Using the ACS Approach to Solve Continuous Mathematical Problems in Engineering

Ant colony system (ACS) has been widely applied for solving discrete domain problems in recent years. In particular, they are efficient and effective in finding nearly optimal solutions to discrete search spaces. Because of the restriction of ant-based algorithms, when the solution space of a problem to be solved is continuous, it is not so appropriate to use the original ACS to solve it. However, engineering mathematics in the real applications are always applied in the continuous domain. This paper thus proposes an extended ACS approach based on binary-coding to provide a standard process for solving problems with continuous variables. It first encodes solution space for continuous domain into a discrete binary-coding space (searching map), and a modified ACS can be applied to find the solution. Each selected edge in a complete path represents a part of a candidate solution. Different from the previous ant-based algorithms for continuous domain, the proposed binary coding ACS (BCACS) could retain the original operators and keep the benefits and characteristics of the traditional ACS. Besides, the proposed approach is easy to implement and could be applied in different kinds of problems in addition to mathematical problems. Several constrained functions are also evaluated to demonstrate the performance of the proposed algorithm

Population Diversity in Ant-inspired Optimization Algorithms

Finding a balance between exploration and exploitation is very important in the case of metaheuristics optimization, especially in the systems leveraging population of individuals expressing (as in Evolutionary Algorithms, etc.) or constructing (as in Ant Colony Optimization) solutions. Premature convergence is a real problem and finding means of its automatic detection and counteracting are of great importance. Measuring diversity in Evolutionary Algorithms working in real-value search space is often computationally complex, but feasible while measuring diversity in combinatorial domain is practically impossible (cf. Closest String Problem). Nevertheless, we propose several practical and feasible diversity measurement techniques dedicated to Ant Colony Optimization algorithms, leveraging the fact that even though analysis of the search space is at least an NP problem, we can focus on the pheromone table, where the direct outcomes of the search are expressed and can be analyzed. Besides proposing the measurement techniques, we apply them to assess the diversity of several variants of ACO, and closely analyze their features for the classic ACO. The discussion of the results is the first step towards applying the proposed measurement techniques in auto-adaptation of the parameters affecting directly the exploitation and exploration features in ACO in the future

Nature-Inspired Topology Optimization of Recurrent Neural Networks

Hand-crafting effective and efficient structures for recurrent neural networks (RNNs) is a difficult, expensive, and time-consuming process. To address this challenge, this work presents three nature-inspired (NI) algorithms for neural architecture search (NAS), introducing the subfield of nature-inspired neural architecture search (NI-NAS). These algorithms, based on ant colony optimization (ACO), progress from memory cell structure optimization, to bounded discrete-space architecture optimization, and finally to unbounded continuous-space architecture optimization. These methods were applied to real-world data sets representing challenging engineering problems, such as data from a coal-fired power plant, wind-turbine power generators, and aircraft flight data recorder (FDR) data. Initial work utilized ACO to select optimal connections inside recurrent long short-term memory (LSTM) cell structures. Viewing each LSTM cell as a graph, ants would choose potential input and output connections based on the pheromones previously laid down over those connections as done in a standard ACO search. However, this approach did not optimize the overall network of the RNN, particularly its synaptic parameters. I addressed this issue by introducing the Ant-based Neural Topology Search (ANTS) algorithm to directly optimize the entire RNN topology. ANTS utilizes a discrete-space superstructure representing a completely connected RNN where each node is connected to every other node, forming an extremely dense mesh of edges and recurrent edges. ANTS can select from a library of modern RNN memory cells. ACO agents (ants), in this thesis, build RNNs from the superstructure determined by pheromones laid out on the superstructure\u27s connections. Backpropagation is then used to train the generated RNNs in an asynchronous parallel computing design to accelerate the optimization process. The pheromone update depends on the evaluation of the tested RNN against a population of best performing RNNs. Several variations of the core algorithm was investigated to test several designed heuristics for ANTS and evaluate their efficacy in the formation of sparser synaptic connectivity patterns. This was done primarily by formulating different functions that drive the underlying pheromone simulation process as well as by introducing ant agents with 3 specialized roles (inspired by real-world ants) to construct the RNN structure. This characterization of the agents enables ants to focus on specific structure building roles. ``Communal intelligence\u27\u27 was also incorporated, where the best set of weights was across locally-trained RNN candidates for weight initialization, reducing the number of backpropagation epochs required to train each candidate RNN and speeding up the overall search process. However, the growth of the superstructure increased by an order of magnitude, as more input and deeper structures are utilized, proving to be one limitation of the proposed procedure. The limitation of ANTS motivated the development of the continuous ANTS algorithm (CANTS), which works with a continuous search space for any fixed network topology. In this process, ants moving within a (temporally-arranged) set of continuous/real-valued planes based on proximity and density of pheromone placements. The motion of the ants over these continuous planes, in a sense, more closely mimicks how actual ants move in the real world. Ants traverse a 3-dimensional space from the inputs to the outputs and across time lags. This continuous search space frees the ant agents from the limitations imposed by ANTS\u27 discrete massively connected superstructure, making the structural options unbounded when mapping the movements of ants through the 3D continuous space to a neural architecture graph. In addition, CANTS has fewer hyperparameters to tune than ANTS, which had five potential heuristic components that each had their own unique set of hyperparameters, as well as requiring the user to define the maximum recurrent depth, number of layers and nodes within each layer. CANTS only requires specifying the number ants and their pheromone sensing radius. The three applied strategies yielded three important successes. Applying ACO on optimizing LSTMs yielded a 1.34\% performance enhancement and more than 55% sparser structures (which is useful for speeding up inference). ANTS outperformed the NAS benchmark, NEAT, and the NAS state-of-the-art algorithm, EXAMM. CANTS showed competitive results to EXAMM and competed with ANTS while offering sparser structures, offering a promising path forward for optimizing (temporal) neural models with nature-inspired metaheuristics based the metaphor of ants

