One of the most common questions in artificial intelligence is deceptively simple: Is there one algorithm that can solve any problem?<\/p>\n\n\n\n
It is an appealing idea. A single universal method that, given any problem, finds the best solution. No need to choose between approaches, no specialisation required, just one tool for everything.<\/p>\n\n\n\n
The answer, grounded in theory and practical experience, is both illuminating and humbling. There is no single algorithm that solves every type of problem optimally. But there is a principled framework, a general approach to problem formulation, algorithm selection, and adaptive strategy that guides AI systems to tackle virtually any challenge effectively.<\/p>\n\n\n\n
This article explores that framework. It examines the major AI algorithmic families, the concept of meta-learning, and the No Free Lunch theorem, the theoretical result that explains why no universal algorithm exists while showing how practitioners select and combine techniques to solve problems across every domain.<\/p>\n\n\n\n
\u2022 No single algorithm solves all problems optimally; this is formally proven by the No Free Lunch theorem.<\/p>\n\n\n\n
\u2022 The closest approximations to universal solvers are search algorithms, genetic algorithms, and reinforcement learning.<\/p>\n\n\n\n
\u2022 Effective AI problem solving begins with problem formulation, converting a real challenge into a structure that an algorithm can process.<\/p>\n\n\n\n
\u2022 Meta-learning and AutoML aim to automate algorithm selection, getting closer to general-purpose AI problem solving.<\/p>\n\n\n\n
\u2022 The right algorithmic approach depends on the problem type, data availability, and computational constraints.<\/p>\n\n\n\n
\n General problem solving in AI refers to the use of systematic algorithms and reasoning strategies to solve a wide variety of problems across different domains. Instead of relying on a single universal method, AI systems formulate problems, analyze constraints, select suitable search or optimization techniques, and iteratively refine solutions based on the problem structure. This approach enables AI to handle tasks such as navigation, scheduling, planning, classification, and game-playing in a flexible and intelligent manner.\n <\/p>\n\n <\/div>\n\n<\/div>\n\n\n\n
Before exploring which algorithms come closest to universality, it is important to understand why true universality is theoretically impossible.<\/p>\n\n\n\n
The No Free Lunch (NFL) theorem, formalised by David Wolpert and William Macready in 1997, states that when averaged across all possible problems, every search and optimisation algorithm performs equally well. No algorithm has a general advantage over any other.<\/p>\n\n\n\n
This means that any algorithm that performs better than random on one class of problems must perform worse on some other class. Specialisation is the price of performance. An algorithm tuned for one type of problem will pay for that advantage elsewhere.<\/p>\n\n\n\n
The NFL theorem does not mean all algorithms are equal in real-world applications. In practice, we do not care about performance across all conceivable problems; we care about performance on the specific problems we actually face. And for any specific problem, there are algorithms that perform dramatically better than others.<\/p>\n\n\n\n
The practical implication is clear: effective AI<\/a> problem solving requires problem understanding first, algorithm selection second. The algorithm must be matched to the structure of the problem, and this matching is itself a significant intellectual task.<\/p>\n\n\n\n Before any algorithm can be applied, a problem must be translated into a form that algorithms can operate on. This process of problem formulation is arguably the most important step in AI problem solving.<\/p>\n\n\n\n A well-formulated problem defines:<\/p>\n\n\n\n \u2022 State space: <\/strong>The set of all possible configurations the problem can be in.<\/p>\n\n\n\n \u2022 Initial state: <\/strong>The starting configuration.<\/p>\n\n\n\n \u2022 Goal state(s): <\/strong>The configurations that represent a solution.<\/p>\n\n\n\n \u2022 Actions: <\/strong>The operations that can transform one state into another.<\/p>\n\n\n\n \u2022 Cost function: <\/strong>A measure of the quality or expense of a solution path.<\/p>\n\n\n\n The structure of this formulation directly determines which algorithmic families are applicable. A problem with a well-defined cost function and a discrete state space is a candidate for search algorithms<\/a>. A problem with continuous parameters and a differentiable objective is a candidate for gradient-based optimisation. A problem with unknown dynamics and sparse feedback is a candidate for reinforcement learning.<\/p>\n\n\n\n The algorithm does not choose the problem. The problem, once properly formulated, reveals which algorithms are appropriate.<\/p>\n\n\n\n \n The General Problem Solver (GPS)<\/strong>, created by Herbert Simon<\/strong> and Allen Newell<\/strong> in 1957<\/strong>, was one of the earliest attempts to design a truly general-purpose artificial intelligence system<\/strong>. GPS introduced a strategy called means-ends analysis<\/strong>, where the system continuously compared the current state with the desired goal state and selected actions that would reduce the difference between them. This idea became highly influential in later AI research, especially in automated planning, search algorithms, cognitive architectures, and problem-solving systems.