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What you will learn in Optimization Algorithms: AI techniques for design, planning, and control problems

AI techniques for design, planning, and control problems

by Alaa Khamis

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Chapter by chapter

Concepts explained in this book

• reward signalA numerical feedback signal indicating the immediate value of an agent's action in a state.
• objective functionA loss is a scalar measure of discrepancy between a model prediction and a target that an optimization procedure seeks to reduce.
• supervised learningSupervised learning is a machine-learning paradigm in which a model learns mappings from inputs to labeled target outputs.
• simulated annealingThe original form of simulated annealing that uses a temperature-controlled probability of accepting worsening moves.
• machine learningMachine learning is the computational study of methods that improve predictions or decisions by learning patterns from data or experience.
• crossoverCrossover is a genetic operator that combines genetic material from parent candidate solutions to produce offspring.
• tabu listA memory structure that records recently explored moves, neighborhoods, or solutions and temporarily prohibits their reconsideration.
• ant colony optimizationAnt colony optimization is a population-based optimization algorithm inspired by ants’ collective foraging behavior and pheromone-based path selection.
• mutationA genetic operator that randomly modifies one or more elements of a candidate solution to introduce variation into a population.
• optimizationAn algorithm that assigns values to decision variables to optimize an objective function subject to constraints.
• populationIn evolutionary computation, a population is a set of candidate solutions maintained and evolved across iterations or generations.
• policyA policy is a reinforcement-learning decision rule that maps observed states or observations to actions or action probabilities.
• fitnessA fitness value is a numerical score assigned to a candidate solution according to its quality in an evolutionary algorithm.
• actionAn action is a choice made by a reinforcement-learning agent in a given state that affects subsequent states and rewards.
• genetic algorithmA genetic algorithm is a stochastic evolutionary optimization algorithm that generates candidate solutions through selection and variation of a population.
• adjacency matrixAn adjacency matrix is a matrix whose entries indicate whether pairs of graph nodes are connected, and possibly encode connection weights.
• tabu searchTabu search is a memory-guided local search technique that restricts recently used moves or solutions to discourage cycling and escape local optima.
• Traveling Salesman problemThe traveling salesman problem is the optimization problem of finding a minimum-time tour that visits every specified city, potentially with asymmetric travel times between cities.
• cooling scheduleA prescribed progression of temperature values and cooling-rate settings during a simulated annealing process.
• embeddingA function that maps input entities or features into numerical representations used by a model.
• pheromoneA pheromone concentration is a numerical measure of trail strength assigned to an edge to influence subsequent ant transitions in an ant-colony algorithm.
• tabu tenureTabu tenure is the number of iterations for which a recently used move remains restricted by tabu memory.
• temperatureA simulated-annealing control value that influences the likelihood of accepting worsening state transitions.
• evolutionary computationEvolutionary computation is a family of computational methods inspired by biological evolution that iteratively improves candidate solutions through variation and selection.
• artificial bee colony algorithmThe artificial bee colony algorithm is a swarm intelligence optimization algorithm modeled on honeybee foraging, role differentiation, and resource communication.
• graph machine learningGraph machine learning is machine learning on graph-structured data that models relationships among entities as well as entity attributes.
• contraction hierarchiesContraction hierarchies are a shortest-path preprocessing technique that accelerates graph queries by contracting and ordering vertices.
• graph convolutional networkA graph convolutional network is a neural network that aggregates information from graph neighborhoods to compute node, edge, or graph representations and predictions.
• softmaxSoftmax is a function that converts a vector of real-valued scores into nonnegative class probabilities that sum to one.
• swarm intelligenceA swarm intelligence algorithm is a distributed search or optimization method inspired by the collective behavior of social animals or other simple agents.
• contextual banditA contextual multi-armed bandit is a bandit model in which an agent observes contextual information before choosing an action and receiving action-specific feedback.
• advantage functionAn advantage is the estimated improvement in expected future reward from taking an action in a state compared with the average action in that state.
• admissible heuristicAn admissible heuristic estimates remaining cost without exceeding the true minimum remaining cost.
• samplingA sampling method that generates candidate points using random draws from a specified space or distribution.
• genetic operationA genetic operator is a variation operation that modifies or combines candidate individuals to generate evolutionary alternatives.
• particle swarm optimizationParticle swarm optimization is a population-based optimization algorithm in which candidate particles adjust their movement using individual and collective experience.
• reinforcement learningReinforcement learning is a machine-learning paradigm in which an agent learns action policies from interactions and evaluative feedback.
• selectionA genetic-algorithm procedure that chooses individuals from a population to serve as parents for reproduction.
• heuristicA problem-solving rule or approximation that guides search toward promising solutions without guaranteeing feasibility or optimality.
• Markov decision processA Markov decision process is a model of sequential decision-making defined by states, actions, transition probabilities, and rewards with future dynamics dependent only on the current state and action.
• message passingMessage passing is a graph-learning technique in which nodes exchange and aggregate information with neighboring nodes to update representations.
• Proximal Policy OptimizationProximal policy optimization is a policy-gradient reinforcement-learning algorithm that limits policy updates to maintain stable improvement.
• global-best PSOGlobal-best PSO is a particle swarm optimization variant in which every particle can access the best solution found by the entire swarm.
