A tensor based hyper-heuristic for nurse rostering

Nurse rostering is a well-known highly constrained scheduling problem requiring assignment of shifts to nurses satisfying a variety of constraints. Exact algorithms may fail to produce high quality solutions, hence (meta)heuristics are commonly preferred as solution methods which are often designed and tuned for specific (group of) problem instances. Hyper-heuristics have emerged as general search methodologies that mix and manage a predefined set of low level heuristics while solving computationally hard problems. In this study, we describe an online learning hyper-heuristic employing a data science technique which is capable of self-improvement via tensor analysis for nurse rostering. The proposed approach is evaluated on a well-known nurse rostering benchmark consisting of a diverse collection of instances obtained from different hospitals across the world. The empirical results indicate the success of the tensor-based hyper-heuristic, improving upon the best-known solutions for four of the instances

Randomized Contractions for Multiobjective Minimum Cuts

We show that Karger\u27s randomized contraction method (SODA 93) can be adapted to multiobjective global minimum cut problems with a constant number of edge or node budget constraints to give efficient algorithms. For global minimum cuts with a single edge-budget constraint, our extension of the randomized contraction method has running time tilde{O}(n^3) in an n-node graph improving upon the best-known randomized algorithm with running time tilde{O}(n^4) due to Armon and Zwick (Algorithmica 2006). Our analysis also gives a new upper bound of O(n^3) for the number of optimal solutions for a single edge-budget min cut problem. For the case of (k-1) edge-budget constraints, the extension of our algorithm saves a logarithmic factor from the best-known randomized running time of O(n^{2k} log^3 n). A main feature of our algorithms is to adaptively choose, at each step, the appropriate cost function used in the random selection of edges to be contracted. For the global min cut problem with a constant number of node budgets, we give a randomized algorithm with running time tilde{O}(n^2), improving the current best determinisitic running time of O(n^3) due to Goemans and Soto (SIAM Journal on Discrete Mathematics 2013). Our method also shows that the total number of distinct optimal solutions is bounded by O(n^2) as in the case of global min-cuts. Our algorithm extends to the node-budget constrained global min cut problem excluding a given sink with the same running time and bound on number of optimal solutions, again improving upon the best-known running time by a factor of O(n). For node-budget constrained problems, our improvements arise from incorporating the idea of merging any infeasible super-nodes that arise during the random contraction process. In contrast to cuts excluding a sink, we note that the node-cardinality constrained min-cut problem containing a given source is strongly NP-hard using a reduction from graph bisection

Geo-polymer binder as portland cement alternative: challenges, current developments and future prospects

Ordinary Portland Cement (OPC), a material which built the world is now devastating it. Environmental impact has raised concerns over its continued usage while its multifaceted problems are also biting the production companies hard. Hence, alternative geopolymer binder has demonstrated excellent properties to stand ordinary Portland cement even though it is still being faced with technical drawbacks. Therefore, these paper reviews attempt made on improving discoveries and understanding about proper implementation of geopolymer binder. The geopolymer binder is curable at ambient temperature by the use of Fly Ash/Ground Granulated Blast Furnace Slag (GGBS) blend. This has been an alternative have been discovered for cheaper activating solutions rather than the expensive Sodium Hydroxide/Sodium Silicate solution. However, various of chemical composition known as Supplementary Cementitious Materials (SCMs) still an issues to fabricate a geopolymer binder

Offline Learning for Sequence-based Selection Hyper-heuristics

This thesis is concerned with finding solutions to discrete NP-hard problems. Such problems occur in a wide range of real-world applications, such as bin packing, industrial flow shop problems, determining Boolean satisfiability, the traveling salesman and vehicle routing problems, course timetabling, personnel scheduling, and the optimisation of water distribution networks. They are typically represented as optimisation problems where the goal is to find a ``best'' solution from a given space of feasible solutions. As no known polynomial-time algorithmic solution exists for NP-hard problems, they are usually solved by applying heuristic methods. Selection hyper-heuristics are algorithms that organise and combine a number of individual low level heuristics into a higher level framework with the objective of improving optimisation performance. Many selection hyper-heuristics employ learning algorithms in order to enhance optimisation performance by improving the selection of single heuristics, and this learning may be classified as either online or offline. This thesis presents a novel statistical framework for the offline learning of subsequences of low level heuristics in order to improve the optimisation performance of sequenced-based selection hyper-heuristics. A selection hyper-heuristic is used to optimise the HyFlex set of discrete benchmark problems. The resulting sequences of low level heuristic selections and objective function values are used to generate an offline learning database of heuristic selections. The sequences in the database are broken down into subsequences and the mathematical concept of a logarithmic return is used to discriminate between ``effective'' subsequences, that tend to lead to improvements in optimisation performance, and ``disruptive'' subsequences that tend to lead to worsening performance. Effective subsequences are used to improve hyper-heuristics performance directly, by embedding them in a simple hyper-heuristic design, and indirectly as the inputs to an appropriate hyper-heuristic learning algorithm. Furthermore, by comparing effective subsequences across different problem domains it is possible to investigate the potential for cross-domain learning. The results presented here demonstrates that the use of well chosen subsequences of heuristics can lead to small, but statistically significant, improvements in optimisation performance

Iterated responsive threshold search for the quadratic multiple knapsack problem

The quadratic multiple knapsack problem (QMKP) consists in assigning objects with both individual and pairwise profits to a set of limited knapsacks in order to maximize the total profit. QMKP is a NP-hard combinatorial optimization problem with a number of applications. In this paper, we present an iterated responsive threshold search (IRTS) approach for solving the QMKP. Based on a combined use of three neighborhoods, the algorithm alternates between a threshold-based exploration phase where solution transitions are allowed among those satisfying a responsive threshold and a descent-based improvement phase where only improving solutions are accepted. A dedicated perturbation strategy is utilized to ensure a global diversification of the search procedure. Extensive experiments performed on a set of 60 benchmark instances in the literature show that the proposed approach competes very favorably with the current state-of-the-art methods for the QMKP. In particular, it discovers 41 improved lower bounds and attains all the best known results for the remaining instances. The key components of IRTS are analyzed to shed light on their impact on the performance of the algorithm

Maximum Persistency in Energy Minimization

We consider discrete pairwise energy minimization problem (weighted constraint satisfaction, max-sum labeling) and methods that identify a globally optimal partial assignment of variables. When finding a complete optimal assignment is intractable, determining optimal values for a part of variables is an interesting possibility. Existing methods are based on different sufficient conditions. We propose a new sufficient condition for partial optimality which is: (1) verifiable in polynomial time (2) invariant to reparametrization of the problem and permutation of labels and (3) includes many existing sufficient conditions as special cases. We pose the problem of finding the maximum optimal partial assignment identifiable by the new sufficient condition. A polynomial method is proposed which is guaranteed to assign same or larger part of variables than several existing approaches. The core of the method is a specially constructed linear program that identifies persistent assignments in an arbitrary multi-label setting.Comment: Extended technical report for the CVPR 2014 paper. Update: correction to the proof of characterization theore