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

Developing New Multidimensional Knapsack Heuristics Based on Empirical Analysis of Legacy Heuristics

The multidimensional knapsack problem (MKP) has been used to model a variety of practical optimization and decision-making applications. Due to its combinatorial nature, heuristics are often employed to quickly find good solutions to MKPs. While there have been a variety of heuristics proposed for the MKP, and a plethora of empirical studies comparing the performance of these heuristics, little has been done to garner a deeper understanding of heuristic performance as a function of problem structure. This dissertation presents a research methodology, empirical and theoretical results explicitly aimed at gaining a deeper understanding of heuristic procedural performance as a function of test problem characteristics. This work first employs an available, robust set of two-dimensional knapsack problems in an empirical study to garner performance insights. These performance insights are tested against a larger set of problems, five-dimensional knapsack problems specifically generated for empirical testing purposes. The performance insights are found to hold in the higher dimensions. These insights are used to formulate and test a suite of three new greedy heuristics for the MKP, each improving upon its successor. These heuristics are found to outperform available legacy heuristics across a complete spectrum of test problems. Problem reduction heuristics are examined and the subsequent performance insights garnered are used to derive a new problem reduction heuristic, which is then further extended to employ a local improvement phase. These problem reduction heuristics are also found to outperform currently available approaches. Available problem test sets are shown lacking along multiple dimensions of importance for viable empirical testing. A new problem generation methodology is developed and shown to overcome the current limitations in available problem test sets. This problem generation methodology is used to generate a new set of empirical test problems specifically designed for competitive computational tests. This new test set is shown to stress existing heuristics; not only does the computational time required by these legacy heuristics increase with problem size, but solution quality is found to decrease with problem size. However, the solution quality obtained by the suite of heuristics developed in this dissertation are shown to be unaffected by problem size thereby providing a level of robust solution quality not previously seen in heuristic development for the MKP. This research demonstrates that the test problems can have a profound, and sometimes misleading, impact on the general insights gained via empirical testing, provides six new quality heuristics, and two new robust sets of test problems, one focused on empirical testing, the other focused on competitive testing

Meta-raps: Parameter Setting And New Applications

Recently meta-heuristics have become a popular solution methodology, in terms of both research and application, for solving combinatorial optimization problems. Meta-heuristic methods guide simple heuristics or priority rules designed to solve a particular problem. Meta-heuristics enhance these simple heuristics by using a higher level strategy. The advantage of using meta-heuristics over conventional optimization methods is meta-heuristics are able to find good (near optimal) solutions within a reasonable computation time. Investigating this line of research is justified because in most practical cases with medium to large scale problems, the use of meta-heuristics is necessary to be able to find a solution in a reasonable time. The specific meta-heuristic studied in this research is, Meta-RaPS; Meta-heuristic for Randomized Priority Search which is developed by DePuy and Whitehouse in 2001. Meta-RaPS is a generic, high level strategy used to modify greedy algorithms based on the insertion of a random element (Moraga, 2002). To date, Meta-RaPS had been applied to different types of combinatorial optimization problems and achieved comparable solution performance to other meta-heuristic techniques. The specific problem studied in this dissertation is parameter setting of Meta-RaPS. The topic of parameter setting for meta-heuristics has not been extensively studied in the literature. Although the parameter setting method devised in this dissertation is used primarily on Meta-RaPS, it is applicable to any meta-heuristic\u27s parameter setting problem. This dissertation not only enhances the power of Meta-RaPS by parameter tuning but also it introduces a robust parameter selection technique with wide-spread utility for many meta-heuristics. Because the distribution of solution values generated by meta-heuristics for combinatorial optimization problems is not normal, the current parameter setting techniques which employ a parametric approach based on the assumption of normality may not be appropriate. The proposed method is Non-parametric Based Genetic Algorithms. Based on statistical tests, the Non-parametric Based Genetic Algorithms (NPGA) is able to enhance the solution quality of Meta-RaPS more than any other parameter setting procedures benchmarked in this research. NPGA sets the best parameter settings, of all the methods studied, for 38 of the 41 Early/Tardy Single Machine Scheduling with Common Due Date and Sequence-Dependent Setup Time (ETP) problems and 50 of the 54 0-1 Multidimensional Knapsack Problems (0-1 MKP). In addition to the parameter setting procedure discussed, this dissertation provides two Meta-RaPS combinatorial optimization problem applications, the 0-1 MKP, and the ETP. For the ETP problem, the Meta-RaPS application in this dissertation currently gives the best meta-heuristic solution performance so far in the literature for common ETP test sets. For the large ETP test set, Meta-RaPS provided better solution performance than Simulated Annealing (SA) for 55 of the 60 problems. For the small test set, in all four different small problem sets, the Meta-RaPS solution performance outperformed exiting algorithms in terms of average percent deviation from the optimal solution value. For the 0-1 MKP, the present Meta-RaPS application performs better than the earlier Meta-RaPS applications by other researchers on this problem. The Meta-RaPS 0-1 MKP application presented here has better solution quality than the existing Meta-RaPS application (Moraga, 2005) found in the literature. Meta-RaPS gives 0.75% average percent deviation, from the best known solutions, for the 270 0-1 MKP test problems