\n <\/p>\n<\/div>\n\n\n\n If any algorithmic family deserves the label of general-purpose problem solver, it is search algorithms. Search is the most broadly applicable technique in AI; it applies to any problem that can be represented as a state space with defined transitions.<\/p>\n\n\n\n Uninformed search algorithms Breadth-First Search (BFS), Depth-First Search (DFS)<\/a>, and Uniform Cost Search explore the state space systematically without any domain knowledge. They are complete (they will find a solution if one exists) and some are optimal (they find the lowest-cost solution), but they are computationally expensive for large search spaces.<\/p>\n\n\n\n \u2022 BFS: <\/strong>Explores all nodes at the current depth before moving deeper. Optimal for unweighted graphs.<\/p>\n\n\n\n \u2022 DFS: <\/strong>Explores as deep as possible before backtracking. Memory-efficient but not optimal.<\/p>\n\n\n\n \u2022 Uniform Cost Search: <\/strong>Expands the lowest-cost node first. Optimal for weighted graphs.<\/p>\n\n\n\n Informed search algorithms use domain knowledge encoded in a heuristic function to guide the search toward the goal more efficiently. A* is the most important informed search algorithm, using f(n) = g(n) + h(n) to balance the known cost of the current path with an estimate of the remaining cost.<\/p>\n\n\n\n Informed search dramatically reduces the number of nodes explored compared to uninformed methods, making it practical for much larger problems, including GPS navigation, game AI, and robotic planning.<\/p>\n\n\n\n Search applies to any problem that can be represented as a graph of states and transitions. This includes:<\/p>\n\n\n\n \u2022 Pathfinding and navigation problems.<\/p>\n\n\n\n \u2022 Puzzle solving and combinatorial problems.<\/p>\n\n\n\n \u2022 Planning and scheduling problems.<\/p>\n\n\n\n \u2022 Game-playing and adversarial problems.<\/p>\n\n\n\n With the right state space representation and an appropriate heuristic, search algorithms can tackle a remarkably diverse range of AI challenges, making them the closest practical approximation to a general solver. <\/p>\n\n\n\n Many real-world problems are optimisation problems as the goal is to find the values of a set of parameters that minimise or maximise some objective function. Several algorithmic families address this class of problems. <\/p>\n\n\n\n Gradient descent and its variants, Stochastic Gradient Descent (SGD), Adam, and RMSProp, are the workhorses of modern machine learning. They navigate a continuous parameter space by following the gradient of the objective function downhill, iteratively reducing the loss.<\/p>\n\n\n\n Gradient-based methods are extremely powerful when the objective function is differentiable and the parameter space is continuous. They are the foundation of training neural networks, logistic regression, and support vector machines.<\/p>\n\n\n\n Genetic algorithms (GAs) are heuristic optimisation methods inspired by biological evolution. They maintain a population of candidate solutions, select the fittest individuals, and apply crossover and mutation operators to produce new candidate solutions over successive generations.<\/p>\n\n\n\n GAs do not require the objective function to be differentiable, making them applicable to problems where gradient information is unavailable, such as combinatorial optimisation, parameter tuning for non-differentiable systems, and problems with highly irregular, multi-modal landscapes.<\/p>\n\n\n\n Simulated annealing is a probabilistic optimisation technique that explores the solution space by accepting both improvements and worsening moves with decreasing probability. This allows it to escape local optima that trap purely greedy methods.<\/p>\n\n\n\n It is widely used for combinatorial problems such as the Travelling Salesman Problem, VLSI circuit design, and scheduling, where the solution space is discrete and gradient information does not exist.<\/p>\n\n\n\n For problems where the relationship between inputs and outputs is too complex to specify manually, machine learning offers a different approach: instead of designing the solution algorithm, you provide data and let the algorithm learn the solution from examples.<\/p>\n\n\n\n Supervised learning algorithms, such as decision trees<\/a>, random forests, neural networks<\/a>, and support vector machines, learn from labelled training data. They are the right choice when you have a defined input-output mapping and sufficient labelled examples. Applications include image classification, sentiment analysis, fraud detection, and medical diagnosis.<\/p>\n\n\n\nProblem Formulation: The First Step in AI Problem Solving<\/strong><\/h2>\n\n\n\n
Search Algorithms: The Closest to Universal Solvers<\/strong><\/h2>\n\n\n\n
Uninformed Search<\/strong><\/h3>\n\n\n\n
Informed (Heuristic) Search<\/strong><\/h3>\n\n\n\n
Why Search Is the Closest to Universal<\/strong><\/h3>\n\n\n\n
Optimisation Algorithms: Solving Problems with Continuous Objectives<\/strong><\/h2>\n\n\n\n
Gradient-Based Optimisation<\/strong><\/h3>\n\n\n\n
Genetic Algorithms and Evolutionary Computation<\/strong><\/h3>\n\n\n\n
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Simulated Annealing<\/strong><\/h3>\n\n\n\n
Machine Learning: When the Problem Defines Itself Through Data<\/strong><\/h2>\n\n\n\n
Supervised Learning<\/strong><\/h3>\n\n\n\n
Unsupervised Learning<\/strong><\/h3>\n\n\n\n