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An efficient approach by adjusting bounds for heuristic optimization algorithms

  • Methodologies and Application
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Abstract

In this article, a novel method is suggested for solving heuristic optimization problems. A pre-study was performed to define proper bounds. Different problems with these bounds were solved using genetic, accelerated particle swarm, and cuckoo search algorithms. Three different problems (multi-pass turning, welded beam design, and tension spring) were used as case studies. The results of the studies were compared with the earlier studies. As a result, the proposed method requires less computing time and has better objective function values compared to the solutions in the literature. The proposed method provides effective decision-making for operators and engineers dealing with different design and manufacturing environments in terms of cost and time.

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Abbreviations

UC:

The cost of unit production without material cost ($/piece)

\( C_{M} \) :

The cost of machine idle resulting from setup operations and tool idle motion time ($/piece)

\( C_{R} \) :

The cost of tool replacement process ($/piece)

\( C_{T} \) :

The cost of tools ($/piece)

\( V_{r} ,V_{s} \) :

Cutting speeds in rough and finish machining (m/min)

\( V_{rL} ,V_{rU} \) :

Lower and upper bounds of cutting speed in rough machining (m/min)

\( V_{sL} ,V_{sU} \) :

Lower and upper bounds of cutting speed in finish machining (m/min)

\( f_{r} ,f_{s} \) :

Feed rates in rough and finish machining (mm/rev)

\( f_{rL} ,f_{rU} \) :

Lower and upper bounds of feed rates in rough machining (mm/rev)

\( f_{sL} ,f_{sU} \) :

Lower and upper bounds of feed rates in finish machining (mm/rev)

\( d_{r} ,d_{s} \) :

Cutting depth at rough and finish machining (mm)

\( d_{rL} ,d_{rU} \) :

Lower and upper bounds of depth of cut in rough machining (mm)

\( d_{sL} ,d_{sU} \) :

Lower and upper bounds of depth of cut in finish machining (mm)

\( n \) :

Number of rough cuts

\( d_{t} \) :

Total depth of cut at machining (mm)

\( D,L \) :

Diameter and length of workpiece (mm)

\( k_{0} \) :

Direct labor cost overheads included ($/min)

\( k_{t} \) :

The cost of cutting edge ($/piece)

\( t_{mr} ,t_{ms} \) :

Rough and finish machining time (min)

\( t_{m} \) :

Actual machining time (min)

\( t_{c} ,t_{e} ,t_{i} \) :

Constant term of machine idling time, tool change time, total machine idle time (min)

\( h_{1} ,h_{2} \) :

Constants of pertaining of tool travel and approach/departure time (min)

\( T_{r} ,T_{s} \) :

Expected tool life for rough and finishing operations (min)

\( T_{p} \) :

Tool life weighted combination of \( T_{r} ,T_{s} \) (min)

\( T_{L} ,T_{U} \) :

Lower and upper bounds for tool life (min)

\( \alpha ,\beta ,\gamma ,C \) :

Constants of the tool life equation

SR:

Maximum allowed surface roughness value (mm)

SC:

Limit of stable cutting region

\( R \) :

Nose radius of cutting tool (mm)

\( F_{r} ,F_{s} \) :

Cutting forces during rough and finishing operations (kgf)

\( k_{1} ,u,v \) :

Constants of cutting force equation

\( F_{u} \) :

Maximum allowable cutting force (kgf)

\( P_{r} ,P_{s} \) :

Cutting power requirement for rough and finishing operations (kW)

\( P_{U} \) :

Maximum allowable cutting power limit (kW)

\( \eta \) :

Efficiency of power consumption

\( \lambda ,\nu \) :

Constants related to expression of stable cutting region

\( Q_{r} ,Q_{s} \) :

Limit of stable cutting region constraint chip–tool interface temperatures during rough and finish machining, respectively (°C)

\( Q_{U} \) :

Maximum allowable chip–tool interference (°C)

\( k_{2} ,\tau ,\phi ,\delta \) :

Constants of chip–tool interference temperature calculation

\( k_{3} ,k_{4} ,k_{5} \) :

Constants for roughing and finishing parameter relations

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Authors and Affiliations

  1. Department of Mechanical Engineering, Eskişehir Osmangazi University, 26480, Eskisehir, Turkey

    Mehmet Alper Sofuoğlu

  2. Eskişehir Vocational School, Eskişehir Osmangazi University, 26110, Eskisehir, Turkey

    Fatih Hayati Çakır & Selim Gürgen

Authors
  1. Mehmet Alper Sofuoğlu
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  2. Fatih Hayati Çakır
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  3. Selim Gürgen
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Correspondence to Fatih Hayati Çakır.

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Communicated by V. Loia.

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Sofuoğlu, M.A., Çakır, F.H. & Gürgen, S. An efficient approach by adjusting bounds for heuristic optimization algorithms. Soft Comput 23, 5199–5212 (2019). https://doi.org/10.1007/s00500-018-3327-2

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