Automated discovery of local search heuristics for satisfiability testing

The development of successful metaheuristic algorithms such as local search for a difficult problem such as satisfiability testing (SAT) is a challenging task. We investigate an evolutionary approach to automating the discovery of new local search heuristics for SAT. We show that several well-known SAT local search algorithms such as Walksat and Novelty are composite heuristics that are derived from novel combinations of a set of building blocks. Based on this observation, we developed CLASS, a genetic programming system that uses a simple composition operator to automatically discover SAT local search heuristics. New heuristics discovered by CLASS are shown to be competitive with the best Walksat variants, including Novelty+. Evolutionary algorithms have previously been applied to directly evolve a solution for a particular SAT instance. We show that the heuristics discovered by CLASS are also competitive with these previous, direct evolutionary approaches for SAT. We also analyze the local search behavior of the learned heuristics using the depth, mobility, and coverage metrics proposed by Schuurmans and Southey.     

A parallel hybrid greedy branch and bound scheme for the maximum distance-2 matching problem

We present a new highly parallel algorithm for fast determination of near-optimal solutions to the NP-hard problem of identifying a maximum distance-2 matching in arbitrary graphs. This problem, known as D2EMIS, has important applications such as determining the maximum capacity of the media access (MAC) layer in wireless ad-hoc networks [1]. It can also be seen as a maximum 2-packing problem [2] on the edge-to-vertex dual graph of the original graph. Our algorithm extends the GRASP [3] philosophy in that partial solutions are constructed by adding in a greedy adaptive manner the “best” nodes that can be found; however, when there are multiple alternatives that can be selected in an iteration, the algorithm branches into as many paths as there are (greedy) alternatives. The algorithm, using appropriate bounds to prune partial solutions that cannot be optimal, produces very fast near-optimal solutions that compare very well against other distributed algorithms and random greedy heuristics proposed before or variants thereof, or exact methods (Integer Programming or Maximum Satisfiability state-of-the-art solvers).     

Boolean lexicographic optimization: algorithms & applications

Multi-Objective Combinatorial Optimization (MOCO) problems find a wide range of practical application problems, some of which involving Boolean variables and constraints. This paper develops and evaluates algorithms for solving MOCO problems, defined on Boolean domains, and where the optimality criterion is lexicographic. The proposed algorithms build on existing algorithms for either Maximum Satisfiability (MaxSAT), Pseudo-Boolean Optimization (PBO), or Integer Linear Programming (ILP). Experimental results, obtained on problem instances from haplotyping with pedigrees and software package dependencies, show that the proposed algorithms can provide significant performance gains over state of the art MaxSAT, PBO and ILP algorithms. Finally, the paper also shows that lexicographic optimization conditions are observed in the majority of the problem instances from the MaxSAT evaluations, motivating the development of dedicated algorithms that can exploit lexicographic optimization conditions in general MaxSAT problem instances.     

Minimizing the stretch when scheduling flows of divisible requests

In this paper, we consider the problem of scheduling distributed biological sequence comparison applications. This problem lies in the divisible load framework with negligible communication costs. Thus far, very few results have been proposed for this model. We discuss and select relevant metrics for this framework: namely max-stretch and sum-stretch. We explain the relationship between our model and the preemptive single processor case, and we show how to extend algorithms that have been proposed in the literature for the single processor model to the divisible multi-processor problem domain. We recall known results on closely related problems, we show how to minimize the max-stretch on unrelated machines either in the divisible load model or with preemption, we derive new lower bounds on the competitive ratio of any online algorithm, we present new competitiveness results for existing algorithms, and we develop several new online heuristics. We also address the Pareto optimization of max-stretch. Then, we extensively study the performance of these algorithms and heuristics under realistic scenarios. Our study shows that all previously proposed guaranteed heuristics for max-stretch for the single processor model are inefficient in practice. In contrast, we show that our online algorithms based on linear programming are in practice near-optimal solutions for max-stretch. Our study also clearly suggests heuristics that are efficient for both metrics, although a combined optimization is in theory not possible in the general case.     

