9 research outputs found
On the Complexity of Parameterized Local Search for the Maximum Parsimony Problem
Maximum Parsimony is the problem of computing a most parsimonious phylogenetic tree for a taxa set X from character data for X. A common strategy to attack this notoriously hard problem is to perform a local search over the phylogenetic tree space. Here, one is given a phylogenetic tree T and wants to find a more parsimonious tree in the neighborhood of T. We study the complexity of this problem when the neighborhood contains all trees within distance k for several classic distance functions. For the nearest neighbor interchange (NNI), subtree prune and regraft (SPR), tree bisection and reconnection (TBR), and edge contraction and refinement (ECR) distances, we show that, under the exponential time hypothesis, there are no algorithms with running time |I|^o(k) where |I| is the total input size. Hence, brute-force algorithms with running time |X|^?(k) ? |I| are essentially optimal.
In contrast to the above distances, we observe that for the sECR-distance, where the contracted edges are constrained to form a subtree, a better solution within distance k can be found in k^?(k) ? |I|^?(1) time
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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
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Metaheuristic approach for solving scheduling and financial derivative problems
This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University LondonThe objective of this thesis is to implement metaheuristic approaches to solve di erent
types of combinatorial problems. The thesis is focused on neighborhood heuristic optimisation
techniques such as Variable Neighborhood Search (VNS) and Ant Colony Optimisation
(ACO) algorithms. The thesis will focus on two diverse combinatorial problems.
A job shop scheduling problem, and a nancial derivative matching problem. The rst
is a NP-hard 2-stage assembly problem, where we will be focussing on the rst stage. It
consists of sequencing a set of jobs having multiple components to be processed. Each job
has to be worked on independently on a speci c machine. We consider these jobs to form
a vector of tasks. Our objective is to schedule jobs on the particular machines in order
to minimise the completion time before the second stage starts. In this thesis, we have
constructed a new hybrid metaheuristic approach to solve this unique job shop scheduling
problem.
The second problem has arisen in the nancial sector, where the nancial regulators collects
transaction data across regulated assets classes. Our focus is to identify any unhedged
derivative, Contract for Di erence (CFD), with its corresponding underlying asset that
has been reported to the corresponding component authorities. The underlying asset
and CFD transaction contain di erent variables, like volume and price. Therefore, we are
looking for a combination of underlying asset variables that may hedge the equivalent CFD
variables. Our aim is to identify unhedged or unmatched CFD's with their corresponding
underlying asset. This problem closely relates to the goal programming problem with
variable parameters. We have developed two new local search methods and embedded the
newly constructed local search methods with basic VNS, to attain a new modi ed variant
of the VNS algorithm. We then used these newly constructed VNS variants to solve this
nancial matching problem.
In tackling the Vector Job Scheduling problem, we developed a new hybrid optimisation
heuristic algorithm by combining VNS and ACO. We then compared the results of this hybrid algorithm with VNS and ACO on their own. We found that the hybrid algorithm
performance is better than the other two independent heuristic algorithms. In tackling
the nancial derivative problem, our objective is to match the CFD trades with their
corresponding underlying equity trades. Our goal is to identify the mismatched CFD
trades while optimising the search process. We have developed two new local search
techniques and we have implemented a VNS algorithm with the newly developed local
search techniques to attain better solutions
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