Finding and Exploring Promising Search Space for the 0-1 Multidimensional Knapsack Problem

The 0-1 multidimensional knapsack problem(MKP) is a classical NP-hard combinatorial optimization problem. In this paper, we propose a novel heuristic algorithm simulating evolutionary computation and large neighbourhood search for the MKP. It maintains a set of solutions and abstracts information from the solution set to generate good partial assignments. To find high-quality solutions, integer programming is employed to explore the promising search space specified by the good partial assignments. Extensive experimentation with commonly used benchmark sets shows that our approach outperforms the state of the art heuristic algorithms, TPTEA and DQPSO, in solution quality. It finds new lower bound for 8 large and hard instance

Solving large 0–1 multidimensional knapsack problems by a new simplified binary artificial fish swarm algorithm

The artificial fish swarm algorithm has recently been emerged in continuous global optimization. It uses points of a population in space to identify the position of fish in the school. Many real-world optimization problems are described by 0-1 multidimensional knapsack problems that are NP-hard. In the last decades several exact as well as heuristic methods have been proposed for solving these problems. In this paper, a new simpli ed binary version of the artificial fish swarm algorithm is presented, where a point/ fish is represented by a binary string of 0/1 bits. Trial points are created by using crossover and mutation in the different fi sh behavior that are randomly selected by using two user de ned probability values. In order to make the points feasible the presented algorithm uses a random heuristic drop item procedure followed by an add item procedure aiming to increase the profit throughout the adding of more items in the knapsack. A cyclic reinitialization of 50% of the population, and a simple local search that allows the progress of a small percentage of points towards optimality and after that refines the best point in the population greatly improve the quality of the solutions. The presented method is tested on a set of benchmark instances and a comparison with other methods available in literature is shown. The comparison shows that the proposed method can be an alternative method for solving these problems.The authors wish to thank three anonymous referees for their comments and valuable suggestions to improve the paper. The first author acknowledges Ciˆencia 2007 of FCT (Foundation for Science and Technology) Portugal for the fellowship grant C2007-UMINHO-ALGORITMI-04. Financial support from FEDER COMPETE (Operational Programme Thematic Factors of Competitiveness) and FCT under project FCOMP-01-0124-FEDER-022674 is also acknowledged

Hybrid Nested Partitions method with Intelligent Greedy Search for solving Weapon-Target Assignment Problem

The Weapon-Target Assignment (WTA) problem is one of the most important problems of military applications of operations research. The objective of the WTA problem is to find proper assignments of weapons to targets which minimize the expected damage of defensive side. The WTA problem is known to be NP-complete. In this paper, hybrid Nested Partitions (NP) method is proposed to solve WTA problems. The proposed algorithm is named as Hybrid NP method with intelligent greedy search . The NP method has been found to be very effective for solving complex large-scale discrete optimization problems. In addition to that, due to the inherent flexibility of the NP method, any other heuristic for generating good feasible solutions can be incorporated and improve the performance of the NP method. The intelligent greedy search is an improved version of greedy search which finds good solutions very quickly. The proposed algorithm combines the advantages of the NP method and intelligent greedy search. The simulation results show that the proposed algorithm is very efficient for solving the WTA problem