Stochastic Local Search Algorithms for Graph Set <Emphasis Type="Italic">T</Emphasis>-colouring and Frequency Assignment

The graph set T-colouring problem (GSTCP) generalises the classical graph colouring problem; it asks for the assignment of sets of integers to the vertices of a graph such that constraints on the separation of any two numbers assigned to a single vertex or to adjacent vertices are satisfied and some objective function is optimised. Among the objective functions of interest is the minimisation of the difference between the largest and the smallest integers used (the span). In this article, we present an experimental study of local search algorithms for solving general and large size instances of the GSTCP. We compare the performance of previously known as well as new algorithms covering both simple construction heuristics and elaborated stochastic local search algorithms. We investigate systematically different models and search strategies in the algorithms and determine the best choices for different types of instance. The study is an example of design of effective local search for constraint optimisation problems.     

An Overview of Backtrack Search Satisfiability Algorithms

Propositional Satisfiability (SAT) is often used as the underlying model for a significant number of applications in Artificial Intelligence as well as in other fields of Computer Science and Engineering. Algorithmic solutions for SAT include, among others, local search, backtrack search and algebraic manipulation. In recent years, several different organizations of local search and backtrack search algorithms for SAT have been proposed, in many cases allowing larger problem instances to be solved in different application domains. While local search algorithms have been shown to be particularly useful for random instances of SAT, recent backtrack search algorithms have been used for solving large instances of SAT from real-world applications. In this paper we provide an overview of backtrack search SAT algorithms. We describe and illustrate a number of techniques that have been empirically shown to be highly effective in pruning the amount of search on significant and representative classes of problem instances. In particular, we review strategies for non-chronological backtracking, procedures for clause recording and for the identification of necessary variable assignments, and mechanisms for the structural simplification of instances of SAT.     

Evolutionary algorithms for the satisfiability problem

Several evolutionary algorithms have been proposed for the satisfiability problem. We review the solution representations suggested in literature and choose the most promising one - the bit string representation - for further evaluation. An empirical comparison on commonly used benchmarks is presented for the most successful evolutionary algorithms and for WSAT, a prominent local search algorithm for the satisfiability problem. The key features of successful evolutionary algorithms are identified, thereby providing useful methodological guidelines for designing new heuristics. Our results indicate that evolutionary algorithms are competitive to WSAT.     

Optimal switch location in mobile communication networks using hybrid genetic algorithms

The optimal positioning of switches in a mobile communication network is an important task, which can save costs and improve the performance of the network. In this paper we propose a model for establishing which are the best nodes of the network for allocating the available switches, and several hybrid genetic algorithms to solve the problem. The proposed model is based on the so-called capacitated p-median problem, which have been previously tackled in the literature. This problem can be split in two subproblems: the selection of the best set of switches, and a terminal assignment problem to evaluate each selection of switches. The hybrid genetic algorithms for solving the problem are formed by a conventional genetic algorithm, with a restricted search, and several local search heuristics. In this work we also develop novel heuristics for solving the terminal assignment problem in a fast and accurate way. Finally, we show that our novel approaches, hybridized with the genetic algorithm, outperform existing algorithms in the literature for the p-median problem.     

Robust hyper-heuristic algorithms for the offline oriented/non-oriented 2D bin packing problems

The offline 2D bin packing problem (2DBPP) is an NP-hard combinatorial optimization problem in which objects with various width and length sizes are packed into minimized number of 2D bins. Various versions of this well-known industrial engineering problem can be faced frequently. Several heuristics have been proposed for the solution of 2DBPP but it has not been possible to find the exact solutions for large problem instances. Next fit, first fit, best fit, unified tabu search, genetic and memetic algorithms are some of the state-of-the-art methods successfully applied to this important problem. In this study, we propose a set of novel hyper-heuristic algorithms that select/combine the state-of-the-art heuristics and local search techniques for minimizing the number of 2D bins. The proposed algorithms introduce new crossover and mutation operators for the selection of the heuristics. Through the results of exhaustive experiments on a set of offline 2DBPP benchmark problem instances, we conclude that the proposed algorithms are robust with their ability to obtain high percentage of the optimal solutions.     

Global optima for the Zhou–Rozvany problem

We consider the minimum compliance topology design problem with a volume constraint and discrete design variables. In particular, our interest is to provide global optimal designs to a challenging benchmark example proposed by Zhou and Rozvany. Global optimality is achieved by an implementation of a local branching method in which the subproblems are solved by a special purpose nonlinear branch-and-cut algorithm. The convergence rate of the branch-and-cut method is improved by strengthening the problem formulation with valid linear inequalities and variable fixing techniques. With the proposed algorithms, we find global optimal designs for several values on the available volume. These designs can be used to validate other methods and heuristics for the considered class of problems.     

