Exact and heuristic approaches for multi-component optimisation problems

Modern real world applications are commonly complex, consisting of multiple subsystems that may interact with or depend on each other. Our case-study about wave energy converters (WEC) for the renewable energy industry shows that in such a multi-component system, optimising each individual component cannot yield global optimality for the entire system, owing to the influence of their interactions or the dependence on one another. Moreover, modelling a multi-component problem is rarely easy due to the complexity of the issues, which leads to a desire for existent models on which to base, and against which to test, calculations. Recently, the travelling thief problem (TTP) has attracted significant attention in the Evolutionary Computation community. It is intended to offer a better model for multicomponent systems, where researchers can push forward their understanding of the optimisation of such systems, especially for understanding of the interconnections between the components. The TTP interconnects with two classic NP-hard problems, namely the travelling salesman problem and the 0-1 knapsack problem, via the transportation cost that non-linearly depends on the accumulated weight of items. This non-linear setting introduces additional complexity. We study this nonlinearity through a simplified version of the TTP - the packing while travelling (PWT) problem, which aims to maximise the total reward for a given travelling tour. Our theoretical and experimental investigations demonstrate that the difficulty of a given problem instance is significantly influenced by adjusting a single parameter, the renting rate, which prompted our method of creating relatively hard instances using simple evolutionary algorithms. Our further investigations into the PWT problem yield a dynamic programming (DP) approach that can solve the problem in pseudo polynomial time and a corresponding approximation scheme. The experimental investigations show that the new approaches outperform the state-of-the-art ones. We furthermore propose three exact algorithms for the TTP, based on the DP of the PWT problem. By employing the exact DP for the underlying PWT problem as a subroutine, we create a novel indicator-based hybrid evolutionary approach for a new bi-criteria formulation of the TTP. This hybrid design takes advantage of the DP approach, along with a number of novel indicators and selection mechanisms to achieve better solutions. The results of computational experiments show that the approach is capable to outperform the state-of-the-art results.Thesis (Ph.D.) -- University of Adelaide, School of Computer Science, 201

New Heuristics For The 0-1 Multi-dimensional Knapsack Problems

This dissertation introduces new heuristic methods for the 0-1 multi-dimensional knapsack problem (0-1 MKP). 0-1 MKP can be informally stated as the problem of packing items into a knapsack while staying within the limits of different constraints (dimensions). Each item has a profit level assigned to it. They can be, for instance, the maximum weight that can be carried, the maximum available volume, or the maximum amount that can be afforded for the items. One main assumption is that we have only one item of each type, hence the problem is binary (0-1). The single dimensional version of the 0-1 MKP is the uni-dimensional single knapsack problem which can be solved in pseudo-polynomial time. However the 0-1 MKP is a strongly NP-Hard problem. Reduced cost values are rarely used resources in 0-1 MKP heuristics; using reduced cost information we introduce several new heuristics and also some improvements to past heuristics. We introduce two new ordering strategies, decision variable importance (DVI) and reduced cost based ordering (RCBO). We also introduce a new greedy heuristic concept which we call the sliding concept and a sub-branch of the sliding concept which we call sliding enumeration . We again use the reduced cost values within the sliding enumeration heuristic. RCBO is a brand new ordering strategy which proved useful in several methods such as improving Pirkul\u27s MKHEUR, a triangular distribution based probabilistic approach, and our own sliding enumeration. We show how Pirkul\u27s shadow price based ordering strategy fails to order the partial variables. We present a possible fix to this problem since there tends to be a high number of partial variables in hard problems. Therefore, this insight will help future researchers solve hard problems with more success. Even though sliding enumeration is a trivial method it found optima in less than a few seconds for most of our problems. We present different levels of sliding enumeration and discuss potential improvements to the method. Finally, we also show that in meta-heuristic approaches such as Drexl\u27s simulated annealing where random numbers are abundantly used, it would be better to use better designed probability distributions instead of random numbers

