Genetic Transfer or Population Diversification? Deciphering the Secret Ingredients of Evolutionary Multitask Optimization

Evolutionary multitasking has recently emerged as a novel paradigm that enables the similarities and/or latent complementarities (if present) between distinct optimization tasks to be exploited in an autonomous manner simply by solving them together with a unified solution representation scheme. An important matter underpinning future algorithmic advancements is to develop a better understanding of the driving force behind successful multitask problem-solving. In this regard, two (seemingly disparate) ideas have been put forward, namely, (a) implicit genetic transfer as the key ingredient facilitating the exchange of high-quality genetic material across tasks, and (b) population diversification resulting in effective global search of the unified search space encompassing all tasks. In this paper, we present some empirical results that provide a clearer picture of the relationship between the two aforementioned propositions. For the numerical experiments we make use of Sudoku puzzles as case studies, mainly because of their feature that outwardly unlike puzzle statements can often have nearly identical final solutions. The experiments reveal that while on many occasions genetic transfer and population diversity may be viewed as two sides of the same coin, the wider implication of genetic transfer, as shall be shown herein, captures the true essence of evolutionary multitasking to the fullest.Comment: 7 pages, 6 figure

Solving Sudoku with Ant Colony Optimization

In this paper we present a new algorithm for the well-known and computationally-challenging Sudoku puzzle game. Our Ant Colony Optimization-based method significantly out-performs the state-of-the-art algorithm on the hardest, large instances of Sudoku. We provide evidence that – compared to traditional backtracking methods – our algorithm offers a much more efficient search of the solution space, and demonstrate the utility of a novel anti-stagnation operator. This work lays the foundation for future work on a general-purpose puzzle solver, and establishes Japanese pencil puzzles as a suitable platform for benchmarking a wide range of algorithms

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

A Novel Evolutionary Algorithm with Column and Sub-Block Local Search for Sudoku Puzzles

Sudoku puzzles are not only popular intellectual games but also NP-hard combinatorial problems related to various real-world applications, which have attracted much attention worldwide. Although many efficient tools, such as evolutionary computation (EC) algorithms, have been proposed for solving Sudoku puzzles, they still face great challenges with regard to hard and large instances of Sudoku puzzles. Therefore, to efficiently solve Sudoku puzzles, this paper proposes a genetic algorithm (GA)-based method with a novel local search technology called local search-based GA (LSGA). The LSGA includes three novel design aspects. First, it adopts a matrix coding scheme to represent individuals and designs the corresponding crossover and mutation operations. Second, a novel local search strategy based on column search and sub-block search is proposed to increase the convergence speed of the GA. Third, an elite population learning mechanism is proposed to let the population evolve by learning the historical optimal solution. Based on the above technologies, LSGA can greatly improve the search ability for solving complex Sudoku puzzles. LSGA is compared with some state-of-the-art algorithms at Sudoku puzzles of different difficulty levels and the results show that LSGA performs well in terms of both convergence speed and success rates on the tested Sudoku puzzle instances

Sudokube Using Genetic Algorithms To Simultaneously Solve Multiple Combinatorial Problems

School of Electrical & Computer Engineerin

Some Enhancement Methods For Backtracking-Search In Solving Multiple Permutation Problems

In this dissertation, we present some enhancement methods for backtracking-search in solving multiple permutation problems. Some well-known NP-complete multiple permutation problems are Quasigroup Completion Problem and Sudoku. Multiple permutation problems have been getting a lot of attention in the literature in the recent years due to having a highly structured nature and being a challenging combinatorial search problem. Furthermore, it has been shown that many real-world problems in scheduling and experimental design take the form of multiple permutation problems. Therefore, it has been suggested that they can be used as a benchmark problem to test various enhancement methods for solving constraint satisfaction problems. Then it is hoped that the insight gained from studying them can be applied to other hard structured as well as unstructured problems. Our supplementary and novel enhancement methods for backtracking-search in solving these multiple permutation problems can be summarized as follows: We came up with a novel way to encode multiple permutation problems and then we designed and developed an arc-consistency algorithm that is tailored towards this modeling. We implemented five versions of this arc-consistency algorithm where the last version eliminates almost all of the possible propagation redundancy. Then we introduced the novel notion of interlinking dynamic variable ordering with dynamic value ordering, where the dynamic value ordering is also used as a second tie-breaker for the dynamic variable ordering. We also proposed the concept of integrating dynamic variable ordering and dynamic value ordering into an arc-consistency algorithm by using greedy counting assertions. We developed the concept of enforcing local-consistency between variables from different redundant models of the problem. Finally, we introduced an embarrassingly parallel task distribution process at the beginning of the search. We theoretically proved that the limited form of the Hall\u27s theorem is enforced by our modeling of the multiple permutation problems. We showed with our empirical results that the ``fail-first principle is confirmed in terms of minimizing the total number of explored nodes, but is refuted in terms of minimizing the depth of the search tree when finding a single solution, which correlates with previously published results. We further showed that the performance (total number instances solved at the phase transition point within a given time limit) of a given search heuristic is closely related to the underlying pruning algorithm that is being employed to maintain some level of local-consistency during backtracking-search. We also extended the previously established hypothesis, which stated that the second peak of hardness for NP-complete problems is algorithm dependent, to second peak of hardness for NP-complete problems is also search-heuristic dependent. Then we showed with our empirical results that several of our enhancement methods on backtracking-search perform better than the constraint solvers MAC-LAH and Minion as well as the SAT solvers Satz and MiniSat for previously tested instances of multiple permutation problems on these solvers

Virtual Reality Games for Motor Rehabilitation

This paper presents a fuzzy logic based method to track user satisfaction without the need for devices to monitor users physiological conditions. User satisfaction is the key to any product’s acceptance; computer applications and video games provide a unique opportunity to provide a tailored environment for each user to better suit their needs. We have implemented a non-adaptive fuzzy logic model of emotion, based on the emotional component of the Fuzzy Logic Adaptive Model of Emotion (FLAME) proposed by El-Nasr, to estimate player emotion in UnrealTournament 2004. In this paper we describe the implementation of this system and present the results of one of several play tests. Our research contradicts the current literature that suggests physiological measurements are needed. We show that it is possible to use a software only method to estimate user emotion