Multi-stage stochastic optimization and reinforcement learning for forestry epidemic and covid-19 control planning

This dissertation focuses on developing new modeling and solution approaches based on multi-stage stochastic programming and reinforcement learning for tackling biological invasions in forests and human populations. Emerald Ash Borer (EAB) is the nemesis of ash trees. This research introduces a multi-stage stochastic mixed-integer programming model to assist forest agencies in managing emerald ash borer insects throughout the U.S. and maximize the public benets of preserving healthy ash trees. This work is then extended to present the first risk-averse multi-stage stochastic mixed-integer program in the invasive species management literature to account for extreme events. Significant computational achievements are obtained using a scenario dominance decomposition and cutting plane algorithm.The results of this work provide crucial insights and decision strategies for optimal resource allocation among surveillance, treatment, and removal of ash trees, leading to a better and healthier environment for future generations. This dissertation also addresses the computational difficulty of solving one of the most difficult classes of combinatorial optimization problems, the Multi-Dimensional Knapsack Problem (MKP). A novel 2-Dimensional (2D) deep reinforcement learning (DRL) framework is developed to represent and solve combinatorial optimization problems focusing on MKP. The DRL framework trains different agents for making sequential decisions and finding the optimal solution while still satisfying the resource constraints of the problem. To our knowledge, this is the first DRL model of its kind where a 2D environment is formulated, and an element of the DRL solution matrix represents an item of the MKP. Our DRL framework shows that it can solve medium-sized and large-sized instances at least 45 and 10 times faster in CPU solution time, respectively, with a maximum solution gap of 0.28% compared to the solution performance of CPLEX. Applying this methodology, yet another recent epidemic problem is tackled, that of COVID-19. This research investigates a reinforcement learning approach tailored with an agent-based simulation model to simulate the disease growth and optimize decision-making during an epidemic. This framework is validated using the COVID-19 data from the Center for Disease Control and Prevention (CDC). Research results provide important insights into government response to COVID-19 and vaccination strategies

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

Multiobjective metaheuristic approaches for mean-risk combinatorial optimisation with applications to capacity expansion

Tese de doutoramento. Engenharia Electrotécnica e de Computadores. Faculdade de Engenharia. Universidade do Porto. 200

Optimizing Mean Mission Duration for Multiple-Payload Satellites

This thesis addresses the problem of optimally selecting and specifying satellite payloads for inclusion on a satellite bus to be launched into a constellation. The objective is to select and specify payloads so that the total lifetime utility of the constellation is maximized. The satellite bus is limited by finite power, weight, volume, and cost constraints. This problem is modeled as a classical knapsack problem in one and multiple dimensions, and dynamic programming and binary integer programming formulations are provided to solve the problem. Due to the computational complexity of the problem, the solution techniques include exact methods as well as four heuristic procedures including a greedy heuristic, two norm-based heuristics, and a simulated annealing heuristic. The performance of the exact and heuristic approaches is evaluated on the basis of solution quality and computation time by solving a series of notional and randomly-generated problem instances. The numerical results indicate that, when an exact solution is required for a moderately-sized constellation, the integer programming formulation is most reliable in solving the problem to optimality. However, if the problem size is very large, and near-optimal solutions are acceptable, then the simulated annealing algorithm performs best among the heuristic procedures

