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MOMPA: Multi-objective marine predator algorithm for solving multi-objective optimization problems

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Abstract

This paper proposes a new multi-objective algorithm, called Multi-Objective Marine-Predator Algorithm (MOMPA), dependent on elitist non-dominated sorting and crowding distance mechanism. The proposed algorithm is based on the recently proposed Marine-Predator Algorithm, and it was inspired by biological interaction between predator and prey. The proposed MOMPA can address multiple and conflicting objectives when solving optimization problems. The MOMPA is formulated using elitist non-dominated sorting and crowding distance mechanisms. The proposed method is tested on various multi-objective case studies, including 32 unconstrained, constraint, and engineering design problems with different linear, nonlinear, continuous, and discrete characteristics-based Pareto front problems. The results of the proposed MOMPA are compared with several well-regarded Multi-Objective Water-Cycle Algorithm, Multi-Objective Symbiotic-Organism Search, Multi-Objective Moth-Flame Optimizer algorithms qualitatively and quantitatively using several performance indicators. The experimental results demonstrate the merits of the proposed method.

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Authors and Affiliations

  1. Rajasthan Rajya Vidyut Prasaran Nigam Ltd, 132 KV GSS, Losal-Sikar, Rajasthan, 332025, India

    Pradeep Jangir

  2. Government Engineering College, Mavdi Kankot Road, Rajkot, 360005, India

    Hitarth Buch

  3. Centre for Artificial Intelligence Research and Optimisation, Torrens University Australia, Fortitude Valley, Brisbane, QLD, 4006, Australia

    Seyedali Mirjalili

  4. Department of Electrical and Electronics Engineering, Dayananda Sagar College of Engineering, Bengaluru, Karnataka, 560078, India

    Premkumar Manoharan

  5. Yonsei Frontier Lab, Yonsei University, Seoul, 03722, Korea

    Seyedali Mirjalili

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  1. Pradeep Jangir
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  4. Premkumar Manoharan
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Appendix 1

Appendix 1

In general, the multi-objective optimization problems can be written as a maximization/minimization problem, and it can be represented as follows.

$$\frac{Min}{{Max}} F\left( {\vec{x}} \right) = \left\{ {f_{1} \left( {\vec{x}} \right), f_{2} \left( {\vec{x}} \right), \ldots , f_{o} \left( {\vec{x}} \right)} \right\}$$
(I.1)
$$Subject to : g_{i} \left( {\vec{x}} \right) \ge 0, i = 1,2, \ldots ,m$$
(I.2)
$$h_{i} \left( {\vec{x}} \right) = 0, i = 1,2, \ldots ,p$$
(I.3)
$$Lb_{i} \le x_{i} \le Ub_{i} , i = 1,2,...,n$$
(I.4)

The most useful definitions in this regard are as follows:

Def. 1 Pareto Dominance [4, 14]:

$$\forall i \in \left\{ {1,2, \ldots ,k} \right\}: f_{i} \left( {\vec{x}} \right) \le f_{i} \left( {\vec{y}} \right) \wedge \exists i \in \left\{ {1,2, \ldots ,k} \right\}:f_{i} \left( {\vec{x}} \right) < f_{i} \left( {\vec{y}} \right)$$
(I.5)

Def. 2 Pareto Optimality [4, 14]:

$$\nexists \overrightarrow{y}\in X | F\left(\overrightarrow{y}\right)\prec F(\overrightarrow{x})$$
(I.6)

Def. 3 Pareto optimal set [4, 14]

$$P_{s} : = \{ x,y \in X | \exists F\left( {\vec{y}} \right) \succ F\left( {\vec{x}} \right)\}$$
(I.7)

Def. 4 Pareto optimal front [4, 14]:

$$P_{f} : = \{ F\left( {\vec{x}} \right)|\vec{x} \in P_{s} \}$$
(I.8)

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Jangir, P., Buch, H., Mirjalili, S. et al. MOMPA: Multi-objective marine predator algorithm for solving multi-objective optimization problems. Evol. Intel. 16, 169–195 (2023). https://doi.org/10.1007/s12065-021-00649-z

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