• PySwarmsPySwarms is an open-source Python library that implements particle swarm optimization variants and topologies.
• edge differenceEdge difference is a node-importance metric equal to the change in the number of edges, including shortcut edges, caused by contracting a node.
• node contractionGraph contraction is the transformation of a graph that removes selected nodes and adds shortcut edges to preserve relevant path properties.
• binary-coded genetic algorithmA binary-coded genetic algorithm is a genetic algorithm whose candidate solutions use binary encoding.
• pymooA Python framework for multi-objective optimization that provides evolutionary algorithms, metaheuristics, visualization tools, and decision-making capabilities.
• search spaceA search space is the set of candidate states or solutions that an optimization or search procedure may consider.
• aspiration criterionAn aspiration criterion is a rule that permits a tabu move when it meets a specified exception condition, such as producing an especially good solution.
• exploitationA search strategy that concentrates effort in a region where good solutions have already been found.
• data explorationA search strategy that investigates new or insufficiently tested actions to gather information about their potential value.
• transition probabilityThe probability of moving from a current state to a specified next state.
• binary particle swarm optimizationBinary particle swarm optimization is a particle swarm variant whose particle positions represent binary decisions rather than continuous parameter values.
• brute-force searchA graph-search strategy that explores states without using problem-specific information to prioritize promising alternatives.
• value functionA function that estimates the expected cumulative future reward from a state when subsequent actions follow a specified policy.
• constraintA condition in an optimization problem that restricts the values or combinations allowed for decision variables.
• velocityA sequence of swaps that specifies how a particle's permutation is transformed in permutation-based particle swarm optimization.
• feedforward networkA feedforward neural network is a neural network in which information flows from inputs through successive layers to outputs without recurrent connections.
• chromosomeA chromosome is an encoded candidate solution in a genetic algorithm, with elements representing decision values or solution components.
• roulette-wheel selectionA fitness-proportionate selection method that gives higher-selection-probability individuals with better fitness values.
• discount factorA discount factor is a scalar between zero and one that determines how strongly future rewards contribute to an action value.
• trajectory-based searchAn optimization algorithm that generates a sequence of successive candidate states or solutions during its search.
• preprocessingA preprocessing phase is an initial computation that transforms or augments data before subsequent queries or operations.
• augmented graphA graph containing the original vertices and edges together with added shortcut edges created during hierarchical preprocessing.
• shortcut edgeAn added graph edge representing a path through contracted nodes while preserving the path's total cost.
• population-based searchA metaheuristic optimization strategy that maintains multiple agents or candidate solutions while searching for a global solution.
• combinatorial optimizationA combinatorial optimization problem is an optimization problem whose solutions are discrete combinations, sets, or permutations of elements.
• environmentAn environment is the external set of conditions that interacts with an organism’s genotype to influence its characteristics.
• offspringOffspring are candidate individuals generated by applying evolutionary variation operators to parent individuals.
• multi-armed banditA multi-armed bandit is a sequential decision model in which an agent repeatedly chooses among uncertain actions to maximize cumulative reward without changing the underlying state.
• graph hierarchical searchA search algorithm that organizes states or graph elements into levels and uses that hierarchy to reduce the amount of search required.
• highway hierarchiesA hierarchical shortest-path technique that accelerates routing by identifying and using higher-level highway edges.
• node importanceA dynamic priority estimate indicating how attractive it is to contract a graph node next.
• query phaseThe online phase of an algorithm that answers a specific search or shortest-path query using preprocessed structures.
• witness pathA path that is no more expensive than the path through a candidate contracted node and therefore proves that a shortcut is unnecessary.
• fitness-proportionate selectionFitness-proportionate selection is a survivor-selection method that determines retention or replacement of individuals according to their fitness values.
• onlooker beeAn onlooker bee is an artificial-bee-colony agent that probabilistically selects food sources according to the quality of their solutions.
• scout beeA scout bee is an artificial-bee-colony agent that explores for new food sources or candidate solutions independently of existing assignments.
• returnThe total reward accumulated by an agent over a sequence of decisions, often considered in expectation.
• Pointer NetworkA pointer network is a sequence-to-sequence neural architecture that outputs positions or elements from its input sequence through attention-based pointers.
• unsupervised learningUnsupervised learning is a machine-learning paradigm in which a model discovers structure or patterns in data without labeled target outputs.
• encoderAn encoder is a neural-network component that transforms each element of an input sequence into a context-dependent hidden representation.
• decodeA decoder is a neural-network component that generates an output sequence from prior outputs, hidden states, and encoded input information.
• SymPyAn open-source Python library for symbolic mathematics, including algebra, calculus, equation solving, and combinatorics.
• epsilon-greedyAn action-selection strategy that chooses a random action with a specified probability and otherwise selects the currently best-known action.
• upper confidence boundUpper confidence bound is an action-selection strategy that combines estimated reward with an uncertainty bonus to balance exploitation and exploration.
• Stable-Baselines3Stable-Baselines3 is a Python library providing implementations of reinforcement-learning algorithms based on PyTorch.
• adaptive memoryFrequency-based memory records how often moves or attributes occur so their historical frequency can influence search decisions.
• greedy algorithmGreedy decoding constructs an output sequence by selecting the locally highest-scoring available choice at each decoding step.
• acceptance probabilityThe probability that a stochastic optimization algorithm accepts a proposed state transition, including a worsening move.