Ant colony meta-heuristics - Schemes and software framework

Master'sMASTER OF SCIENC

Explicit Building-Block Multiobjective Genetic Algorithms: Theory, Analysis, and Developing

This dissertation research emphasizes explicit Building Block (BB) based MO EAs performance and detailed symbolic representation. An explicit BB-based MOEA for solving constrained and real-world MOPs is developed the Multiobjective Messy Genetic Algorithm II (MOMGA-II) which is designed to validate symbolic BB concepts. The MOMGA-II demonstrates that explicit BB-based MOEAs provide insight into solving difficult MOPs that is generally not realized through the use of implicit BB-based MOEA approaches. This insight is necessary to increase the effectiveness of all MOEA approaches. In order to increase MOEA computational efficiency parallelization of MOEAs is addressed. Communications between processors in a parallel MOEA implementation is extremely important, hence innovative migration and replacement schemes for use in parallel MOEAs are detailed and tested. These parallel concepts support the development of the first explicit BB-based parallel MOEA the pMOMGA-II. MOEA theory is also advanced through the derivation of the first MOEA population sizing theory. The multiobjective population sizing theory presented derives the MOEA population size necessary in order to achieve good results within a specified level of confidence. Just as in the single objective approach the MOEA population sizing theory presents a very conservative sizing estimate. Validated results illustrate insight into building block phenomena good efficiency excellent effectiveness and motivation for future research in the area of explicit BB-based MOEAs. Thus the generic results of this research effort have applicability that aid in solving many different MOPs

Model based test suite minimization using metaheuristics

Software testing is one of the most widely used methods for quality assurance and fault detection purposes. However, it is one of the most expensive, tedious and time consuming activities in software development life cycle. Code-based and specification-based testing has been going on for almost four decades. Model-based testing (MBT) is a relatively new approach to software testing where the software models as opposed to other artifacts (i.e. source code) are used as primary source of test cases. Models are simplified representation of a software system and are cheaper to execute than the original or deployed system. The main objective of the research presented in this thesis is the development of a framework for improving the efficiency and effectiveness of test suites generated from UML models. It focuses on three activities: transformation of Activity Diagram (AD) model into Colored Petri Net (CPN) model, generation and evaluation of AD based test suite and optimization of AD based test suite. Unified Modeling Language (UML) is a de facto standard for software system analysis and design. UML models can be categorized into structural and behavioral models. AD is a behavioral type of UML model and since major revision in UML version 2.x it has a new Petri Nets like semantics. It has wide application scope including embedded, workflow and web-service systems. For this reason this thesis concentrates on AD models. Informal semantics of UML generally and AD specially is a major challenge in the development of UML based verification and validation tools. One solution to this challenge is transforming a UML model into an executable formal model. In the thesis, a three step transformation methodology is proposed for resolving ambiguities in an AD model and then transforming it into a CPN representation which is a well known formal language with extensive tool support. Test case generation is one of the most critical and labor intensive activities in testing processes. The flow oriented semantic of AD suits modeling both sequential and concurrent systems. The thesis presented a novel technique to generate test cases from AD using a stochastic algorithm. In order to determine if the generated test suite is adequate, two test suite adequacy analysis techniques based on structural coverage and mutation have been proposed. In terms of structural coverage, two separate coverage criteria are also proposed to evaluate the adequacy of the test suite from both perspectives, sequential and concurrent. Mutation analysis is a fault-based technique to determine if the test suite is adequate for detecting particular types of faults. Four categories of mutation operators are defined to seed specific faults into the mutant model. Another focus of thesis is to improve the test suite efficiency without compromising its effectiveness. One way of achieving this is identifying and removing the redundant test cases. It has been shown that the test suite minimization by removing redundant test cases is a combinatorial optimization problem. An evolutionary computation based test suite minimization technique is developed to address the test suite minimization problem and its performance is empirically compared with other well known heuristic algorithms. Additionally, statistical analysis is performed to characterize the fitness landscape of test suite minimization problems. The proposed test suite minimization solution is extended to include multi-objective minimization. As the redundancy is contextual, different criteria and their combination can significantly change the solution test suite. Therefore, the last part of the thesis describes an investigation into multi-objective test suite minimization and optimization algorithms. The proposed framework is demonstrated and evaluated using prototype tools and case study models. Empirical results have shown that the techniques developed within the framework are effective in model based test suite generation and optimizatio