Combinatorial optimization and metaheuristics

Today, combinatorial optimization is one of the youngest and most active areas of discrete mathematics. It is a branch of optimization in applied mathematics and computer science, related to operational research, algorithm theory and computational complexity theory. It sits at the intersection of several fields, including artificial intelligence, mathematics and software engineering. Its increasing interest arises for the fact that a large number of scientific and industrial problems can be formulated as abstract combinatorial optimization problems, through graphs and/or (integer) linear programs. Some of these problems have polynomial-time (“efficient”) algorithms, while most of them are NP-hard, i.e. it is not proved that they can be solved in polynomial-time. Mainly, it means that it is not possible to guarantee that an exact solution to the problem can be found and one has to settle for an approximate solution with known performance guarantees. Indeed, the goal of approximate methods is to find “quickly” (reasonable run-times), with “high” probability, provable “good” solutions (low error from the real optimal solution). In the last 20 years, a new kind of algorithm commonly called metaheuristics have emerged in this class, which basically try to combine heuristics in high level frameworks aimed at efficiently and effectively exploring the search space. This report briefly outlines the components, concepts, advantages and disadvantages of different metaheuristic approaches from a conceptual point of view, in order to analyze their similarities and differences. The two very significant forces of intensification and diversification, that mainly determine the behavior of a metaheuristic, will be pointed out. The report concludes by exploring the importance of hybridization and integration methods

Submodular memetic approximation for multiobjective parallel test paper generation

Parallel test paper generation is a biobjective distributed resource optimization problem, which aims to generate multiple similarly optimal test papers automatically according to multiple user-specified assessment criteria. Generating high-quality parallel test papers is challenging due to its NP-hardness in both of the collective objective functions. In this paper, we propose a submodular memetic approximation algorithm for solving this problem. The proposed algorithm is an adaptive memetic algorithm (MA), which exploits the submodular property of the collective objective functions to design greedy-based approximation algorithms for enhancing steps of the multiobjective MA. Synergizing the intensification of submodular local search mechanism with the diversification of the population-based submodular crossover operator, our algorithm can jointly optimize the total quality maximization objective and the fairness quality maximization objective. Our MA can achieve provable near-optimal solutions in a huge search space of large datasets in efficient polynomial runtime. Performance results on various datasets have shown that our algorithm has drastically outperformed the current techniques in terms of paper quality and runtime efficiency

Ant colony optimisation and local search for bin-packing and cutting stock problems

The Bin Packing Problem and the Cutting Stock Problem are two related classes of NP-hard combinatorial optimization problems. Exact solution methods can only be used for very small instances, so for real-world problems, we have to rely on heuristic methods. In recent years, researchers have started to apply evolutionary approaches to these problems, including Genetic Algorithms and Evolutionary Programming. In the work presented here, we used an ant colony optimization (ACO) approach to solve both Bin Packing and Cutting Stock Problems. We present a pure ACO approach, as well as an ACO approach augmented with a simple but very effective local search algorithm. It is shown that the pure ACO approach can compete with existing evolutionary methods, whereas the hybrid approach can outperform the best-known hybrid evolutionary solution methods for certain problem classes. The hybrid ACO approach is also shown to require different parameter values from the pure ACO approach and to give a more robust performance across different problems with a single set of parameter values. The local search algorithm is also run with random restarts and shown to perform significantly worse than when combined with ACO

Indicator Based Ant Colony Optimization for Multi-objective Knapsack Problem

AbstractThe use of metaheuristics to solve multi-objective optimization problems (MOP) is a very active research topic. Ant Colony Optimization (ACO) has received a growing interest in the last years for such problems. Many algorithms have been proposed in the literature to solve different MOP. This paper presents an indicator-based ant colony optimization algorithm called IBACO for the multi-objective knapsack problem (MOKP). The IBACO algorithm proposes a new idea that uses binary quality indicators to guide the search of artificial ants. These indicators were initially used by Zitzler and Künzli in the selection process of their evolutionary algorithm IBEA. In this paper, we use the indicator optimization principle to reinforce the best solutions by rewarding pheromone trails. We carry out a set of experiments on MOKP benchmark instances by applying the two binary indicators: epsilon indicator and hypervolume indicator. The comparison of the proposed algorithm with IBEA, ACO and other state-of-the-art evolutionary algorithms shows that IBACO is significantly better on most instances

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

Parallel ant system applied to the multiple knapsack problem

Interesting real world combinatorial problems are NP-complete and many of them are hard to solve by using traditional methods. However, several heuristic methods have been developed in order to obtain timely suboptimal solutions. Most of those heuristic methods are also naturally suitable for a parallel implementation and consequently, an additional improvement on the response time can be obtained. One way of increasing the computational power is by using multiple processors operating together on a single problem. The overall problem is split into parts, each of which is operated by a separate processor in parallel. Unfortunately problems cannot be divided perfectly into separate parts and interaction is necessary between the parts like data transfer and process synchronization. However, substantial improvement can be achieved, depending on the problem and the amount of parallelism in the problem. Our work aims to exploit the capability of a distributed computing environment by using PVM and implementing a parallel version of an Ant System for solving the Multiple Knapsack Problem (MKP). An Ant System (a distributed algorithm) is a set of agents working independently and cooperating sporadically in a common problem solving activity. Regarding the above characteristics, an Ant System can be naturally considered as a nearly embarrassingly parallel computation. The proposed parallel implementations of an Ant System are based on two different approaches, static and dynamic task assignment. The computational study involves processors of different velocities and several MKP test cases of different sizes and difficulties (tight and loose constraints). The performance on the response time is measured by two indexes, Speedup Factor and Efficiency when is compared to a serial version of an Ant System. The results obtained show the potential power of exploiting the parallelism underlying in an Ant System regarding the good quality of the results and a remarkable decreasing on the computation time.Sistemas InteligentesRed de Universidades con Carreras en Informática (RedUNCI

The ant colony metaphor for multiple knapsack problem

This paper presents an Ant Colony (AC) model for the Multiple Knapsack Problem (MKP). The ant colony metaphor, as well as other evolutionary metaphors, was applied successfully to diverse heavily constrained problems. An AC system is also considered a class of multiagent distributed algorithm for combinatorial optimisation. The principle of an AC system is adapted to the MKP. We present some results regarding its performance against known optimum for different instances of MKP. The obtained results show the potential power of this particular evolutionary approach for optimisation problems.Eje: Workshop sobre Aspectos Teoricos de la Inteligencia ArtificialRed de Universidades con Carreras en Informática (RedUNCI