• locally optimal solutionA solution that is optimal relative to a neighborhood but may not be optimal over the entire feasible search space.
• discrete problemA problem with a finite or countable set of distinct configurations, decisions, or values rather than continuously varying ones.
• political districtingA problem of grouping smaller geographic or administrative units into electoral districts subject to planning criteria and constraints.
• graphA graph is a nonlinear data structure consisting of vertices and edges that represent entities and relationships.
• permutationA permutation is an ordered arrangement of elements in which each element appears exactly once.
• attentionAn attention mechanism computes weights over representations so a model can focus on selected input information when producing an output.
• convolutional layerA transformation that applies shared learned weights to neighboring feature representations.
• inductive embeddingInductive embedding is a graph embedding technique that learns a general representation-generating function applicable to unseen entities or graphs.
• k-hop neighborhoodA k-hop neighborhood is the set of graph nodes whose shortest-path distance from a specified node is at most k.
• permutation invariancePermutation invariance is the property that a function produces the same output regardless of the ordering of its inputs.
• latent spaceA latent space is a lower-dimensional representation space whose vectors encode information about observed data or structures.
• transductive learningTransductive embedding is a graph embedding technique that learns representations only for entities observed during training.
• activation functionAn activation function is a function applied to a neural-network unit’s pre-activation value to produce its output and introduce nonlinear behavior.
• backpropagationBackpropagation is an algorithm that computes derivatives of a neural-network loss with respect to its parameters by propagating error information backward through the network.
• forward passForward propagation is the computation that passes inputs through successive neural-network layers to produce an output.
• logitA logit is an unnormalized output score produced by a model before conversion into class probabilities.
• negative log-likelihoodNegative log likelihood is a loss equal to the negative logarithm of the probability assigned to the true label.
• tanhThe hyperbolic tangent is an activation function that maps real-valued inputs to the interval from -1 to 1.
• neuronAn artificial neuron is a computational unit that combines weighted inputs and a bias before applying an activation function to produce an output.
• local searchA local search algorithm iteratively moves from a feasible solution to a neighboring solution according to an improvement rule.
• informed searchA graph-search strategy that uses problem-specific heuristic information to prioritize promising states or paths.
• action spaceAn action space is the set of actions available to an agent in an environment.
• trajectoryA sequence of states and actions generated during an agent's interaction with an environment.
• decision variableA decision variable is a variable whose value is chosen to optimize an objective function subject to constraints.
• best positionThe best position an individual particle has achieved so far according to the optimization objective or fitness value.
• hillclimbingA local search algorithm that repeatedly moves from a candidate solution to an improving neighboring solution.
• A2CAdvantage actor-critic is a synchronous, model-free reinforcement-learning algorithm that jointly learns a policy and a value function using estimated action advantages.
• breadth-first searchBreadth-first search explores all reachable states at one depth before exploring states at greater depth.
• real-valued genetic algorithmA genetic algorithm that represents candidate solutions with real-valued chromosomes rather than binary or Gray-coded strings.
• continuous optimizationAn optimization problem whose decision variables or feasible solutions range over continuous domains.
• policy gradient methodA policy gradient is a reinforcement-learning method that optimizes a policy by estimating gradients of expected return with respect to policy parameters.
• mixed-integer optimization problemAn optimization problem containing both continuous-valued and integer-valued decision variables.
• multivariate optimization problemAn optimization problem with multiple decision variables.
• univariateAn optimization problem with exactly one decision variable.
• payoff distributionA payoff distribution is a probability distribution describing the rewards produced by a particular bandit action.
• regretRegret is the cumulative difference between the reward obtainable by always choosing the best action and the reward actually obtained.
• minimum spanning treeAn algorithm that finds a minimum-weight tree connecting every node of a connected weighted graph.
• Dijkstra's algorithmA graph algorithm that computes shortest paths from a source node when all edge weights are nonnegative.
• convex hullThe convex hull problem is the computational problem of finding the smallest convex boundary containing a given set of points.
• backtrackingA search technique that returns to an earlier decision point after reaching a dead end and tries another alternative.
• control problemA problem of repeatedly determining actions or inputs to regulate the behavior of a dynamic system.
• design problemA problem of selecting or configuring a system or artifact to achieve a desired quality objective.
• operational functionA control-oriented decision function that requires repeated solutions with very low latency.
• planning problemA problem of selecting and organizing actions or decisions over time to achieve specified goals.
• strategic functionA design-oriented decision function in which solution quality is prioritized over rapid response.
• tactical functionA planning-oriented decision function that must produce solutions within a short operational time span.
• global bestThe best candidate solution found by the search process up to the current point.
• pheromone updatePheromone reinforcement increases simulated pheromone levels on solution components selected by high-quality ant solutions.
• 8-puzzleA sliding-tile puzzle consisting of eight numbered tiles and one blank position on a three-by-three grid.
• determinismA deterministic model is a model in which each action and current state uniquely determine the resulting state or outcome.
• Christofides algorithmA polynomial-time approximation algorithm for the metric traveling salesman problem with a worst-case tour-length guarantee.
• clusteringThe task of partitioning objects into groups whose members are more similar to one another than to members of other groups.
• decision problemA computational problem whose answer is whether an input satisfies a specified property, typically expressed as yes or no.