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

Recent Advances on GPU Computing in Operations Research

In the last decade, Graphics Processing Units (GPUs) have gained an increasing popularity as accelerators for High Performance Computing (HPC) applications. Recent GPUs are not only powerful graphics engines but also highly threaded parallel computing processors that can achieve sustainable speedup as compared with CPUs. In this context, researchers try to exploit the capability of this architecture to solve difficult problems in many domains in science and engineering. In this article, we present recent advances on GPU Computing in Operations Research. We focus in particular on Integer Programming and Linear Programming

Recent Advances on GPU Computing in Operations Research

Abstract-In the last decade, Graphics Processing Units (GPUs) have gained an increasing popularity as accelerators for High Performance Computing (HPC) applications. Recent GPUs are not only powerful graphics engines but also highly threaded parallel computing processors that can achieve sustainable speedup as compared with CPUs. In this context, researchers try to exploit the capability of this architecture to solve difficult problems in many domains in science and engineering. In this article, we present recent advances on GPU Computing in Operations Research. We focus in particular on Integer Programming and Linear Programming

Mixed strategy may outperform pure strategy: An initial study

In pure strategy meta-heuristics, only one search strategy is applied for all time. In mixed strategy meta-heuristics, each time one search strategy is chosen from a strategy pool with a probability and then is applied. An example is classical genetic algorithms, where either a mutation or crossover operator is chosen with a probability each time. The aim of this paper is to compare the performance between mixed strategy and pure strategy meta-heuristic algorithms. First an experimental study is implemented and results demonstrate that mixed strategy evolutionary algorithms may outperform pure strategy evolutionary algorithms on the 0-1 knapsack problem in up to 77.8% instances. Then Complementary Strategy Theorem is rigorously proven for applying mixed strategy at the population level. The theorem asserts that given two meta-heuristic algorithms where one uses pure strategy 1 and another uses pure strategy 2, the condition of pure strategy 2 being complementary to pure strategy 1 is sufficient and necessary if there exists a mixed strategy meta-heuristics derived from these two pure strategies and its expected number of generations to find an optimal solution is no more than that of using pure strategy 1 for any initial population, and less than that of using pure strategy 1 for some initial population

Evolutionary Computation 2020

Intelligent optimization is based on the mechanism of computational intelligence to refine a suitable feature model, design an effective optimization algorithm, and then to obtain an optimal or satisfactory solution to a complex problem. Intelligent algorithms are key tools to ensure global optimization quality, fast optimization efficiency and robust optimization performance. Intelligent optimization algorithms have been studied by many researchers, leading to improvements in the performance of algorithms such as the evolutionary algorithm, whale optimization algorithm, differential evolution algorithm, and particle swarm optimization. Studies in this arena have also resulted in breakthroughs in solving complex problems including the green shop scheduling problem, the severe nonlinear problem in one-dimensional geodesic electromagnetic inversion, error and bug finding problem in software, the 0-1 backpack problem, traveler problem, and logistics distribution center siting problem. The editors are confident that this book can open a new avenue for further improvement and discoveries in the area of intelligent algorithms. The book is a valuable resource for researchers interested in understanding the principles and design of intelligent algorithms

BQIABC: A new Quantum-Inspired Artificial Bee Colony Algorithm for Binary Optimization Problems

Artificial bee colony (ABC) algorithm is a swarm intelligence optimization algorithm inspired by the intelligent behavior of honey bees when searching for food sources. The various versions of the ABC algorithm have been widely used to solve continuous and discrete optimization problems in different fields. In this paper a new binary version of the ABC algorithm inspired by quantum computing, called binary quantum-inspired artificial bee colony algorithm (BQIABC), is proposed. The BQIABC combines the main structure of ABC with the concepts and principles of quantum computing such as, quantum bit, quantum superposition state and rotation Q-gates strategy to make an algorithm with more exploration ability. The proposed algorithm due to its higher exploration ability can provide a robust tool to solve binary optimization problems. To evaluate the effectiveness of the proposed algorithm, several experiments are conducted on the 0/1 knapsack problem, Max-Ones and Royal-Road functions. The results produced by BQIABC are compared with those of ten state-of-the-art binary optimization algorithms. Comparisons show that BQIABC presents the better results than or similar to other algorithms. The proposed algorithm can be regarded as a promising algorithm to solve binary optimization problems