Co-evolutionary Hybrid Bi-level Optimization

Multi-level optimization stems from the need to tackle complex problems involving multiple decision makers. Two-level optimization, referred as ``Bi-level optimization'', occurs when two decision makers only control part of the decision variables but impact each other (e.g., objective value, feasibility). Bi-level problems are sequential by nature and can be represented as nested optimization problems in which one problem (the ``upper-level'') is constrained by another one (the ``lower-level''). The nested structure is a real obstacle that can be highly time consuming when the lower-level is $\mathcal{NP}-hard$. Consequently, classical nested optimization should be avoided. Some surrogate-based approaches have been proposed to approximate the lower-level objective value function (or variables) to reduce the number of times the lower-level is globally optimized. Unfortunately, such a methodology is not applicable for large-scale and combinatorial bi-level problems. After a deep study of theoretical properties and a survey of the existing applications being bi-level by nature, problems which can benefit from a bi-level reformulation are investigated. A first contribution of this work has been to propose a novel bi-level clustering approach. Extending the well-know ``uncapacitated k-median problem'', it has been shown that clustering can be easily modeled as a two-level optimization problem using decomposition techniques. The resulting two-level problem is then turned into a bi-level problem offering the possibility to combine distance metrics in a hierarchical manner. The novel bi-level clustering problem has a very interesting property that enable us to tackle it with classical nested approaches. Indeed, its lower-level problem can be solved in polynomial time. In cooperation with the Luxembourg Centre for Systems Biomedicine (LCSB), this new clustering model has been applied on real datasets such as disease maps (e.g. Parkinson, Alzheimer). Using a novel hybrid and parallel genetic algorithm as optimization approach, the results obtained after a campaign of experiments have the ability to produce new knowledge compared to classical clustering techniques combining distance metrics in a classical manner. The previous bi-level clustering model has the advantage that the lower-level can be solved in polynomial time although the global problem is by definition $\mathcal{NP}$-hard. Therefore, next investigations have been undertaken to tackle more general bi-level problems in which the lower-level problem does not present any specific advantageous properties. Since the lower-level problem can be very expensive to solve, the focus has been turned to surrogate-based approaches and hyper-parameter optimization techniques with the aim of approximating the lower-level problem and reduce the number of global lower-level optimizations. Adapting the well-know bayesian optimization algorithm to solve general bi-level problems, the expensive lower-level optimizations have been dramatically reduced while obtaining very accurate solutions. The resulting solutions and the number of spared lower-level optimizations have been compared to the bi-level evolutionary algorithm based on quadratic approximations (BLEAQ) results after a campaign of experiments on official bi-level benchmarks. Although both approaches are very accurate, the bi-level bayesian version required less lower-level objective function calls. Surrogate-based approaches are restricted to small-scale and continuous bi-level problems although many real applications are combinatorial by nature. As for continuous problems, a study has been performed to apply some machine learning strategies. Instead of approximating the lower-level solution value, new approximation algorithms for the discrete/combinatorial case have been designed. Using the principle employed in GP hyper-heuristics, heuristics are trained in order to tackle efficiently the $\mathcal{NP}-hard$ lower-level of bi-level problems. This automatic generation of heuristics permits to break the nested structure into two separated phases: \emph{training lower-level heuristics} and \emph{solving the upper-level problem with the new heuristics}. At this occasion, a second modeling contribution has been introduced through a novel large-scale and mixed-integer bi-level problem dealing with pricing in the cloud, i.e., the Bi-level Cloud Pricing Optimization Problem (BCPOP). After a series of experiments that consisted in training heuristics on various lower-level instances of the BCPOP and using them to tackle the bi-level problem itself, the obtained results are compared to the ``cooperative coevolutionary algorithm for bi-level optimization'' (COBRA). Although training heuristics enables to \emph{break the nested structure}, a two phase optimization is still required. Therefore, the emphasis has been put on training heuristics while optimizing the upper-level problem using competitive co-evolution. Instead of adopting the classical decomposition scheme as done by COBRA which suffers from the strong epistatic links between lower-level and upper-level variables, co-evolving the solution and the mean to get to it can cope with these epistatic link issues. The ``CARBON'' algorithm developed in this thesis is a competitive and hybrid co-evolutionary algorithm designed for this purpose. In order to validate the potential of CARBON, numerical experiments have been designed and results have been compared to state-of-the-art algorithms. These results demonstrate that ``CARBON'' makes possible to address nested optimization efficiently

Incorporating Memory and Learning Mechanisms Into Meta-RaPS

Due to the rapid increase of dimensions and complexity of real life problems, it has become more difficult to find optimal solutions using only exact mathematical methods. The need to find near-optimal solutions in an acceptable amount of time is a challenge when developing more sophisticated approaches. A proper answer to this challenge can be through the implementation of metaheuristic approaches. However, a more powerful answer might be reached by incorporating intelligence into metaheuristics. Meta-RaPS (Metaheuristic for Randomized Priority Search) is a metaheuristic that creates high quality solutions for discrete optimization problems. It is proposed that incorporating memory and learning mechanisms into Meta-RaPS, which is currently classified as a memoryless metaheuristic, can help the algorithm produce higher quality results. The proposed Meta-RaPS versions were created by taking different perspectives of learning. The first approach taken is Estimation of Distribution Algorithms (EDA), a stochastic learning technique that creates a probability distribution for each decision variable to generate new solutions. The second Meta-RaPS version was developed by utilizing a machine learning algorithm, Q Learning, which has been successfully applied to optimization problems whose output is a sequence of actions. In the third Meta-RaPS version, Path Relinking (PR) was implemented as a post-optimization method in which the new algorithm learns the good attributes by memorizing best solutions, and follows them to reach better solutions. The fourth proposed version of Meta-RaPS presented another form of learning with its ability to adaptively tune parameters. The efficiency of these approaches motivated us to redesign Meta-RaPS by removing the improvement phase and adding a more sophisticated Path Relinking method. The new Meta-RaPS could solve even the largest problems in much less time while keeping up the quality of its solutions. To evaluate their performance, all introduced versions were tested using the 0-1 Multidimensional Knapsack Problem (MKP). After comparing the proposed algorithms, Meta-RaPS PR and Meta-RaPS Q Learning appeared to be the algorithms with the best and worst performance, respectively. On the other hand, they could all show superior performance than other approaches to the 0-1 MKP in the literature