• npThe complexity class of decision problems whose proposed solutions can be verified in polynomial time.
• np-complete problemThe class of decision problems that are in NP and are at least as hard as every problem in NP.
• NP-hard problemThe class of problems at least as hard as the hardest problems in NP, whether or not they are decision problems in NP.
• pThe complexity class of decision problems solvable in polynomial time by deterministic algorithms.
• polynomial timeA computational-time bound that grows no faster than a polynomial function of input size.
• particleA candidate agent in particle swarm optimization whose position and velocity define its location and movement through the search space.
• non-Euclidean dataNon-Euclidean data has relational or geometric structure for which ordinary straight-line distance is not the defining notion of proximity.
• A-star algorithmAn informed graph search algorithm that ranks states using path cost plus a heuristic estimate of remaining cost.
• self-organizing mapA self-organizing map is an unsupervised neural model that maps high-dimensional data onto a usually low-dimensional topology-preserving grid of units.
• local neighborhoodThe set of candidate solutions reachable from a current solution by permitted local moves.
• parameterA fixed input value that specifies an optimization problem without being selected as a decision variable.
• metaheuristicA high-level optimization strategy that guides or coordinates heuristic search to explore promising solutions without guaranteeing optimality.
• recency-based memoryA tabu-search memory that records recently visited moves or search attributes and temporarily restricts their reuse.
• geometric cooling scheduleA cooling schedule that multiplies the temperature by a fixed factor at successive cooling steps.
• Problem classThe pymoo base class for defining an optimization problem's variables, objectives, constraints, bounds, and evaluation behavior.
• geometric deep learningGeometric deep learning is a family of deep-learning methods designed to operate on data with geometric or relational structure.
• Kruskal's algorithmA minimum-spanning-tree algorithm that processes edges in increasing weight order and adds edges that extend the growing forest without creating a cycle.
• employed beeAn employed bee is an artificial-bee-colony agent that searches the neighborhood of an associated food source for improved solutions.
• weighted graphA graph whose edges have numerical weights representing quantities such as distance or cost.
• velocity clampingVelocity clamping is a particle-swarm constraint that limits each particle’s velocity to a specified minimum and maximum.
• contextContext is observed information describing the current situation that conditions the expected reward of an action.
• gaussian mutationGaussian mutation perturbs candidate-solution variables using random values governed by a Gaussian distribution.
• stochastic algorithmA search method or algorithm that uses random choices or probabilistic transitions to explore candidate states.
• constraint-satisfaction problemA constraint-satisfaction problem is a problem formulation whose goal is to find an assignment satisfying a specified set of constraints without requiring an explicit objective function.
• assembly line balancing problemAn assembly line balancing problem assigns production tasks to workstations while satisfying constraints and optimizing measures such as station count, cycle time, or idle time.
• cycle timeCycle time is the time allocated for a workstation to complete its assigned tasks and pass the product onward.
• pairwise exchangeA pairwise exchange is a neighborhood move that swaps the positions or assignments of two tasks.
• precedence constraintA precedence constraint requires one task or operation to occur before another dependent task or operation.
• precedence graphA precedence graph is a directed representation of task dependencies that specifies which tasks must be completed before others can begin.
• simple assembly line balancing problemA simple assembly line balancing problem concerns producing one product on a serial line with one-sided workstations.
• smoothing indexA smoothing index is a quantitative measure of how uniformly workload is distributed among workstations.
• time and space assembly line balancing problemA time and space assembly line balancing problem assigns tasks to stations subject to precedence, workload-time, and station-space constraints.
• ride-sharing problemA transportation assignment problem that matches passengers and drivers and orders passenger trips across a vehicle fleet under multiple objectives and constraints.
• edgeAn edge is a graph connection between two vertices, optionally representing a directed or weighted relationship.
• nodeA vertex is a node in a graph that can be connected to other vertices by edges.
• actor networkAn actor network is a neural network that represents a reinforcement-learning policy and produces action choices or action probabilities.
• CartPoleCartPole is a control-task environment in which an agent moves a cart left or right to keep a pole upright.
• OpenAI GymOpenAI Gym is a software toolkit that provides standardized environments and interfaces for developing and evaluating reinforcement-learning agents.
• PyTorchPyTorch is an open-source machine-learning library that provides tensor computation and automatic differentiation for building and training neural networks.
• depth-first searchDepth-first search explores a path as deeply as possible before backtracking to an alternative path.
• graph search methodA graph search algorithm explores nodes and edges of a graph to find reachable states, paths, or solutions.
• queueA first-in, first-out data structure in which the earliest inserted element is removed first.
• MEALPYMEALPY is a Python library that provides implementations of nature-inspired metaheuristic optimization algorithms.
• Rosenbrock functionThe Rosenbrock function is a nonconvex test function with a narrow valley leading to its global minimum, commonly used to evaluate optimization algorithms.
• Euclidean distanceEuclidean distance is the straight-line distance between points calculated from the square root of the sum of squared coordinate differences.
• gradient estimatorA gradient estimator is a computed approximation of a gradient based on finite samples or other available information.
• partially observed processA partially observable Markov decision process is a sequential decision model in which the agent receives only partial observations of the underlying state.
• policy iterationPolicy iteration is an iterative method that alternates between evaluating a policy and improving it until convergence.
