Nested Monte Carlo Tree Search as Applied to Samurai Sudoku

As Sudoku has come into prominence as a favorite logic puzzle, mathematicians and computer scientists alike have analyzed the game for interesting properties. The large search space presents a challenge for both generating and solving Sudoku puzzles without relying on techniques that simply permute a valid puzzle. These permutations result in puzzles that are essentially the same since they follow the same solution path. Many Sudoku generating or solving programs rely on brute-force methods to avoid this pitfall, but this is inefficient since there is no heuristic to navigate the huge search space. A nested Monte Carlo tree search has some basis in brute-force methods, but guides the search in order to achieve better results by using random games within nested search stages. In this paper, we show that when the nested Monte Carlo search algorithm is implemented for solving Samurai Sudoku, a version of Sudoku in which a standard Sudoku puzzle is placed with four other standard Sudoku puzzles overlapping on each of the corners, it performs better than a completely random brute-force algorithm. Additionally, an improvement to the nested Monte Carlo search is made by implementing a heuristic that is used at each level of search

PhD. Subject: Strategies to design life-long learning heuristic based algorithms

Nowadays combinatorial optimization problems arise in many circumstances, and we need to be able to solve these problems e ciently. Unfortunately, many of these problems are proven to be NP-hard, but problems can be related in some way. Analysing di erent combinatorial problems we can see some similarities between them. If we work with this similarities, we could improve the search process of an algorithm, because there exists some concurrent knowledge about solving a problem that could be exploited. For example, if an algorithm can solve an instance X for Sudoku puzzle ensuring uniqueness in blocks before rows and colums, this strategy can be useful for another instance Y when the algorithm is in a local optimum. In other words, some heuristics that can nd interesting candidate solutions can be reused in future during the execution of an algorithm. To do this, an algorithm should learn over time to determine how, when and which heuristic apply. The idea of this investigation is to create strategies to design life-long learning heuristic based algorithms. There have been some investigations in this area applied to 1-D Bin Packing problem, for Traveling Sales Problem and the most important thing, is that can be applied in different kinds of problem. (Párrafo extraído del texto a modo de resumen)Sociedad Argentina de Informática e Investigación Operativa (SADIO

PhD. Subject: Strategies to design life-long learning heuristic based algorithms

Nowadays combinatorial optimization problems arise in many circumstances, and we need to be able to solve these problems e ciently. Unfortunately, many of these problems are proven to be NP-hard, but problems can be related in some way. Analysing di erent combinatorial problems we can see some similarities between them. If we work with this similarities, we could improve the search process of an algorithm, because there exists some concurrent knowledge about solving a problem that could be exploited. For example, if an algorithm can solve an instance X for Sudoku puzzle ensuring uniqueness in blocks before rows and colums, this strategy can be useful for another instance Y when the algorithm is in a local optimum. In other words, some heuristics that can nd interesting candidate solutions can be reused in future during the execution of an algorithm. To do this, an algorithm should learn over time to determine how, when and which heuristic apply. The idea of this investigation is to create strategies to design life-long learning heuristic based algorithms. There have been some investigations in this area applied to 1-D Bin Packing problem, for Traveling Sales Problem and the most important thing, is that can be applied in different kinds of problem. (Párrafo extraído del texto a modo de resumen)Sociedad Argentina de Informática e Investigación Operativa (SADIO

Two-Stage Multi-Objective Meta-Heuristics for Environmental and Cost-Optimal Energy Refurbishment at District Level

Energy efficiency and environmental performance optimization at the district level are following an upward trend mostly triggered by minimizing the Global Warming Potential (GWP) to 20% by 2020 and 40% by 2030 settled by the European Union (EU) compared with 1990 levels. This paper advances over the state of the art by proposing two novel multi-objective algorithms, named Non-dominated Sorting Genetic Algorithm (NSGA-II) and Multi-Objective Harmony Search (MOHS), aimed at achieving cost-effective energy refurbishment scenarios and allowing at district level the decision-making procedure. This challenge is not trivial since the optimisation process must provide feasible solutions for a simultaneous environmental and economic assessment at district scale taking into consideration highly demanding real-based constraints regarding district and buildings’ specific requirements. Consequently, in this paper, a two-stage optimization methodology is proposed in order to reduce the energy demand and fossil fuel consumption with an affordable investment cost at building level and minimize the total payback time while minimizing the GWP at district level. Aimed at demonstrating the effectiveness of the proposed two-stage multi-objective approaches, this work presents simulation results at two real district case studies in Donostia-San Sebastian (Spain) for which up to a 30% of reduction of GWP at district level is obtained for a Payback Time (PT) of 2–3 years.Part of this work has been developed from results obtained during the H2020 “Optimised Energy Efficient Design Platform for Refurbishment at District Level” (OptEEmAL) project, Grant No. 680676

Diversification and Intensification in Hybrid Metaheuristics for Constraint Satisfaction Problems