New variants of variable neighbourhood search for 0-1 mixed integer programming and clustering

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Many real-world optimisation problems are discrete in nature. Although recent rapid developments in computer technologies are steadily increasing the speed of computations, the size of an instance of a hard discrete optimisation problem solvable in prescribed time does not increase linearly with the computer speed. This calls for the development of new solution methodologies for solving larger instances in shorter time. Furthermore, large instances of discrete optimisation problems are normally impossible to solve to optimality within a reasonable computational time/space and can only be tackled with a heuristic approach. In this thesis the development of so called matheuristics, the heuristics which are based on the mathematical formulation of the problem, is studied and employed within the variable neighbourhood search framework. Some new variants of the variable neighbourhood searchmetaheuristic itself are suggested, which naturally emerge from exploiting the information from the mathematical programming formulation of the problem. However, those variants may also be applied to problems described by the combinatorial formulation. A unifying perspective on modern advances in local search-based metaheuristics, a so called hyper-reactive approach, is also proposed. Two NP-hard discrete optimisation problems are considered: 0-1 mixed integer programming and clustering with application to colour image quantisation. Several new heuristics for 0-1 mixed integer programming problem are developed, based on the principle of variable neighbourhood search. One set of proposed heuristics consists of improvement heuristics, which attempt to find high-quality near-optimal solutions starting from a given feasible solution. Another set consists of constructive heuristics, which attempt to find initial feasible solutions for 0-1 mixed integer programs. Finally, some variable neighbourhood search based clustering techniques are applied for solving the colour image quantisation problem. All new methods presented are compared to other algorithms recommended in literature and a comprehensive performance analysis is provided. Computational results show that the methods proposed either outperform the existing state-of-the-art methods for the problems observed, or provide comparable results. The theory and algorithms presented in this thesis indicate that hybridisation of the CPLEX MIP solver and the VNS metaheuristic can be very effective for solving large instances of the 0-1 mixed integer programming problem. More generally, the results presented in this thesis suggest that hybridisation of exact (commercial) integer programming solvers and some metaheuristic methods is of high interest and such combinations deserve further practical and theoretical investigation. Results also show that VNS can be successfully applied to solving a colour image quantisation problem.Support from the Mathematical Institute, Serbian Academy of Sciences and Arts, are acknowledged for this research

New variants of variable neighbourhood search for 0-1 mixed integer programming and clustering

Many real-world optimisation problems are discrete in nature. Although recent rapid developments in computer technologies are steadily increasing the speed of computations, the size of an instance of a hard discrete optimisation problem solvable in prescribed time does not increase linearly with the computer speed. This calls for the development of new solution methodologies for solving larger instances in shorter time. Furthermore, large instances of discrete optimisation problems are normally impossible to solve to optimality within a reasonable computational time/space and can only be tackled with a heuristic approach. In this thesis the development of so called matheuristics, the heuristics which are based on the mathematical formulation of the problem, is studied and employed within the variable neighbourhood search framework. Some new variants of the variable neighbourhood searchmetaheuristic itself are suggested, which naturally emerge from exploiting the information from the mathematical programming formulation of the problem. However, those variants may also be applied to problems described by the combinatorial formulation. A unifying perspective on modern advances in local search-based metaheuristics, a so called hyper-reactive approach, is also proposed. Two NP-hard discrete optimisation problems are considered: 0-1 mixed integer programming and clustering with application to colour image quantisation. Several new heuristics for 0-1 mixed integer programming problem are developed, based on the principle of variable neighbourhood search. One set of proposed heuristics consists of improvement heuristics, which attempt to find high-quality near-optimal solutions starting from a given feasible solution. Another set consists of constructive heuristics, which attempt to find initial feasible solutions for 0-1 mixed integer programs. Finally, some variable neighbourhood search based clustering techniques are applied for solving the colour image quantisation problem. All new methods presented are compared to other algorithms recommended in literature and a comprehensive performance analysis is provided. Computational results show that the methods proposed either outperform the existing state-of-the-art methods for the problems observed, or provide comparable results. The theory and algorithms presented in this thesis indicate that hybridisation of the CPLEX MIP solver and the VNS metaheuristic can be very effective for solving large instances of the 0-1 mixed integer programming problem. More generally, the results presented in this thesis suggest that hybridisation of exact (commercial) integer programming solvers and some metaheuristic methods is of high interest and such combinations deserve further practical and theoretical investigation. Results also show that VNS can be successfully applied to solving a colour image quantisation problem.EThOS - Electronic Theses Online ServiceMathematical Institute, Serbian Academy of Sciences and ArtsGBUnited Kingdo

