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3  TOMLAB /GENO Solver Reference

A detailed description of the TOMLAB /GENO solver interface is given below. Also see the M-file help for genoTL.m .

3.1  genoTL

Purpose
Solve global optimization problems as described below.



where x Rⁿ, f(x) R, A R^{m₁ × n}, b_L,b_U R^m₁ and c(x) R^m₂.
The variables x I, the index subset of 1,...,n, are restricted to be integers.
or the general format for multi-objective optimization:

where x, x_L, x_U Rⁿ, r(x) R^M, A R^{m₁ × n}, b_L,b_U R^m₁ and c_L,c(x),c_U R^m₂.
The variables x I, the index subset of 1,...,n, are restricted to be integers.

Calling Syntax
Prob = clsAssign( ... );
Result = tomRun('GENO',Prob,...)

Prob	Problem description structure. The following fields are used:
A	Linear constraints coefficient matrix.
x_L, x_U	Bounds on variables.
b_L, b_U	Bounds on linear constraints.
c_L, c_U	Bounds on nonlinear constraints.
MIP	Structure with fields defining the integer properties of the problem. The following fields are used:
IntVars	Vector designating which variables are restricted to integer values. This field is interpreted differently depending on the length.
	If length(IntVars) = length(x), it is interpreted as a zero-one vector where all non-zero elements indicate integer values only for the corresponding variable.
	A length less than the problem dimension indicates that IntVars is a vector of indices for the integer variables, for example [1 2 3 6 7 12]
	A scalar value K restricts variables x(1) through x(K) to take integer value only.
PriLevOpt	Print level for the solver.
GENO	Structure with GENO solver specific fields.
PrintFile	Name of file to print progress information and results to.
GENO.options	Structure with special fields for the GENO solver:
adj_mode	This parameter is problem-dependent. It should be set to 's' for uni-objective optimization problems, or if one seeks a Nash equilibrium solution of a multi-objective problem; it should be to 'g' in all other cases.
	Default: None
bm_rate	This parameter is the probability of boundary mutation and is returned from a simple function. It is problem-dependent but the default value is usually efficient.
	Default: 0.005
constraints_check	This parameter allows one to choose whether or not to display (1) values of the constraints at the end of the program run.
	Default: 0
d_factor	This is a weighting factor on the direction component of the differential cross-over operator. The parameter is problem-dependent but the default range is usually efficient.
	Default: 0.15 - 0.8
m_rate	This parameter is the probability of ordinary mutation and is returned from a simple function. It is problem-dependent but the default value is usually efficient.
	Default: 0.05
maximise	This parameter is problem-specific: set this to true (1) if the problem is about maximization.
	Default: 0
p_a_xover	This parameter is problem-dependent: it specifies the probability threshold for the arithmetic cross-over operator. The default value is usually efficient.
	Default: 0.55
p_agents	This parameter is problem-specific: it declares the number of sub-objective in a multi-objective problem.
	Default: None
p_b_xover	This parameter is problem-dependent: it specifies the probability threshold for the boundary cross-over operator. The default value is usually efficient.
	Default: 0.005
p_d_xover	This parameter is problem-dependent: it specifies the probability threshold for the differential cross-over operator. The default value is usually efficient.
	Default: 0.55
p_eqms	A constant equal to 1.
	Default: 1
p_h_xover	This parameter is problem-dependent: it specifies the probability threshold for the heuristic cross-over operator. The default value is usually efficient.
	Default: 0.55
p_maxgens	This parameter specifies the maximum number of generations that the algorithm will execute. The most efficient value is dependent on the problem and the population size but it would be safe to assume that GENO solves most problems within 500 generations.
	Default: None
p_mingens	This parameter should always be 2.
	Default: 2
p_order	This parameter is problem-specific: it specifies the total number of variables in the problem.
	Default: None
p_plan	This parameter is problem-specific: it specifies the length of the control vector along the time dimension.
	Default: None
p_popsize	This parameter specifies the population size. The most efficient value is problem-dependent but most likely to be within the range shown.
	Default: 10 - 30
p_s_xover	This parameter is problem-dependent: it specifies the probability threshold for the simple cross-over operator. The default value is usually efficient.
	Default: 0.55
p_shuffle	This parameter is problem-dependent: it specifies the probability threshold for shuffling the population. The default value is usually efficient.
	Default: 0.55
p_u_xover	This parameter is problem-dependent: it specifies the probability threshold for the uniform cross-over operator. The default value is usually efficient.
	Default: 0.55
pos_orth	This parameter is problem-specific: set this to false (0) if the static constraints are of the 'less than' type.
	Default: 1
quantum_0	This parameter is problem-dependent: is specifies the initial size of quanta. In setting this parameter, the object should be to ensure that the initial population is sufficiently diverse on all dimensions. In this regard, a choice of the smaller between 0.1 and 10% of the smallest variable range is normally efficient. But if one seeks an integer solution, then this parameter should be set to 1.
	Default: None
rand_seed	This is a seed value for the random number generator.
	Default: None
solution_type	This parameter is problem-dependent: it defines the type of solution sought.
	Default: None
timer	This parameter declares whether to display (1) GENO's loop time at the end of the program run.
	Default: 0
vars	This parameter is problem-specific: it is an 'incidence matrix' that shows what variables are in each sub-problem of the multi-agent optimization problem.
	Default: None
vdu_output	This parameter declares whether to display (1) progress of the best chromosome or its fitness.
	Default: 0
view_vars	In conjunction with vdu_output, this parameter allows one to choose between viewing (1) the variables in the best chromosome or its fitness.
	Default: 0

Description of Outputs

Result	Structure with result from optimization. The following fields are set:
	f_k	Function value at optimum.
	x_k	Solution vector.
	x_0	Initial solution vector.
	c_k	Nonlinear constraint residuals.
	xState	State of variables. Free == 0; On lower == 1; On upper == 2; Fixed == 3;
	bState	State of linear constraints. Free == 0; Lower == 1; Upper == 2; Equality == 3;
	cState	State of nonlinear constraints. Free == 0; Lower == 1; Upper == 2; Equality == 3;
	Ax	Values of linear constraints.
	ExitFlag	Exit status from GENO (TOMLAB standard). 0 = Optimal solution found.
	ExitText	Exit text from GENO.
	Inform	GENO information parameter.
		0 = Optimal: found an optimal solution.
		Other = No optimal solution found.
	FuncEv	Number of function evaluations.
	ConstrEv	Number of constraint evaluations.
	QP.B	Basis vector in TOMLAB QP standard.
	Solver	Name of the solver (GENO).
	SolverAlgorithm	Description of the solver.
	GENO	Subfield with GENO specific results.

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