• action-value functionAn action-value function estimates the expected cumulative future reward from taking a specified action in a state and then following a policy.
• stochastic gradient ascentStochastic gradient ascent is an iterative optimization method that increases an objective using gradient estimates computed from sampled data.
• stochastic policyA stochastic policy assigns probabilities to selecting available actions given a state or observation.
• value iterationValue iteration is an iterative reinforcement-learning or dynamic-programming method that updates state values toward optimal expected returns.
• antAn ant is a simulated search agent that incrementally constructs a candidate path in an ant-colony algorithm.
• control signalA control signal is a controller-generated input that drives an actuator or process to influence system behavior.
• control systemA control system is a set of rules and mechanisms that guides a device or process toward specified goals.
• derivative gainA derivative gain is a PID parameter that scales the response to the rate of change of error.
• derivative termA derivative term is a controller component whose output is proportional to the rate of change of error.
• error signalAn error signal is the difference between a desired system state and the corresponding measured or feedback state.
• IAEIAE is an integral performance metric equal to the accumulated absolute control error over time.
• integral gainAn integral gain is a PID parameter that scales the response to accumulated error over time.
• integral termAn integral term is a controller component whose output reflects the accumulated magnitude of error over time.
• ISEISE is an integral performance metric equal to the accumulated squared control error over time.
• ITAEITAE is an integral performance metric that weights absolute control error by elapsed time.
• continuous improvementA closed-loop system is a control system that measures its output and uses feedback to adjust its input toward a desired value.
• ITSEITSE is an integral performance metric that weights squared control error by elapsed time.
• peak overshootPeak overshoot is the deviation of a response at its peak from its final value.
• PID controllerA PID controller is a feedback control algorithm that combines proportional, integral, and derivative responses to reduce error between a measured and desired state.
• pid tuning problemA PID tuning problem is the optimization problem of selecting PID controller parameter values to obtain a desired control response.
• proportional gainA proportional gain is a PID parameter that scales the controller response to the current error.
• proportional termA proportional term is a controller component whose output is proportional to the current error.
• rise timeRise time is the time required for a response to increase from 10% to 90% of its final value.
• settling timeSettling time is the time required for a response to reach steady state and remain within specified tolerance bands.
• steady-state errorSteady-state error is the difference between a desired output and the actual output after the system reaches a stable condition.
• step responseA step response is the time-varying output of a system when its input changes abruptly between constant levels.
• transfer functionA transfer function is a mathematical representation of the input-output relationship of a system in a transform domain.
• cyclingCycling is repetitive search behavior in which an algorithm repeatedly performs the same moves or revisits the same solutions.
• stopping criterionA condition that determines when an iterative algorithm should stop.
• multiple edgeA parallel edge is one of multiple edges connecting the same pair of vertices in a multigraph.
• elitismElitist selection is a survivor-selection method that retains the best individuals from the existing population and newly generated offspring.
• genotypeA genotype is the complete genetic constitution of an organism, including its combination of alleles.
• linear programmingAn optimization problem with a linear objective function and linear constraints.
• nonlinear programmingAn optimization problem with a nonlinear objective function or at least one nonlinear constraint.
• encoder-decoder architectureA neural model that transforms an input sequence into an output sequence, typically allowing the two sequences to have different lengths.
• acyclic graphAn acyclic graph is a graph that contains no cycles.
• cycleA cycle is a closed path in a graph that begins and ends at the same vertex.
• hyperedgeA hyperedge is a generalized graph edge that can join an arbitrary number of vertices.
• hypergraphA hypergraph is a generalization of a graph whose hyperedges can connect any number of vertices.
• multigraphA multigraph is a graph that can contain multiple parallel edges between the same pair of vertices.
• OpenStreetMapOpenStreetMap is a crowdsourced geographic database containing worldwide map and location data.
• OSMnxOSMnx is a Python library for retrieving, modeling, and manipulating street-network data from OpenStreetMap.
• treeA connected acyclic data structure consisting of nodes linked by hierarchical edges.
• branching factorThe number of successor states available from a node, commonly represented by the maximum or average number of children.
• ACOpyACOpy is a Python library that provides an implementation of ant colony optimization.
• open traveling salesman problemAn open traveling salesman problem seeks a minimum-cost route visiting each specified location without requiring the route to return to its starting location.
• symmetric traveling salesman problemA traveling salesman problem in which cities are points in a Euclidean plane and travel costs are symmetric distances.
• OR-ToolsGoogle OR-Tools is an open-source software suite providing optimization and constraint-programming solvers.
• bin packing problemA combinatorial problem of assigning objects with sizes to the fewest fixed-capacity bins without exceeding bin capacity.
• first-fit decreasing heuristicA bin-packing heuristic that sorts objects by decreasing size before placing each object into the first available bin.
• first-fit heuristicA bin-packing heuristic that places objects in their given order into the first available bin without ordering them by size.
• repeated solution constructionA search strategy that generates candidate solutions incrementally by repeatedly adding elements to a partial solution.
• repeated solution modificationA search strategy that improves an existing feasible solution by changing its selected elements.
• repeated solution recombinationA search strategy that combines parts of existing solutions to construct new candidate solutions.
• similarity searchA systematic examination of possible states that begins at an initial state and seeks to reach a goal state.
• real-value encodingReal-value encoding represents solution parameters directly as real-valued genes.
