**Ant Colony Optimization In Operation Planning Problems**

The input into the planning problems is set of linear alternate procedure plan of the parts having several operations and machine tools to present the similar. The planning stage simply selects the best process plan between the available alternatives to procedure the part. The operation planning problem mostly deals along with the generation of effective plans based on the machine characteristics and part design specifications and their mutual connection. This is required in make-to-order industries where, there are not same due dates along with each customer order. Hence, the engaged operation sequencing problem can be explained as: "To acquire a proficient operation sequence and to attain a schedule such can minimize the make span value along with due consideration of constraints concern to processing sequence of the jobs of the operations, the available capability of the machine."

Ant Colony Optimization's step-wise process to Planning Problems as:

**Step 1: Initialization**

1 Represent the problem utilizing a weighted directed graph.

2 Randomly distribute ants upon the nodes.

3 Set t # 0 // time counter.

4 Set NC # 1 // Iteration counter.

5 Set τ_{ij} (0) = c // τ_{ij} (0) is the symbol for pheromone trail and c is the small positive quantity.

6 Set Δτ_{ij} = 0 // Δτ_{ij} (0) is the raise in the pheromone trail.

7 Set tabu K = 0 // tabu K is the memory of ants having the information of visited nodes.

**Step 2**

If NC > NC_{max} goto Step 3, otherwise goto Step 4 // NC_{max} is the maximum number of iterations.

**Step 3**

If m > m_{max} goto Step 7, otherwise goto Step 4 // m_{max} is the maximum number of ants.

**Step 4**

If tabu^{k}_{max} > tabu^{k}_{max} goto Step 6, else goto Step 5 // tabu^{k}_{max} is the maximum number of the nodes to be visited by ant k.

**Step 5: Node Selection**

1. Generate random number p (0 < p < 1).

2. If p > = P_{0} goto Step 5(3), else goto Step 5(4).

3. Generate random number q (q ε SK), select q, goto Step 5(10).

4. Compare the probabilities of possible outgoing nodes.

5. Generate a random number q (0 ≤ q ≤ 1).

6. If q > p^{k}_{iI} goto Step 5(8), else goto Step 5(9).

7. Generate a random number q (q ? SK) goto Step 5(10).

8. Select the node with highest probability, choose = 1.

9. Select the node select as next node to move.

10. Add node chosen in the tabu list of corresponding

**Step 6**

m = m + 1.

**Step 7: **Updation

1. Calculate P*_{iter}//P*_{iter} is the iteration excellent objective value.

2. If P*_{iter}>P*_{iter} then P*_{iter} = P*_{best}// P*_{best} is the overall best objective value.

3. Update the pheromone trail.

4. Empty all tabu list.

5. NC = NC + 1.

6. P_{0} = log (NC) / log (NC_{max}), goto Step 2.

**Step 8**

Output the best result, P*_{best}

**Illustration**
In this part, a description of problem specific disassembly sequencing has been provided. Similar has been resolved by an ant colony algorithm along with the steps implies above. Explanation of the problem and the objective function is given below.

**Problem Description**

Generally, there are different solution sets occupied to determine the feasible disassembly sequence. An explanation of them is given below as:

(a) P = {P_{1}, P_{2}, . . . , P_{np}}, is the set of each part in an assembly and P_{np} is the cardinality of set P.

(b) SA = {sa_{1}, sa_{2} , . . . , S_{nsa} } , the set of each the subassembly and n_{SA }being the cardinality of the set SA.

(c) F = { f_{1},f_{2} , . . . , F_{nf } } , the set of each fastener and joints and n_{F} being the cardinality of set F.

(d) FB = { fb_{1},fb_{2} , . . . , fb_{nFb } } , the set of fasteners broken and n_{FB} being FB the joints in reality broken.

(e) PR = { pr_{1}, pr_{2} , . . . , pr_{npr} } , the set of each part recovered after disassembly operation and n_{PR} being the cardinality of set PR.

(f) SR = {sr_{1}, sr_{2} , . . . , sr_{nSR } } , the set of subassemblies recovered and n_{SR} being the cardinality of set SR. PR and SR form whole parts and subassemblies recovered.

(g) SB = {sb_{1}, sb_{2} , .., sb_{nSB} } , the set of subassemblies broken and n_{SB} being the cardinality of set SB.

(h) SOL = {sol_{1} , sol_{2} , . . . , SOL_{nFB+nSB } } , a set formed of an exact feasible sequence from numerous probable permutations of FB ∪ SB.

Consider P = {1, 3, 7, 8, 9, 12}, then n_{p} = 6 and p_{1} = 1, p_{2} = 3, p_{3} = 7, p_{4} = 8, p_{5} = 9, p_{6} = 12. Similar causing stands for elements of other sets. Based on the above sets, a profound mathematical model is illustrated as stated below.