Efficient constructive and composite heuristics for the Permutation Flowshop to minimise total earliness and tardiness

In this paper we address the problem of scheduling jobs in a permutation flowshop with a just-in-time objective, i.e. the minimisation of the sum of total tardiness and total earliness. Since the problem is NP-hard, there are several approximate procedures available for the problem, although their performance largely depends on the due dates of the specific instance to be solved. After an in-depth analysis of the problem, different cases or sub-problems are identified and, by incorporating this knowledge, four heuristics are proposed: a fast constructive heuristic, and three different local search procedures that use the proposed constructive heuristic as initial solution.The proposed Prod. Type: FLPheuristics have been compared on an extensive set of instances with the best-so-far heuristic for the problem, as well as with adaptations of efficient heuristics for similar scheduling problems. The computational results show the excellent performance of the proposed algorithms. Finally, the positive impact of the efficient heuristics is evaluated by including them as seed sequences for one of the best metaheuristic for the problem.     

Completion time variance minimization in single machine and multi-machine systems

In this paper we consider the problem of minimizing the completion time variance of n jobs on a single machine with deterministic processing times. We propose a new heuristic and compare the results with existing popular heuristics for the problem. We also propose a method based on genetic algorithms to solve the problem. We present the worst case performance analysis of the proposed heuristic. We also consider the problem of minimizing the completion time variance of n jobs on m identical parallel machines in both restricted and unrestricted versions. A heuristic method and a method based on genetic algorithms are presented for both the cases and results of computational testing are provided. It is concluded that the proposed methods provide better results compared to existing methods for the single machine case as well as for the multi-machine case.     

An Efficient Hybrid Particle Swarm Optimization Algorithm for Solving the Uncapacitated Continuous Location-Allocation Problem

Location-allocation problems are a class of complicated optimization problems that determine the location of facilities and the allocation of customers to the facilities. In this paper, the uncapacitated continuous location-allocation problem is considered, and a particle swarm optimization approach, which has not previously been applied to this problem, is presented. Two algorithms including classical and hybrid particle swarm optimization algorithms are developed. Local optima of the problem are obtained by two local search heuristics that exist in the literature. These algorithms are combined with particle swarm optimization to construct an efficient hybrid approach. Many large-scale problems are used to measure the effectiveness and efficiency of the proposed algorithms. Our results are compared with the best algorithms in the literature. The experimental results show that the hybrid PSO produces good solutions, is more efficient than the classical PSO, and is competitive with the best results from the literature. Additionally, the proposed hybrid PSO found better solutions for some instances than did the best known solutions in the literature.     

Parallel machine scheduling problems using memetic algorithms

In this paper, we investigate how to apply the hybrid genetic algorithms (the memetic algorithms) to solve the parallel machine scheduling problem. There are two essential issues to be dealt with for all kinds of parallel machine scheduling problems: job partition among machines and job sequence within each machine. The basic idea of the proposed method is that (a) use the genetic algorithms to evolve the job partition and then (b) apply a local optimizer to adjust the job permutation to push each chromosome climb to his local optima. Preliminary computational experiments demonstrate that the hybrid genetic algorithm outperforms the genetic algorithms and the conventional heuristics.     

Local search heuristics for two-stage flow shop problems with secondary criterion

This paper develops and compares different local search heuristics for the two-stage flow shop problem with makespan minimization as the primary criterion and the minimization of either the total flow time, total weighted flow time, or total weighted tardiness as the secondary criterion. We investigate several variants of simulated annealing, threshold accepting, tabu search, and multi-level search algorithms. The influence of the parameters of these heuristics and the starting solution are empirically analyzed. The proposed heuristic algorithms are empirically evaluated and found to be relatively more effective in finding better quality solutions than the existing algorithms.Scope and purposeTraditional research to solve multi-stage scheduling problems has focused on single criterion. However, in industrial scheduling practices, managers develop schedules based on multi-criteria. Scheduling problems involving multiple criteria require significantly more effort in finding acceptable solutions and hence have not received much attention in the literature. This paper considers one such multiple criteria scheduling problem, namely, the two-machine flow shop problem where the primary criterion is the minimization of makespan and the secondary criterion is one of the three most popular performance measures, namely, the total flow time, total weighted flow time, or total weighted tardiness. Based on the principles of local search, development of heuristic algorithms, that can be adapted for several multi-criteria scheduling problems, is discussed. Using the example of the two-machine flow shop problem with secondary criterion, computational experiments are used to evaluate the utility of the proposed algorithms for solving scheduling problems with a secondary criterion.     