Metaheuristics are used to find feasible solutions to hard Combinatorial Optimization Problems (COPs). Constraint Satisfaction Problems (CSPs) may be formulated as COPs, where the objective is to reduce the number of violated constraints to zero. The popular puzzle Sudoku is an NP-complete problem that has been used to study the effectiveness of metaheuristics in solving CSPs. Applying the Simulated Annealing (SA) metaheuristic to Sudoku has been shown to be a successful method to solve CSPs. However, the ‘easy-hard-easy’ phase-transition behavior frequently attributed to a certain class of CSPs makes finding a solution extremely difficult in the hard phase because of the vast search space, the small number of solutions and a fitness landscape marked by many plateaus and local minima. Two key mechanisms that metaheuristics employ for searching are diversification and intensification. Diversification is the method of identifying diverse promising regions of the search space and is achieved through the process of heating/reheating. Intensification is the method of finding a solution in one of these promising regions and is achieved through the process of cooling. The hard phase area of the search terrain makes traversal without becoming trapped very challenging. Running the best available method - a Constraint Propagation/Depth-First Search algorithm - against 30,000 benchmark problem-instances, 20,240 remain unsolved after ten runs at one minute per run which we classify as very hard. This dissertation studies the delicate balance between diversification and intensification in the search process and offers a hybrid SA algorithm to solve very hard instances. The algorithm presents (a) a heating/reheating strategy that incorporates the lowest solution cost for diversification; (b) a more complex two-stage cooling schedule for faster intensification; (c) Constraint Programming (CP) hybridization to reduce the search space and to escape a local minimum; (d) a three-way swap, secondary neighborhood operator for a low expense method of diversification. These techniques are tested individually and in hybrid combinations for a total of 11 strategies, and the effectiveness of each is evaluated by percentage solved and average best run-time to solution. In the final analysis, all strategies are an improvement on current methods, but the most remarkable results come from the application of the “Quick Reset” technique between cooling stages

Design and Optimization of Power Delivery and Distribution Systems Using Evolutionary Computation Techniques

Nowadays computing platforms consist of a very large number of components that require to be supplied with diferent voltage levels and power requirements. Even a very small platform, like a handheld computer, may contain more than twenty diferent loads and voltage regulators. The power delivery designers of these systems are required to provide, in a very short time, the right power architecture that optimizes the performance, meets electrical specifications plus cost and size targets. The appropriate selection of the architecture and converters directly defines the performance of a given solution. Therefore, the designer needs to be able to evaluate a significant number of options in order to know with good certainty whether the selected solutions meet the size, energy eficiency and cost targets. The design dificulties of selecting the right solution arise due to the wide range of power conversion products provided by diferent manufacturers. These products range from discrete components (to build converters) to complete power conversion modules that employ diferent manufacturing technologies. Consequently, in most cases it is not possible to analyze all the alternatives (combinations of power architectures and converters) that can be built. The designer has to select a limited number of converters in order to simplify the analysis. In this thesis, in order to overcome the mentioned dificulties, a new design methodology for power supply systems is proposed. This methodology integrates evolutionary computation techniques in order to make possible analyzing a large number of possibilities. This exhaustive analysis helps the designer to quickly define a set of feasible solutions and select the best trade-off in performance according to each application. The proposed approach consists of two key steps, one for the automatic generation of architectures and other for the optimized selection of components. In this thesis are detailed the implementation of these two steps. The usefulness of the methodology is corroborated by contrasting the results using real problems and experiments designed to test the limits of the algorithms

A Multi-objective Harmony Search Algorithm for Optimal Energy and Environmental Refurbishment at District Level Scale

Nowadays municipalities are facing an increasing commitment regarding the energy and environmental performance of cities and districts. The multiple factors that characterize a district scenario, such as: refurbishment strategies’ selection, combination of passive, active and control measures, the surface to be refurbished and the generation systems to be substituted will highly influence the final impacts of the refurbishment solution. In order to answer this increasing demand and consider all above-mentioned district factors, municipalities need optimisation methods supporting the decision making process at district level scale when defining cost-effective refurbishment scenarios. Furthermore, the optimisation process should enable the evaluation of feasible solutions at district scale taking into account that each district and building has specific boundaries and barriers. Considering these needs, this paper presents a multi-objective approach allowing a simultaneous environmental and economic assessment of refurbishment scenarios at district scale. With the aim at demonstrating the effectiveness of the proposed approach, a real scenario of Gros district in the city of Donostia-San Sebastian (North of Spain) is presented. After analysing the baseline scenario in terms of energy performance, environmental and economic impacts, the multi-objective Harmony Search algorithm has been employed to assess the goal of reducing the environmental impacts in terms of Global Warming Potential (GWP) and minimizing the investment cost obtaining the best ranking of economic and environmental refurbishment scenarios for the Gros district.OptEEmAL project, Grant Agreement Number 68067