• positionA particle's current point in the search space representing its candidate solution.
• premature convergenceThe loss of population variation caused by convergence to a suboptimal region before better solutions are found.
• depth-limited searchA depth-first search variant that stops expanding a branch after a specified maximum depth.
• uniform-cost searchA blind graph-search algorithm that expands the node with the lowest cumulative path cost, or highest utility for maximization problems.
• graph neural networkA graph neural network is a neural network architecture that learns representations and predictions from graph-structured data.
• pretrained modelA pretrained model is a machine-learning model whose parameters were learned previously on a dataset or task before subsequent use.
• signalA node feature is a value or vector associated with a graph node that describes its attributes for computation or learning.
• Latin squareA Latin square is an n × n array containing n symbols such that every symbol occurs exactly once in each row and column.
• stigmergic communicationA form of indirect coordination among social organisms mediated by modifications to the environment.
• Sudoku puzzleA constraint puzzle in which digits must be assigned to cells of a grid so that each required row, column, and subgrid contains each digit according to the puzzle rules.
• tournament selectionTournament selection is a survivor-selection method that randomly groups individuals and retains the best individual from each group.
• hard constraintA hard constraint is a constraint that every acceptable solution must satisfy.
• soft constraintA soft constraint is a desirable constraint whose violation is permitted but whose satisfaction affects solution quality.
• multi-agent reinforcement learningMulti-agent reinforcement learning is reinforcement learning in which multiple agents learn or execute policies while interacting within a shared environment.
• exploit-only greedy strategyAn exploit-only greedy strategy repeatedly selects the action with the highest estimated mean reward after initial action trials.
• explore-only strategyAn explore-only strategy selects actions solely to investigate uncertain alternatives rather than favoring currently estimated rewards.
• ill-structured problemA problem whose scope, state, or environment is dynamic, uncertain, partially observable, or otherwise difficult to specify completely for efficient solution.
• clipped surrogate objectiveA clipped objective function restricts the contribution of an optimization objective to a bounded range of values.
• adaptive tuningAn adaptive approach changes algorithm parameters using feedback from the observed search process or performance.
• local-best PSOLocal-best PSO is a particle swarm optimization variant in which each particle follows the best solution found within its local neighborhood.
• Michalewicz functionThe Michalewicz function is a nonconvex benchmark function with multiple local minima used to test optimization algorithms.
• neighborhood topologyA neighborhood topology is a communication structure that determines which particles in a particle swarm can share information.
• animal feed mix problemThe animal feed mix problem determines ingredient proportions that satisfy nutritional constraints while minimizing feed cost.
• linear constraintA linear constraint restricts decision variables through a linear equality or inequality.
• linear objective functionA linear objective function is an objective function that is a weighted sum of decision variables plus an optional constant.
• PuLPPuLP is an open-source Python library for modeling and solving linear and mixed-integer linear programming problems through solver interfaces.
• quadratic assignment problemA quadratic assignment problem assigns facilities to locations while minimizing interaction flow weighted by assigned-location distances.
• quadratic programQuadratic programming is optimization with a quadratic objective function and typically linear constraints.
• cooling rateA cooling rate is a parameter controlling how quickly the temperature decreases in an annealing schedule.
• n-queens problemThe n-queens problem is the puzzle of placing n queens on an n-by-n chessboard so that no two queens share a row, column, or diagonal.
• AI agentAn agent is an autonomous computational entity that senses information, interacts with other entities or its environment, and adapts its behavior.
• neighborhood bestThe best position among a restricted neighborhood containing only a few particles.
• global searchA search strategy that explores broadly across the search space to seek a global optimum rather than concentrating only near one current solution.
• muddy city problemThe muddy city problem is a graph-connectivity problem that selects roads or edges to connect all locations while minimizing total edge weight.
• spanning treeA spanning tree is a cycle-free subgraph of an undirected graph that contains every vertex and connects them with the minimum number of edges.
• single-objective optimization problemAn optimization problem with one objective function whose value is optimized.
• Box-Muller transformA transformation that converts pairs of independent uniform random variables into pairs of independent standard normal random variables.
• central limit theorem samplingA sampling method that approximates a normal distribution by generating means of sufficiently large samples.
• Latin hypercube samplingA stratified sampling method that partitions each dimension into equal-probability intervals and samples combinations so each interval is represented.
• pseudo-random number generatorA deterministically generated number sequence that exhibits statistical properties resembling randomness.
• quasi-random numberA deterministically generated sample sequence designed to distribute points evenly across a space rather than mimic probabilistic randomness.
• Sobol sequenceA quasi-random low-discrepancy sequence designed to distribute points evenly throughout a multidimensional sample space.
• genetic diversityThe degree of variation among individuals in an evolutionary algorithm population.
• rank selectionA selection strategy that assigns probabilities according to individuals' relative fitness ranks rather than their absolute fitness values.
• selective pressureThe relative likelihood that the fittest individual is selected compared with the average likelihood of selection across the population.
• stochastic universal samplingA selection strategy that uses one random roulette-wheel spin with evenly spaced pointers to select multiple individuals.
• constraint functionA constraint function is a function that expresses a feasibility restriction on the values of decision variables in an optimization problem.
• explicit memoryExplicit memory is a search mechanism that records previously visited moves or solutions.