New Genetic Algorithms Based Approaches to Continuous <Emphasis Type="Italic">p</Emphasis>-Median Problem

We proposed new genetic algorithms (GAs) to address well-known p-median problem in continuous space. Two GA approaches with different replacement procedures are developed to solve this problem. To make the approaches more efficient in finding near-optimal solution two hybrid algorithms are developed combining the new GAs and a traditional local search heuristic. The performance of the newly developed models is compared to that of the traditional alternating location-allocation heuristics by numerical simulation and it is found that the models are effective in finding optimum facility locations.     

A genetic algorithm approach for the single machine scheduling problem with linear earliness and quadratic tardiness penalties

In this paper, we consider the single machine scheduling problem with linear earliness and quadratic tardiness costs, and no machine idle time. We propose a genetic approach based on a random key alphabet. Several genetic algorithms based on this approach are presented. These versions differ on the generation of the initial population, as well as on the use of local search. The proposed procedures are compared with existing heuristics, as well as with optimal solutions for the smaller instance sizes.     

Randomized local search,evolutionary algorithms,and the minimum spanning tree problem

Randomized search heuristics, among them randomized local search and evolutionary algorithms, are applied to problems whose structure is not well understood, as well as to problems in combinatorial optimization. The analysis of these randomized search heuristics has been started for some well-known problems, and this approach is followed here for the minimum spanning tree problem. After motivating this line of research, it is shown that randomized search heuristics find minimum spanning trees in expected polynomial time without employing the global technique of greedy algorithms.     

A comparison of scheduling algorithms for flexible flow shop problems with unrelated parallel machines,setup times,and dual criteria

This paper considers a flexible flow shop scheduling problem, where at least one production stage is made up of unrelated parallel machines. Moreover, sequence- and machine-dependent setup times are given. The objective is to find a schedule that minimizes a convex sum of makespan and the number of tardy jobs in a static flexible flow shop environment. For this problem, a 0–1 mixed integer program is formulated. The problem is, however, a combinatorial optimization problem which is too difficult to be solved optimally for large problem sizes, and hence heuristics are used to obtain good solutions in a reasonable time. The proposed constructive heuristics for sequencing the jobs start with the generation of the representatives of the operating time for each operation. Then some dispatching rules and flow shop makespan heuristics are developed. To improve the solutions obtained by the constructive algorithms, fast polynomial heuristic improvement algorithms based on shift moves and pairwise interchanges of jobs are applied. In addition, metaheuristics are suggested, namely simulated annealing (SA), tabu search (TS) and genetic algorithms. The basic parameters of each metaheuristic are briefly discussed in this paper. The performance of the heuristics is compared relative to each other on a set of test problems with up to 50 jobs and 20 stages and with an optimal solution for small-size problems. We have found that among the constructive algorithms the insertion-based approach is superior to the others, whereas the proposed SA algorithms are better than TS and genetic algorithms among the iterative metaheuristic algorithms.     

Parallel hyper heuristic algorithm based on reinforcement learning for the corridor allocation problem and parallel row ordering problem

Hyper heuristics is a relatively new optimisation algorithm. Numerous studies have reported that hyper heuristics are well applied in combinatorial optimisation problems. As a classic combinatorial optimisation problem, the row layout problem has not been publicly reported on applying hyper heuristics to its various sub-problems. To fill this gap, this study proposes a parallel hyper-heuristic approach based on reinforcement learning for corridor allocation problems and parallel row ordering problems. For the proposed algorithm, an outer layer parallel computing framework was constructed based on the encoding of the problem. The simulated annealing, tabu search, and variable neighbourhood algorithms were used in the algorithm as low-level heuristic operations, and Q-learning in reinforcement learning was used as a high-level strategy. A state space containing sequences and fitness values was designed. The algorithm performance was then evaluated for benchmark instances of the corridor allocation problem (37 groups) and parallel row ordering problem (80 groups). The results showed that, in most cases, the proposed algorithm provided a better solution than the best-known solutions in the literature. Finally, the meta-heuristic algorithm applied to three low-level heuristic operations is taken as three independent algorithms and compared with the proposed hyper-heuristic algorithm on four groups of parallel row ordering problem instances. The effectiveness of Q-learning in selection is illustrated by analysing the comparison results of the four algorithms and the number of calls of the three low-level heuristic operations in the proposed method.