Applying the big bang-big crunch metaheuristic to large-sized operational problems

In this study, we present an investigation of comparing the capability of a big bang-big crunch metaheuristic (BBBC) for managing operational problems including combinatorial optimization problems. The BBBC is a product of the evolution theory of the universe in physics and astronomy. Two main phases of BBBC are the big bang and the big crunch. The big bang phase involves the creation of a population of random initial solutions, while in the big crunch phase these solutions are shrunk into one elite solution exhibited by a mass center. This study looks into the BBBC’s effectiveness in assignment and scheduling problems. Where it was enhanced by incorporating an elite pool of diverse and high quality solutions; a simple descent heuristic as a local search method; implicit recombination; Euclidean distance; dynamic population size; and elitism strategies. Those strategies provide a balanced search of diverse and good quality population. The investigation is conducted by comparing the proposed BBBC with similar metaheuristics. The BBBC is tested on three different classes of combinatorial optimization problems; namely, quadratic assignment, bin packing, and job shop scheduling problems. Where the incorporated strategies have a greater impact on the BBBC's performance. Experiments showed that the BBBC maintains a good balance between diversity and quality which produces high-quality solutions, and outperforms other identical metaheuristics (e.g. swarm intelligence and evolutionary algorithms) reported in the literature

Q-Learnheuristics: towards data-driven balanced metaheuristics

One of the central issues that must be resolved for a metaheuristic optimization process to work well is the dilemma of the balance between exploration and exploitation. The metaheuristics (MH) that achieved this balance can be called balanced MH, where a Q-Learning (QL) integration framework was proposed for the selection of metaheuristic operators conducive to this balance, particularly the selection of binarization schemes when a continuous metaheuristic solves binary combinatorial problems. In this work the use of this framework is extended to other recent metaheuristics, demonstrating that the integration of QL in the selection of operators improves the exploration-exploitation balance. Specifically, the Whale Optimization Algorithm and the Sine-Cosine Algorithm are tested by solving the Set Covering Problem, showing statistical improvements in this balance and in the quality of the solutions

HEDCOS: High Efficiency Dynamic Combinatorial Optimization System using Ant Colony Optimization algorithm

This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University LondonDynamic combinatorial optimization is gaining popularity among industrial practitioners due to the ever-increasing scale of their optimization problems and efforts to solve them to remain competitive. Larger optimization problems are not only more computationally intense to optimize but also have more uncertainty within problem inputs. If some aspects of the problem are subject to dynamic change, it becomes a Dynamic Optimization Problem (DOP). In this thesis, a High Efficiency Dynamic Combinatorial Optimization System is built to solve challenging DOPs with high-quality solutions. The system is created using Ant Colony Optimization (ACO) baseline algorithm with three novel developments. First, introduced an extension method for ACO algorithm called Dynamic Impact. Dynamic Impact is designed to improve convergence and solution quality by solving challenging optimization problems with a non-linear relationship between resource consumption and fitness. This proposed method is tested against the real-world Microchip Manufacturing Plant Production Floor Optimization (MMPPFO) problem and the theoretical benchmark Multidimensional Knapsack Problem (MKP). Second, a non-stochastic dataset generation method was introduced to solve the dynamic optimization research replicability problem. This method uses a static benchmark dataset as a starting point and source of entropy to generate a sequence of dynamic states. Then using this method, 1405 Dynamic Multidimensional Knapsack Problem (DMKP) benchmark datasets were generated and published using famous static MKP benchmark instances as the initial state. Third, introduced a nature-inspired discrete dynamic optimization strategy for ACO by modelling real-world ants’ symbiotic relationship with aphids. ACO with Aphids strategy is designed to solve discrete domain DOPs with event-triggered discrete dynamism. The strategy improved inter-state convergence by allowing better solution recovery after dynamic environment changes. Aphids mediate the information from previous dynamic optimization states to maximize initial results performance and minimize the impact on convergence speed. This strategy is tested for DMKP and against identical ACO implementations using Full-Restart and Pheromone-Sharing strategies, with all other variables isolated. Overall, Dynamic Impact and ACO with Aphids developments are compounding. Using Dynamic Impact on single objective optimization of MMPPFO, the fitness value was improved by 33.2% over the ACO algorithm without Dynamic Impact. MKP benchmark instances of low complexity have been solved to a 100% success rate even when a high degree of solution sparseness is observed, and large complexity instances have shown the average gap improved by 4.26 times. ACO with Aphids has also demonstrated superior performance over the Pheromone-Sharing strategy in every test on average gap reduced by 29.2% for a total compounded dynamic optimization performance improvement of 6.02 times. Also, ACO with Aphids has outperformed the Full-Restart strategy for large datasets groups, and the overall average gap is reduced by 52.5% for a total compounded dynamic optimization performance improvement of 8.99 times

