OPTIMISATION OF UNDERGROUND MINE DECLINE DEVELOPMENT SYSTEM USING GENETIC ALGORITHM

: When deposit is composed of few ore bodies it is necessary to interconnect them into one integrated system. Suppose the deposit characteristics indicate that decline development system is preferred one. In such environment we treat development of an underground mine as access infrastructure composed of different decline sections. Access infrastructure designing can be treated as spanning the spatial network which will connect all main terminals (points). In our model we defined spatial network by adequate nonlinear constrained objective function representing the cost of mine development and ore haulage. To find the minimum value of the objective function we use Genetic algorithm


INTRODUCTION
When deposit is composed of few ore bodies it is necessary to interconnect them into one integrated system.There are different development systems (shaft, decline, adit) which can be used to create such system.Suppose the deposit characteristics indicate that decline development system is preferred one.In such environment we treat development of an underground mine as access infrastructure composed of different decline sections.Access infrastructure design can be treated as spanning the spatial network which will connect all main terminals (points).Main terminals are: mineral processing facility, surface breakout point and ore body access points.
Brazil et al. created a software tool called Decline Optimization Toll (DOT).The heuristic methods used in DOT1 are replaced in the new version of the software tool, DOT2, by a method based on an understanding of exact solutions to a constrained 3-dimensional path problem.Their approach is based on the minimization of the cost of the decline, where the cost is a combination of both development and haulage costs, subject to design constraints (Brazil et al. 2003;2008).
In our model we defined spatial network by nonlinear constrained objective function representing the cost of mine development and ore haulage.To find the minimum value of the objective function we use Genetic algorithm.

THE MODEL OF A DECLINE DEVELOPMENT SYSTEM
In many cases, the ore deposit is composed of a few ore bodies that must be interconnected into one integrated system.The main idea that we used to create such system is based on the fact that somewhere in  3u (3-dimensional underground space) there is a point through which we can connect all ore bodies with surface portal (or surface breakout point, SBP) and afterward with mineral processing facility (MPF), with minimum costs.This point is called underground mass concentration point (UMCP).Basic hypothesis used in the optimisation model are as follows: -Location of MPF is fixed; -Location of SBP is allowed to vary; -Location of UMCP is allowed to vary; -Locations of the access points are fixed; - The tonnage of ore to be hauled from each orebody to the surface portal is fixed.A decline development system is modeled as a 3-dimensional or space network interconnecting all main points.Such network must incorporate the navigability constraints caused by the mine trucks and other equipment characteristics.The absolute value of the decline slope must be less or equal to the maximum value of the slope that can be handled by loaded mine truck in a safe way.
Decline optimisation is concerned of determination of locations of SBP and UMCP.A general design optimisation problem is formulated as follows: In this formulation x is the n-dimensional vector of SBP and UMCP coordinates, while x L and x U are the n-dimensional vectors representing the lower and upper bounds of the coordinates, i.e. the design space.The optimisation goal is to minimize the objective function f(x) subject to a given number of constraints: g i ( x) is the r-dimensional vector of inequality constraints, while h j (x) is the m-dimensional vector of equality constraints.The objective function represents the total costs needed to develop surface route section, underground mine decline system and haul up ore reserves from each orebody to MPF via UMCP and SBP.
The optimisation problem of underground mine decline development system can be formulated as the following form.The objective function has to be minimized, subject to (11) where x, y, z -location (coordinates) of the underground mass concentration point; x i , y i , z i -location (coordinates) of the i-th ore body access point; x s , y s , z s -location (coordinates) of the surface breakout point; x m , y m , z m -location (coordinates) of the mineral processing facility; If we take into consideration, the underground mine truck fleet is uniform (all trucks have the same payload capacity), then the unit ore haulage cost is equal for the all underground route sections, i.e., c 1 = c 2 = ,…,= c n = c d .
In our case, the optimisation problem is a non-linear constrained programming problem.In such environment, genetic algorithm is used to figure out optimal values of the design parameters.

BRIEF DESCRIPTION OF GENETIC ALGORITHM (GA)
Genetic algorithms are stochastic techniques whose search methods model a natural evolution.The genetic algorithms start with randomly chosen parent chromosomes from the search space to create a population.They work with chromosome genotype.The population evolves toward the better chromosomes by applying genetic operators modeling the genetic processes occurring in the nature selection, recombination and mutation.
Selection compares the chromosomes in the population aiming to choose these, which will take part in the reproduction process.The selection occurs with a given probability on the base of fitness functions.The fitness function plays a role of the environment to distinguish between good and bad solutions.
The recombination is carried out after selection process is finished.It combines, with predefined probability, the features of two selected parent chromosomes forming similar children.
After recombination offspring undergoes to mutation.Generally, the mutation refers to the creation of a new chromosome from one and only one individual with predefined probability.
After three operators are carried the offspring is inserted into the population, replacing the parent chromosomes in which they were derived from, producing a new generation.This cycle is performed until the optimization criterion is met (Shopova and Vaklieva-Banacheva, 2006).
In GA the equality and inequality constraints can be treated by different strategies.The penalty function technique is used to transform the constrained optimisation problem to unconstrained optimisation problem by penalizing the constraints and forming a new objective function as follows (Ali, 2014): where 0 if no constraint is violated penalty( ) There are two kinds of points in the search space of the constrained optimisation problems, feasible points which satisfy all constraints and unfeasible points which violate at least one of the constraints.At the feasible points, the penalty function value is equal the value of objective function, but at the infeasible points the penalty function value is equal to high value as shown in (12) (Ali, 2014).

NUMERICAL EXAMPLE
Proposed optimisation model based on GA application is tested in design task for development of ore deposit composed of four ore bodies.The Pb-Zn deposit is to be developed, the situation is hypothetical and the numbers used are in to permit calculation.The hypothetical deposit includes four ore bodies A through D with access points i = 1, 2, 3, 4 respectively.The relevant operational data are shown in Table 1 and Figure 1.Value of the total cost function is 13,581,387 USD.

CONCLUSION
In this paper we have presented the application of Genetic algorithm for designing underground mine decline development system in the case when the deposit is composed of few ore bodies.Underground mine development system is treated as spatial network connecting all main terminals with minimum cost.Such network is defined by adequate objective function.Optimisation model is based on the minimisation of the nonlinear constrained objective function representing the cost of mine development and ore haulage.The model is not closed and allows the underground mining engineers to incorporate additional components according to their needs.
δ i -the unit cost of decline development from the underground mass concentration point to the i-th ore body [USD/m]; c i -the unit ore haulage cost from the i-th ore body access point to the underground mass concentration point [USD/tm]; R i -ore reserves of the i-th ore body [t]; n -number of ore bodies; d -the unit cost of decline development from the underground mass concentration point to the surface breakout point [USD/m]; c d -the unit ore haulage cost from the underground mass concentration point to the surface breakout point [USD/tm]; s -the unit cost of the surface transportation route development from the surface breakout point to the mineral processing facility [USD/m]; c s -the unit ore transportation cost from the surface breakout point to the mineral processing facility [USD/tm]; r max -maximum absolute value of the decline slope [%]; β max -maximum absolute value of the slope of the surface transportation section [%].

Figure 2 -
Figure 2 -Underground mine decline development system (plan view)

Table 2 -
Design parameters