Multi-objective optimizationMulti-objective optimization or Pareto optimization (also known as multi-objective programming, vector optimization, multicriteria optimization, or multiattribute optimization) is an area of multiple-criteria decision making that is concerned with mathematical optimization problems involving more than one objective function to be optimized simultaneously. Multi-objective is a type of vector optimization that has been applied in many fields of science, including engineering, economics and logistics where optimal decisions need to be taken in the presence of trade-offs between two or more conflicting objectives.
RiverA river is a natural flowing watercourse, usually a freshwater stream, flowing on the surface or inside caves towards another waterbody at a lower elevation, such as an ocean, sea, bay, lake, wetland, or another river. In some cases, a river flows into the ground or becomes dry at the end of its course without reaching another body of water. Small rivers can be referred to by names such as creek, brook, and rivulet. There are no official definitions for the generic term river as applied to geographic features, although in some countries or communities, a stream is defined by its size.
Global optimizationGlobal optimization is a branch of applied mathematics and numerical analysis that attempts to find the global minima or maxima of a function or a set of functions on a given set. It is usually described as a minimization problem because the maximization of the real-valued function is equivalent to the minimization of the function . Given a possibly nonlinear and non-convex continuous function with the global minima and the set of all global minimizers in , the standard minimization problem can be given as that is, finding and a global minimizer in ; where is a (not necessarily convex) compact set defined by inequalities .
Mathematical optimizationMathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.
ReservoirA reservoir (ˈrɛzərvwɑːr; from French réservoir ʁezɛʁvwaʁ) is an enlarged lake behind a dam. Such a dam may be either artificial, usually built to store fresh water, or it may be a natural formation. Reservoirs can be created in a number of ways, including controlling a watercourse that drains an existing body of water, interrupting a watercourse to form an embayment within it, excavating, or building any number of retaining walls or levees.
Multidisciplinary design optimizationMulti-disciplinary design optimization (MDO) is a field of engineering that uses optimization methods to solve design problems incorporating a number of disciplines. It is also known as multidisciplinary system design optimization (MSDO), and Multidisciplinary Design Analysis and Optimization (MDAO). MDO allows designers to incorporate all relevant disciplines simultaneously. The optimum of the simultaneous problem is superior to the design found by optimizing each discipline sequentially, since it can exploit the interactions between the disciplines.
Water supplyWater supply is the provision of water by public utilities, commercial organisations, community endeavors or by individuals, usually via a system of pumps and pipes. Public water supply systems are crucial to properly functioning societies. These systems are what supply drinking water to populations around the globe. Aspects of service quality include continuity of supply, water quality and water pressure. The institutional responsibility for water supply is arranged differently in different countries and regions (urban versus rural).
Convex optimizationConvex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently, maximizing concave functions over convex sets). Many classes of convex optimization problems admit polynomial-time algorithms, whereas mathematical optimization is in general NP-hard.
Ecosystem serviceEcosystem services are the many and varied benefits to humans provided by the natural environment and healthy ecosystems. Such ecosystems include, for example, agroecosystems, forest ecosystem, grassland ecosystems, and aquatic ecosystems. These ecosystems, functioning in healthy relationships, offer such things as natural pollination of crops, clean air, extreme weather mitigation, and human mental and physical well-being.
Constraint satisfaction problemConstraint satisfaction problems (CSPs) are mathematical questions defined as a set of objects whose state must satisfy a number of constraints or limitations. CSPs represent the entities in a problem as a homogeneous collection of finite constraints over variables, which is solved by constraint satisfaction methods. CSPs are the subject of research in both artificial intelligence and operations research, since the regularity in their formulation provides a common basis to analyze and solve problems of many seemingly unrelated families.
Marine ecosystemMarine ecosystems are the largest of Earth's aquatic ecosystems and exist in waters that have a high salt content. These systems contrast with freshwater ecosystems, which have a lower salt content. Marine waters cover more than 70% of the surface of the Earth and account for more than 97% of Earth's water supply and 90% of habitable space on Earth. Seawater has an average salinity of 35 parts per thousand of water. Actual salinity varies among different marine ecosystems.
Constraint satisfactionIn artificial intelligence and operations research, constraint satisfaction is the process of finding a solution through a set of constraints that impose conditions that the variables must satisfy. A solution is therefore a set of values for the variables that satisfies all constraints—that is, a point in the feasible region. The techniques used in constraint satisfaction depend on the kind of constraints being considered.
Constraint logic programmingConstraint logic programming is a form of constraint programming, in which logic programming is extended to include concepts from constraint satisfaction. A constraint logic program is a logic program that contains constraints in the body of clauses. An example of a clause including a constraint is . In this clause, is a constraint; A(X,Y), B(X), and C(Y) are literals as in regular logic programming. This clause states one condition under which the statement A(X,Y) holds: X+Y is greater than zero and both B(X) and C(Y) are true.
Social classA social class or social stratum is a grouping of people into a set of hierarchical social categories, the most common being the upper, middle and lower classes. Membership in a social class can for example be dependent on education, wealth, occupation, income, and belonging to a particular subculture or social network. "Class" is a subject of analysis for sociologists, political scientists, anthropologists and social historians. The term has a wide range of sometimes conflicting meanings, and there is no broad consensus on a definition of "class".
Operation (mathematics)In mathematics, an operation is a function which takes zero or more input values (also called "operands" or "arguments") to a well-defined output value. The number of operands is the arity of the operation. The most commonly studied operations are binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse. An operation of arity zero, or nullary operation, is a constant.
Binary operationIn mathematics, a binary operation or dyadic operation is a rule for combining two elements (called operands) to produce another element. More formally, a binary operation is an operation of arity two. More specifically, an internal binary operation on a set is a binary operation whose two domains and the codomain are the same set. Examples include the familiar arithmetic operations of addition, subtraction, and multiplication. Other examples are readily found in different areas of mathematics, such as vector addition, matrix multiplication, and conjugation in groups.
Social inequalitySocial inequality occurs when resources in a given society are distributed unevenly, typically through norms of allocation, that engender specific patterns along lines of socially defined categories of persons. It poses and creates a gender gap between individuals that limits the accessibility that women have within society. The differentiation preference of access to social goods in the society is brought about by power, religion, kinship, prestige, race, ethnicity, gender, age, sexual orientation, and class.
Ecosystem-based adaptationEcosystem-based adaptation (EBA) encompasses a broad set of approaches to adapt to climate change. They all involve the management of ecosystems and their services to reduce the vulnerability of human communities to the impacts of climate change. The Convention on Biological Diversity defines EBA as "the use of biodiversity and ecosystem services as part of an overall adaptation strategy to help people to adapt to the adverse effects of climate change".
Surface runoffSurface runoff (also known as overland flow or terrestrial runoff) is the unconfined flow of water over the ground surface, in contrast to channel runoff (or stream flow). It occurs when excess rainwater, stormwater, meltwater, or other sources, can no longer sufficiently rapidly infiltrate in the soil. This can occur when the soil is saturated by water to its full capacity, and the rain arrives more quickly than the soil can absorb it. Surface runoff often occurs because impervious areas (such as roofs and pavement) do not allow water to soak into the ground.
Clean Water ActThe Clean Water Act (CWA) is the primary federal law in the United States governing water pollution. Its objective is to restore and maintain the chemical, physical, and biological integrity of the nation's waters; recognizing the responsibilities of the states in addressing pollution and providing assistance to states to do so, including funding for publicly owned treatment works for the improvement of wastewater treatment; and maintaining the integrity of wetlands.