Evolutionary algorithms and hyper-heuristics for orthogonal packing problems

This thesis investigates two major classes of Evolutionary Algorithms, Genetic Algorithms (GAs) and Evolution Strategies (ESs), and their application to the Orthogonal Packing Problems (OPP). OPP are canonical models for NP-hard problems, the class of problems widely conceived to be unsolvable on a polynomial deterministic Turing machine, although they underlie many optimisation problems in the real world. With the increasing power of modern computers, GAs and ESs have been developed in the past decades to provide high quality solutions for a wide range of optimisation and learning problems. These algorithms are inspired by Darwinian nature selection mechanism that iteratively select better solutions in populations derived from recombining and mutating existing solutions. The algorithms have gained huge success in many areas, however, being stochastic processes, the algorithms' behaviour on different problems is still far from being fully understood. The work of this thesis provides insights to better understand both the algorithms and the problems. The thesis begins with an investigation of hyper-heuristics as a more general search paradigm based on standard EAs. Hyper-heuristics are shown to be able to overcome the difficulty of many standard approaches which only search in partial solution space. The thesis also looks into the fundamental theory of GAs, the schemata theorem and the building block hypothesis, by developing the Grouping Genetic Algorithms (GGA) for high dimensional problems and providing supportive yet qualified empirical evidences for the hypothesis. Realising the difficulties of genetic encoding over combinatorial search domains, the thesis proposes a phenotype representation together with Evolution Strategies that operates on such representation. ESs were previously applied mainly to continuous numerical optimisation, therefore being less understood when searching in combinatorial domains. The work in this thesis develops highly competent ES algorithms for OPP and opens the door for future research in this area

An investigation of novel approaches for optimising retail shelf space allocation

This thesis is concerned with real-world shelf space allocation problems that arise due to the conflict of limited shelf space availability and the large number of products that need to be displayed. Several important issues in the shelf space allocation problem are identified and two mathematical models are developed and studied. The first model deals with a general shelf space allocation problem while the second model specifically concerns shelf space allocation for fresh produce. Both models are closely related to the knapsack and bin packing problem. The thesis firstly studies a recently proposed generic search technique, hyper-heuristics, and introduces a simulated annealing acceptance criterion in order to improve its performance. The proposed algorithm, called simulated annealing hyper-heuristics, is initially tested on the one-dimensional bin packing problem, with very promising and competitive results being produced. The algorithm is then applied to the general shelf space allocation problem. The computational results show that the proposed algorithm is superior to a general simulated annealing algorithm and other types of hyper-heuristics. For the test data sets used in the thesis, the new approach solves every instance to over 98% of the upper bound which was obtained via a two-stage relaxation method. The thesis also studies and formulates a deterministic shelf space allocation and inventory model specifically for fresh produce. The model, for the first time, considers the freshness condition as an important factor in influencing a product's demand. Further analysis of the model shows that the search space of the problem can be reduced by decomposing the problem into a nonlinear knapsack problem and a single-item inventory problem that can be solved optimally by a binary search. Several heuristic and meta-heuristic approaches are utilised to optimise the model, including four efficient gradient based constructive heuristics, a multi-start generalised reduced gradient (GRG) algorithm, simulated annealing, a greedy randomised adaptive search procedure (GRASP) and three different types of hyper-heuristics. Experimental results show that the gradient based constructive heuristics are very efficient and all meta-heuristics can only marginally improve on them. Among these meta-heuristics, two simulated annealing based hyper-heuristic performs slightly better than the other meta-heuristic methods. Across all test instances of the three problems, it is shown that the introduction of simulated annealing in the current hyper-heuristics can indeed improve the performance of the algorithms. However, the simulated annealing hyper-heuristic with random heuristic selection generally performs best among all the other meta-heuristics implemented in this thesis. This research is funded by the Engineering and Physical Sciences Research Council (EPSRC) grant reference GR/R60577. Our industrial collaborators include Tesco Retail Vision and SpaceIT Solutions Ltd