There are several different ways to solve problems in programming. In constraint programming, a problem is viewed as a series of limitations on what could possibly be a valid solution. This paradigm can be applied to effectively solve a group of problems that can be translated to variables and constraints or represented as a mathematical equation. Instead of defining a set of instructions with only one obvious way to compute values, constraint programming declares relationships between variables within constraints. A final model makes it possible to compute the values of variables regardless of direction or changes.
What is Constraint programming?
Constraint programming (CP) is a paradigm for solving combinatorial problems that draws on a wide range of techniques from artificial intelligence, computer science, and operations research. In constraint programming, users declaratively state the constraints on the feasible solutions for a set of decision variables. Constraints differ from the common primitives of imperative programming languages in that they do not specify a step or sequence of steps to execute, but rather the properties of a solution to be found. In addition to constraints, users also need to specify a method to solve these constraints. This typically draws upon standard methods like chronological backtracking and constraint propagation, but may use customized code like a problem specific branching heuristic. CP has been identified as promising techniques for efficiently solving discrete optimization problems. CP has found applications in diverse areas and has enjoyed tremendous success in areas involving combinatorial optimization such as assignment and scheduling problems.
It is well adapted to solving real-life problems because many application domains evoke constraint description naturally. Let’s see some examples: in scheduling exams at an university, the decision variables might be the times and locations of the different exams, and the constraints might be on the capacity of each examination room (e.g., we cannot schedule more students to sit exams in a given room at any one time than the room’s capacity) and on the exams scheduled at the same time (e.g., we cannot schedule two exams at the same time if they share students in common). Another example can be stand allocation for airports, where an aircraft must be parked on an available stand during its stay at the airport, counter allocation for departure halls in airports, berth allocation to ships in a harbor. Personnel assignment where work rules and regulations impose difficult constraints: Production of rosters for nurses in hospitals, crew assignments to flights, staff assignments in railways. Scheduling problems such as forest treatment scheduling, production scheduling in the plastic industry, planning the production of military and business jets. The use of constraints in advanced planning and scheduling systems is increased due to current trends of on-demand manufacturing. Network management and configuration are also about constraint methods: planning of cabling of telecommunication networks in buildings, electric power network reconfiguration for maintenance scheduling without disrupting customer services, etc.
Constraint programming has been successfully applied to problem areas as diverse as DNA structure analysis, time-tabling for hospitals, and industry scheduling.
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