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

Optimizing the Replication of Multi-Quality Web Applications Using ACO and WoLF

This thesis presents the adaptation of Ant Colony Optimization to a new NP-hard problem involving the replication of multi-quality database-driven web applications (DAs) by a large application service provider (ASP). The ASP must assign DA replicas to its network of heterogeneous servers so that user demand is satisfied and replica update loads are minimized. The algorithm proposed, AntDA, for solving this problem is novel in several respects: ants traverse a bipartite graph in both directions as they construct solutions, pheromone is used for traversing from one side of the bipartite graph to the other and back again, heuristic edge values change as ants construct solutions, and ants may sometimes produce infeasible solutions. Experiments show that AntDA outperforms several other solution methods, but there was room for improvement in the convergence rates of the ants. Therefore, in an attempt to achieve the goals of faster convergence and better solution values for larger problems, AntDA was combined with the variable-step policy hill-climbing algorithm called Win or Learn Fast (WoLF). In experimentation, the addition of this learning algorithm in AntDA provided for faster convergence while outperforming other solution methods

Traveling Salesman Problem

The idea behind TSP was conceived by Austrian mathematician Karl Menger in mid 1930s who invited the research community to consider a problem from the everyday life from a mathematical point of view. A traveling salesman has to visit exactly once each one of a list of m cities and then return to the home city. He knows the cost of traveling from any city i to any other city j. Thus, which is the tour of least possible cost the salesman can take? In this book the problem of finding algorithmic technique leading to good/optimal solutions for TSP (or for some other strictly related problems) is considered. TSP is a very attractive problem for the research community because it arises as a natural subproblem in many applications concerning the every day life. Indeed, each application, in which an optimal ordering of a number of items has to be chosen in a way that the total cost of a solution is determined by adding up the costs arising from two successively items, can be modelled as a TSP instance. Thus, studying TSP can never be considered as an abstract research with no real importance

Collective Intelligence for Optimal Power Flow Solution Using Ant Colony Optimization

This paper presents the performance ant collective intelligence efficiency for electrical network. Solutions for Optimal Power Flow (OPF) problem of a power system deliberate via an ant colony optimization metaheuristic method. The objective is to minimize the total fuel cost of thermal generating units and also conserve an acceptable system performance in terms of limits on generator real and reactive power outputs, bus voltages, shunt capacitors/reactors, transformers tap-setting and power flow of transmission lines. Simulation results on the IEEE 30-bus electrical network show that the ant colony optimization method converges quickly to the global optimum

Benchmarking Inverse Optimization Algorithms for Molecular Materials Discovery

Machine learning-based molecular materials discovery has attracted enormous attention recently due to its flexibility in dealing with black box models. Yet, metaheuristic algorithms are not as widely applied to materials discovery applications. We comprehensively compare 11 different optimization algorithms for molecular materials design with targeted properties. These algorithms include Bayesian Optimization (BO) and multiple metaheuristic algorithms. We performed 5000 material evaluations repeated 5 times with different randomized initialization to optimize defined target properties. By maximizing the bulk modulus and minimizing the Fermi energy through perturbing parameterized molecular representations, we estimated the unique counts of molecular materials, mean density scan of the objectives space, mean objectives, and frequency distributed over the materials' representations and objectives. GA, GWO, and BWO exhibit higher variances for materials count, density scan, and mean objectives; and BO and Runge Kutta optimization (RUN) display generally lower variances. These results unveil that nature-inspired algorithms contain more uncertainties in the defined molecular design tasks, which correspond to their dependency on multiple hyperparameters. RUN exhibits higher mean objectives whereas BO displayed low mean objectives compared with other benchmarked methods. Combined with materials count and density scan, we propose that BO strives to approximate a more accurate surrogate of the design space by sampling more molecular materials and hence have lower mean objectives, yet RUN will repeatedly sample the targeted molecules with higher objective values. Our work shed light on automated digital molecular materials design and is expected to elicit future studies on materials optimization such as composite and alloy design based on specific desired properties.Comment: 15 pages, 5 figures, for the main manuscrip