Integer programmingAn integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers. In many settings the term refers to integer linear programming (ILP), in which the objective function and the constraints (other than the integer constraints) are linear. Integer programming is NP-complete. In particular, the special case of 0-1 integer linear programming, in which unknowns are binary, and only the restrictions must be satisfied, is one of Karp's 21 NP-complete problems.
Cutting-plane methodIn mathematical optimization, the cutting-plane method is any of a variety of optimization methods that iteratively refine a feasible set or objective function by means of linear inequalities, termed cuts. Such procedures are commonly used to find integer solutions to mixed integer linear programming (MILP) problems, as well as to solve general, not necessarily differentiable convex optimization problems. The use of cutting planes to solve MILP was introduced by Ralph E. Gomory.
Biomass (energy)Biomass, in the context of energy production, is matter from recently living (but now dead) organisms which is used for bioenergy production. Examples include wood, wood residues, energy crops, agricultural residues including straw, and organic waste from industry and households. Wood and wood residues is the largest biomass energy source today. Wood can be used as a fuel directly or processed into pellet fuel or other forms of fuels. Other plants can also be used as fuel, for instance maize, switchgrass, miscanthus and bamboo.
Linear programmingLinear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization). More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints.
BioenergyBioenergy is energy made or generated from biomass, which consists of recently living (but now dead) organisms, mainly plants. Types of biomass commonly used for bioenergy include wood, food crops such as corn, energy crops and waste from forests, yards, or farms. The IPCC (Intergovernmental Panel on Climate Change) defines bioenergy as a renewable form of energy. Bioenergy can either mitigate (i.e. reduce) or increase greenhouse gas emissions. There is also agreement that local environmental impacts can be problematic.
Ellipsoid methodIn mathematical optimization, the ellipsoid method is an iterative method for minimizing convex functions. When specialized to solving feasible linear optimization problems with rational data, the ellipsoid method is an algorithm which finds an optimal solution in a number of steps that is polynomial in the input size. The ellipsoid method generates a sequence of ellipsoids whose volume uniformly decreases at every step, thus enclosing a minimizer of a convex function. The ellipsoid method has a long history.
Algae fuelAlgae fuel, algal biofuel, or algal oil is an alternative to liquid fossil fuels that uses algae as its source of energy-rich oils. Also, algae fuels are an alternative to commonly known biofuel sources, such as corn and sugarcane. When made from seaweed (macroalgae) it can be known as seaweed fuel or seaweed oil. In December 2022, ExxonMobil, the last large oil company to invest in algae biofuels, ended its research funding. In 1942 Harder and Von Witsch were the first to propose that microalgae be grown as a source of lipids for food or fuel.
Cutting stock problemIn operations research, the cutting-stock problem is the problem of cutting standard-sized pieces of stock material, such as paper rolls or sheet metal, into pieces of specified sizes while minimizing material wasted. It is an optimization problem in mathematics that arises from applications in industry. In terms of computational complexity, the problem is an NP-hard problem reducible to the knapsack problem. The problem can be formulated as an integer linear programming problem.
Bioconversion of biomass to mixed alcohol fuelsThe bioconversion of biomass to mixed alcohol fuels can be accomplished using the MixAlco process. Through bioconversion of biomass to a mixed alcohol fuel, more energy from the biomass will end up as liquid fuels than in converting biomass to ethanol by yeast fermentation. The process involves a biological/chemical method for converting any biodegradable material (e.g., urban wastes, such as municipal solid waste, biodegradable waste, and sewage sludge, agricultural residues such as corn stover, sugarcane bagasse, cotton gin trash, manure) into useful chemicals, such as carboxylic acids (e.
Branch and cutBranch and cut is a method of combinatorial optimization for solving integer linear programs (ILPs), that is, linear programming (LP) problems where some or all the unknowns are restricted to integer values. Branch and cut involves running a branch and bound algorithm and using cutting planes to tighten the linear programming relaxations. Note that if cuts are only used to tighten the initial LP relaxation, the algorithm is called cut and branch. This description assumes the ILP is a maximization problem.
