-Klasse, die eng mit ganzzahligen Programmen verwandt ist. OIPs erlauben einerseits eine natürliche Verallgemeinerung der Prinzipien von lokaler Suche für SAT. Andererseits sind sie ein Spezialfall der ganzzahligen linearen Programme und ermöglichen die Kombination mit linearer Programmierung zur Berechnung von Schranken, Initialisierung durch Rundung, Suchraum-Reduktion und für Gültigkeits-Tests. OIPs sind ganzzahligen Programmen ähnlich, so daß existierende algebraische Modellierungssprachen als Eingabeschnittstelle für einen Problemlöser benutzt werden können, der auf lokaler Suche basiert. Um die Performanz auf realistischen Problemen zu verbessern, ist WSAT(OIP) mit Strategien der Tabu-Suche ausgestattet. Wir führen eine experimentelle Untersuchung von WSAT(OIP) auf einer Reihe von realistischen ganzzahligen Constraint- und Optimierungsproblemen durch. Die Probleme stammen aus den Domänen Zeitplan-Erstellung, Sport-Ablaufplanung, Radar- Überwachung, Kurs-Zuteilung und Produktions-Planung. Das experimentelle Design untersucht Effizienz, Skalierung mit zunehmender Problemgröße und stärkeren Constraints sowie Robustheit. Die Ergebnisse zeigen, daß ganzzahlige lokale Suche bezüglich Performanz auf diesen Problemklassen zeitgemäße Ansätze der ganzzahligen Programmierung und der Constraint-Programmierung beim Finden nahe-optimaler Lösungen schlägt oder mit ihnen konkurriert. Kernergebnisse der empirischen Untersuchung sind, daß ganzzahlige lokale Suche in der Lage ist, schwierige Constraint-Probleme der Zeitplan-Erstellung und Sport-Ablaufplanung in einer 0-1 Repräsentation zu lösen, die außerhalb der Grenzen der ganzzahligen linearen Programmierung liegen, und für die die Entwicklung eines robustes Constraint-Programms eine nicht-triviale Aufgabe darstellt. Für mehrere realistische Optimierungsprobleme (ganzzahlig 0-1 und endliche Bereiche)zeigen wir, daß ganzzahlige lokale Suche eine günstige Skalierung der Laufzeit mit zunehmender Problemgröße und Constrainedness aufweist. Dadurch zeigt das Verfahren auf großen Problemen und auf Problemen mit starken Constraints deutlich bessere Performanz für das Finden nahe-Lösungen als die Branch-and-Bound Strategie der ganzzahligen Programmierung. Die untersuchten Probleme liegen zumeist außerhalb der Grenzen einer existierenden Simulated Annealing Strategie für allgemeine lineare 0-1 Programme

Combining Monte-Carlo and hyper-heuristic methods for the multi-mode resource-constrained multi-project scheduling problem

Multi-mode resource and precedence-constrained project scheduling is a well-known challenging real-world optimisation problem. An important variant of the problem requires scheduling of activities for multiple projects considering availability of local and global resources while respecting a range of constraints. A critical aspect of the benchmarks addressed in this paper is that the primary objective is to minimise the sum of the project completion times, with the usual makespan minimisation as a secondary objective. We observe that this leads to an expected different overall structure of good solutions and discuss the effects this has on the algorithm design. This paper presents a carefully-designed hybrid of Monte-Carlo tree search, novel neighbourhood moves, memetic algorithms, and hyper-heuristic methods. The implementation is also engineered to increase the speed with which iterations are performed, and to exploit the computing power of multicore machines. Empirical evaluation shows that the resulting information-sharing multi-component algorithm significantly outperforms other solvers on a set of “hidden” instances, i.e. instances not available at the algorithm design phase

A study in grid simulation and scheduling

Grid computing is emerging as an essential tool for large scale analysis and problem solving in scientific and business domains. Whilst the idea of stealing unused processor cycles is as old as the Internet, we are still far from reaching a position where many distributed resources can be seamlessly utilised on demand. One major issue preventing this vision is deciding how to effectively manage the remote resources and how to schedule the tasks amongst these resources. This thesis describes an investigation into Grid computing, specifically the problem of Grid scheduling. This complex problem has many unique features making it particularly difficult to solve and as a result many current Grid systems employ simplistic, inefficient solutions. This work describes the development of a simulation tool, G-Sim, which can be used to test the effectiveness of potential Grid scheduling algorithms under realistic operating conditions. This tool is used to analyse the effectiveness of a simple, novel scheduling technique in numerous scenarios. The results are positive and show that it could be applied to current procedures to enhance performance and decrease the negative effect of resource failure. Finally a conversion between the Grid scheduling problem and the classic computing problem SAT is provided. Such a conversion allows for the possibility of applying sophisticated SAT solving procedures to Grid scheduling providing potentially effective solutions

Proceedings of the 21st Conference on Formal Methods in Computer-Aided Design – FMCAD 2021

The Conference on Formal Methods in Computer-Aided Design (FMCAD) is an annual conference on the theory and applications of formal methods in hardware and system verification. FMCAD provides a leading forum to researchers in academia and industry for presenting and discussing groundbreaking methods, technologies, theoretical results, and tools for reasoning formally about computing systems. FMCAD covers formal aspects of computer-aided system design including verification, specification, synthesis, and testing