• beam searchAn informed search technique that retains only a limited number of the most promising partial solutions at each step.
• population sizePopulation size is the number of candidate solutions maintained in a population-based optimization algorithm.
• swap mutationA swapping operator generates a neighboring permutation by exchanging the positions or values of two elements.
• cognitive componentA particle swarm optimization parameter that weights a particle's attraction toward its own best-known position.
• global optimumA feasible point whose objective-function value is at least as high as that of every candidate in the domain.
• social componentA particle swarm optimization parameter that weights a particle's attraction toward the swarm's or neighborhood's best-known position.
• boundary mutationA mutation method that replaces a real-valued gene with a random value uniformly sampled between its lower and upper bounds.
• cauchy mutationA mutation method that adds a random value sampled from a Cauchy distribution to a real-valued gene.
• curve fittingThe process of selecting function parameters so a curve represents observed data or target relationships.
• distribution indexA parameter controlling the spread of the probability distribution used by polynomial mutation.
• mean squared errorA metric equal to the average of the squared differences between predicted and observed values.
• polynomial mutationA mutation method that samples offspring around a real-valued parent using a polynomially shaped probability distribution.
• forager beeA forager bee is a worker honeybee that searches for and collects resources such as nectar or pollen.
• gradient descentAn iterative optimization algorithm that changes variables in the direction of the negative gradient to reduce a differentiable objective function.
• end-to-end learningA learning approach that trains a model to map inputs directly to desired outputs with minimal separately engineered intermediate stages.
• neural combinatorial optimizationA research area focused on applying machine-learning models and algorithms to combinatorial optimization problems.
• feasible solutionA feasible solution is a candidate solution that satisfies all specified constraints.
• amortized optimizationA technique that learns to predict solutions to repeated optimization problems so computation is shifted from repeated solving to training and inference.
• c-convex functionA c-convex function is a synthetic optimization function defined on a sphere whose parameterized components can be sampled for training.
• amortized modelAn amortized model is a learned predictive model that maps problem parameters to approximate optimization solutions.
• riemannian distanceRiemannian distance is the shortest distance between points on a curved space measured along that space rather than through its surrounding space.
• equality constraintAn equality constraint is a constraint requiring an expression involving decision variables to equal a specified value.
• nondominated solutionA feasible multi-objective solution for which no other feasible solution is at least as good in every objective and strictly better in one.
• Pareto optimizationA multi-objective optimization technique that seeks multiple nondominated trade-off solutions rather than one scalar objective optimum.
• content-based attention mechanismA content-based attention mechanism assigns weights to input elements according to their relevance to a query or internal representation.
• convex hull overlapConvex hull overlap is a measure of the agreement between a predicted convex hull and a reference convex hull.
• ConvexNetConvexNet is the pointer-network model instance described for predicting convex hull point sequences.
• biology-inspired algorithmA nature-inspired algorithm is a computational method that mimics or reverse engineers intelligent behaviors observed in natural systems.
• single-source shortest pathThe problem of finding minimum-cost paths from one source node to every other reachable node in a weighted graph.
• geneA gene is a segment of genetic material that encodes a specific biological property or functional product.
• sequential machine learningSequential machine learning is machine learning on data whose observations have an order that affects interpretation or prediction.
• offline optimizationOptimization performed before operation without requiring decisions to be produced in real time.
• online optimizationOptimization performed during operation to produce decisions within the available execution time.
• competitive learningCompetitive learning is a neural learning technique in which processing units compete to respond to input patterns and update selected units.
• gray codeA binary numeral system in which adjacent numerical values have representations differing in exactly one bit.
• hamming cliffA representation discontinuity in which a small encoded change, such as flipping one bit, causes a large change in the decoded solution value or fitness.
• adaptive simulated annealingAdaptive simulated annealing is a simulated-annealing variant that adjusts search parameters or operators according to problem or search conditions.
• position vectorA permutation encoding the candidate solution represented by a particle in permutation-based particle swarm optimization.
• online step-by-step pheromone updateAn online step-by-step pheromone update deposits pheromone during the incremental construction of a candidate solution.
• pheromone evaporationPheromone evaporation is the reduction of simulated pheromone concentration over time to weaken older search information.
• hyperparameter tuningParameter tuning is the process of selecting suitable values for an algorithm's configurable parameters before or during execution.
• haversine formulaA trigonometric formula that computes spherical distance between two points from their latitude and longitude differences.
• bidirectional searchA search technique that simultaneously explores from an initial state toward a goal and from the goal toward the initial state until the search frontiers meet.
• minimum energy stateAn annealing state in which neither improving nor worsening moves are accepted.
• binary stringA bit string is an ordered sequence whose elements are binary digits.
• cycle crossoverA permutation crossover operator that partitions aligned parent elements into cycles and combines those cycles to form feasible offspring.
• edge crossoverA permutation crossover operator that constructs offspring by preserving adjacency and connectivity information from parent permutations.
• order crossoverA permutation crossover operator that preserves the relative order of elements from a parent while combining genetic material from two parents.
• partially mapped crossoverA permutation crossover operator that combines parent segments while mapping displaced elements to preserve feasible offspring permutations.
• food sourceA food source is a location containing collectable resources such as nectar or pollen for a honeybee colony.
• honeybee foraging behaviorHoneybee foraging behavior is the collective process by which bees search for, evaluate, collect, and communicate information about food resources.