A Polyhedral Study of Mixed 0-1 Set

We consider a variant of the well-known single node fixed charge network flow set with constant capacities. This set arises from the relaxation of more general mixed integer sets such as lot-sizing problems with multiple suppliers. We provide a complete polyhedral characterization of the convex hull of the given set

Computational Design and Experimental Validation of Functional Ribonucleic Acid Nanostructures

In living cells, two major classes of ribonucleic acid (RNA) molecules can be found. The first class called the messenger RNA (mRNA) contains the genetic information that allows the ribosome to read and translate it into proteins. The second class called non-coding RNA (ncRNA), do not code for proteins and are involved with key cellular processes, such as gene expression regulation, splicing, differentiation, and development. NcRNAs fold into an ensemble of thermodynamically stable secondary structures, which will eventually lead the molecule to fold into a specific 3D structure. It is widely known that ncRNAs carry their functions via their 3D structures as well as their molecular composition. The secondary structure of ncRNAs is composed of different types of structural elements (motifs) such as stacking base pairs, internal loops, hairpin loops and pseudoknots. Pseudoknots are specifically difficult to model, are abundant in nature and known to stabilize the functional form of the molecule. Due to the diverse range of functions of ncRNAs, their computational design and analysis have numerous applications in nano-technology, therapeutics, synthetic biology, and materials engineering. The RNA design problem is to find novel RNA sequences that are predicted to fold into target structure(s) while satisfying specific qualitative characteristics and constraints. RNA design can be modeled as a combinatorial optimization problem (COP) and is known to be computationally challenging or more precisely NP-hard. Numerous algorithms to solve the RNA design problem have been developed over the past two decades, however mostly ignore pseudoknots and therefore limit application to only a slice of real-world modeling and design problems. Moreover, the few existing pseudoknot designer methods which were developed only recently, do not provide any evidence about the applicability of their proposed design methodology in biological contexts. The two objectives of this thesis are set to address these two shortcomings. First, we are interested in developing an efficient computational method for the design of RNA secondary structures including pseudoknots that show significantly improved in-silico quality characteristics than the state of the art. Second, we are interested in showing the real-world worthiness of the proposed method by validating it experimentally. More precisely, our aim is to design instances of certain types of RNA enzymes (i.e. ribozymes) and demonstrate that they are functionally active. This would likely only happen if their predicted folding matched their actual folding in the in-vitro experiments. In this thesis, we present four contributions. First, we propose a novel adaptive defect weighted sampling algorithm to efficiently solve the RNA secondary structure design problem where pseudoknots are included. We compare the performance of our design algorithm with the state of the art and show that our method generates molecules that are thermodynamically more stable and less defective than those generated by state of the art methods. Moreover, we show when the effect of fitness evaluation is decoupled from the search and optimization process, our optimization method converges faster than the non-dominated sorting genetic algorithm (NSGA II) and the ant colony optimization (ACO) algorithm do. Second, we use our algorithmic development to implement an RNA design pipeline called Enzymer and make it available as an open source package useful for wet lab practitioners and RNA bioinformaticians. Enzymer uses multiple sequence alignment (MSA) data to generate initial design templates for further optimization. Our design pipeline can then be used to re-engineer naturally occurring RNA enzymes such as ribozymes and riboswitches. Our first and second contributions are published in the RNA section of the Journal of Frontiers in Genetics. Third, we use Enzymer to reengineer three different species of pseudoknotted ribozymes: a hammerhead ribozyme from the mouse gut metagenome, a hammerhead ribozyme from Yarrowia lipolytica and a glmS ribozyme from Thermoanaerobacter tengcogensis. We designed a total of 18 ribozyme sequences and showed the 16 of them were active in-vitro. Our experimental results have been submitted to the RNA journal and strongly suggest that Enzymer is a reliable tool to design pseudoknotted ncRNAs with desired secondary structure. Finally, we propose a novel architecture for a new ribozyme-based gene regulatory network where a hammerhead ribozyme modulates expression of a reporter gene when an external stimulus IPTG is present. Our in-vivo results show expected results in 7 out of 12 cases