• waggle danceA waggle dance is a honeybee communication behavior that conveys the direction and distance of a resource or location to other bees.
• worker beeA worker bee is a female honeybee that performs nonreproductive colony tasks such as foraging, construction, storage, and defense.
• well-structured problemA problem whose states, attainable changes, solution tests, relevant knowledge, and external-world constraints can be represented and computed with effectively available information.
• traversalA graph-search technique that explores a tree or graph by visiting nodes according to a specified rule.
• deceptive functionAn objective-function landscape whose local structure can mislead search away from the global optimum.
• multimodal problemAn objective-function landscape containing multiple local optima.
• unimodal problemAn objective-function landscape with a single dominant optimum or basin of attraction.
• survival methodA survival method determines which individuals remain in the population for the next generation.
• action-dependent featureA feature representation whose values are associated with particular actions in a contextual decision problem.
• Vowpal WabbitVowpal Wabbit is an open-source machine-learning system supporting scalable online learning and contextual bandit algorithms.
• model-free methodModel-free reinforcement learning is reinforcement learning in which an agent learns policies or value functions directly from experience without explicitly constructing an environment dynamics model.
• bacterial chemotaxisBacterial chemotaxis is the movement of bacterial cells through chemical concentration gradients toward attractants or away from repellents.
• collective actionCollective behavior is coordinated activity produced by interactions among members of a group.
• simple ant colony optimizationSimple ant colony optimization is a basic ant-colony metaheuristic that constructs candidate solutions using simulated pheromone trails.
• unconstrained optimization problemAn optimization problem with no explicit constraints restricting its decision variables.
• permutation-based genetic algorithmA genetic algorithm that represents candidate solutions as permutations of discrete elements.
• whole arithmetic crossoverA crossover method that creates offspring by taking weighted arithmetic combinations of corresponding parent values.
• Kullback–Leibler divergenceKullback–Leibler divergence is a metric quantifying the dissimilarity between two probability distributions.
• importance weightA probability ratio is the quotient of an action probability under an updated policy and its probability under an old policy.
• PPO-clipPPO-clip is a proximal policy optimization variant that clips the policy probability ratio in a surrogate objective to limit update magnitude.
• PPO-penaltyPPO-penalty is a proximal policy optimization variant that penalizes divergence between updated and old policies in its objective.
• population equilibriumA condition in which populations are distributed fairly and comparably across geographic districts.
• pheromone depositPheromone deposit is the addition of simulated pheromone to paths or edges traversed by artificial ants.
• base stationA base station is a fixed wireless-network node that communicates with and provides services to mobile user equipment.
• cell selectionCell selection is the process of choosing the cellular base station or cell with which a mobile user connects.
• channel qualityChannel quality is the condition of a wireless communication channel as determined by signal propagation and interference characteristics.
• data transfer rateData rate is the amount of data transmitted over a communication connection per unit of time.
• mobile-envmobile-env is an open platform for modeling and simulating wireless mobile networks for reinforcement-learning research.
• mobile networkA wireless communication system connecting mobile users through cellular base stations.
• quality of experienceQuality of experience is a measure of a user's perceived quality or satisfaction with a networked service.
• Ray RLlibRay RLlib is an open-source reinforcement-learning library for scalable and distributed training with unified APIs.
• user equipmentUser equipment is a mobile device or endpoint that communicates over a wireless network.
• inertia componentThe inertia component is a particle swarm optimization parameter that weights a particle's previous velocity when updating its movement.
• multi-dimensional optimization problemMulti-objective optimization is an optimization formulation involving multiple objective functions that may need to be balanced or traded off.
• deep learning-assisted heuristic tree searchA heuristic tree-search method in which deep neural networks decide which branches to explore and how to bound nodes.
• learning to configure algorithmsA machine-learning approach that selects or tunes parameters of an optimization algorithm.
• machine-learning-assisted optimizationAn optimization approach in which an algorithm repeatedly consults a learned model to make decisions during its search.
• prompt engineeringAn optimization approach that describes an optimization task in natural language and prompts a large language model to generate improved solutions or instructions.
• permutation problemA problem whose candidate solutions are ordered arrangements of a specified set of elements.
• differential evolutionDifferential evolution is a population-based optimization algorithm that creates trial solutions by combining vector differences among candidate solutions.
• gray-coded genetic algorithmA genetic algorithm that represents candidate solutions with Gray-coded strings so adjacent numeric values differ in a single bit.
• attention coefficientA numerical factor that quantifies the importance assigned to one node or input element relative to another.
• multi-head attentionMulti-head self-attention computes several attention operations in parallel so a sequence representation can capture different relationships among its elements.
• transformer architectureA transformer architecture is a neural-network architecture that processes sequences primarily through attention mechanisms rather than recurrence.
• Markov propertyThe property of a stochastic process whereby the distribution of the next state depends only on the current state and not on earlier states.
• Markov chainA stochastic model representing a sequence of states in which each transition probability depends only on the current state.
• quantum annealingQuantum annealing is an optimization method that uses quantum-mechanical fluctuations to seek low-energy solutions.
• quantum tunnelingA quantum phenomenon in which a particle or wave function penetrates a potential barrier despite having less energy than the barrier height.
• stackA last-in, first-out data structure in which elements are added to and removed from the same end.

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