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Beyond LLM-GA: Secure Fluid Antenna Systems with ReEvo-Designed Memetic Algorithm
Hanyong Xu, Zhaolai Dang, Tong Zhang
Intelligence
Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 94%
Last extracted: 10/11/2026, 4:01:25 AM
Summary
This paper proposes a ReEvo-designed memetic algorithm to solve the secure port selection and beamforming problem in Fluid Antenna Systems (FAS). Unlike previous Large Language Model-assisted Genetic Algorithms (LLM-GAs) that only design crossover or mutation operators, this method uses an LLM (DeepSeek Reasoner) to offline-evolve dedicated crossover, mutation, and local-search operators. These operators are embedded into a memetic search framework that optimizes for secure sum-rate using a secure Weighted Minimum Mean-Square Error (WMMSE) beamforming procedure, requiring no online LLM queries. Simulation results demonstrate that the proposed algorithm achieves a higher secure sum-rate compared to conventional GAs and state-of-the-art LLM-GAs.
Entities (10)
Relation Signals (9)
ReEvo-designed Memetic Algorithm → optimizes → Secure Sum-Rate
confidence 96% · Simulation results... demonstrate that our proposed algorithm achieves a higher secure sum-rate...
ReEvo-designed Memetic Algorithm → uses → Crossover Operator
confidence 95% · our algorithm leverages an LLM to evolve dedicated crossover... operators offline.
ReEvo-designed Memetic Algorithm → uses → Mutation Operator
confidence 95% · our algorithm leverages an LLM to evolve dedicated... mutation... operators offline.
ReEvo-designed Memetic Algorithm → uses → Local-Search Operator
confidence 95% · our algorithm leverages an LLM to evolve dedicated... local-search operators offline.
ReEvo-designed Memetic Algorithm → employs → Secure WMMSE Beamforming
confidence 94% · Each candidate port subset is scored by its achievable secure sum rate, computed via a secure weighted minimum mean-square error (WMMSE) beamforming procedure.
ReEvo-designed Memetic Algorithm → solves → Fluid Antenna Systems (FAS)
confidence 94% · we propose a ReEvo-designed memetic optimizer... for secure port selection in downlink multiuser FASs
ReEvo-designed Memetic Algorithm → outperforms → LLM-GA
confidence 93% · outperforms state-of-the-art LLM-GAs in terms of secure sum-rate.
→ →
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Abstract
Abstract:Fluid antenna systems (FASs) offer significant spatial flexibility, yet securing them against eavesdropping is critical for practical FAS deployment in military, satellite, and internet-of-things networks. Although large language model (LLM)-assisted genetic algorithms (LLM-GAs) can address this secure FAS port selection problem, whether further algorithmic improvement is possible warrants deeper investigation. To this end, we propose a memetic algorithm based on reflective evolution (ReEvo). Unlike the state-of-the-art LLM-GAs, which design only crossover or mutation operators with an LLM, our algorithm leverages an LLM to evolve dedicated crossover, mutation, and local-search operators offline. These operators are then embedded into a memetic search framework, thereby obviating any online LLM queries during execution. Simulation results at equal generation counts demonstrate that our proposed algorithm achieves a higher secure sum-rate than the conventional GA and the state-of-the-art LLM-GAs.
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- Source: https://arxiv.org/abs/2610.10235v1
- Canonical: https://arxiv.org/abs/2610.10235v1
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Beyond LLM-GA: Secure Fluid Antenna Systems with ReEvo-Designed Memetic Algorithm Hanyong Xu Zhaolai Dang Tong Zhang †thanks: This work was supported in part by the National Natural Science Foundation of China under Grant 62401229.†thanks: H. Xu and Z. Dang are with the School of Information, Harbin Institute of Technology, Shenzhen, Shenzhen 518055, China (e-mail: 2025311252, 2025310700@stu.hit.edu.cn).†thanks: T. Zhang is with Guangdong Provincial Key Laboratory of Aerospace Communication and Networking Technology, Harbin Institute of Technology, Shenzhen, 518055, China (e-mail: tongzhang@hit.edu.cn). Abstract Fluid antenna systems (FASs) offer significant spatial flexibility, yet securing them against eavesdropping is critical for practical FAS deployment in military, satellite, and internet-of-things networks. Although large language model (LLM)-assisted genetic algorithms (LLM-GAs) can address this secure FAS port selection problem, whether further algorithmic improvement is possible warrants deeper investigation. To this end, we propose a memetic algorithm based on reflective evolution (ReEvo). Unlike the state-of-the-art LLM-GAs, which design only crossover or mutation operators with an LLM, our algorithm leverages an LLM to evolve dedicated crossover, mutation, and local-search operators offline. These operators are then embedded into a memetic search framework, thereby obviating any online LLM queries during execution. Simulation results at equal generation counts demonstrate that our proposed algorithm achieves a higher secure sum-rate than the conventional GA and the state-of-the-art LLM-GAs. Index Terms: Fluid antenna system, large language model, memetic algorithm, physical-layer security. I Introduction The ever-increasing demand for high data rates and massive connectivity in next-generation wireless networks calls for new degrees of freedom to enhance spectral efficiency and link reliability. To this end, fluid antenna systems (FASs) enable antenna port selection over a dense aperture, improving signal strength, interference suppression, and spatial diversity without extra radio frequency (RF) chains [1, 2, 3]. Unfortunately, joint port selection and beamforming, if optimally designed, holds the key to fully unlocking the potential of FAS, yet it poses a mixed-integer nonconvex problem that is computationally challenging [4, 5, 6]. Securing FAS wireless communications against passive eavesdropping poses a distinct and formidable challenge. This, combined with the need to jointly optimize discrete port selections and continuous beamforming vectors, significantly complicates the design, as the secrecy objective is nonconvex and intricately coupled with multiuser interference and power limitations. Analytical studies characterize secrecy capacity, outage probability, and the impact of spatial channel asymmetry between legitimate users and eavesdroppers [7] and [8]. Recent works jointly optimize beamforming and antenna positions in FAS-aided non-orthogonal multiple access (NOMA) systems [9], or use penalty and majorization–minimization procedures for secure and covert links [10]. However, none of the above works has fully addressed the secure port selection problem. Large language models (LLMs) have recently been used to address the port selection/antenna position selection problem [11, 12, 13, 14]. In particular, Wang et al. [13] applied reflective evolution (ReEvo) [15] to a binary-genetic algorithm (GA) crossover for power minimization. Their crossover uses population fitness, elite-port frequencies, and port co-occurrences, with conventional selection, mutation, elitism, and repair. The learned crossover is generated offline, has no explicit local-search stage, and is not evaluated with a secrecy objective. In addition, Zheng et al. [14] proposed an efficient LLM-GA algorithm, which combines a frequency-based crossover with an LLM-designed one-port mutation. Its exchange probability and displacement range are prescribed, after which standard GA selection, elitism, and repair are applied; the target is nonsecure multiuser performance such as max-min signal-to-interference-plus-noise ratio (SINR). Thus, [13] learns only the crossover operator, whereas [14] learns only the mutation operator. Port prediction has also been investigated in [16]. TABLE I: Comparison of the LLM-designed operators in [13], [14], and the proposed algorithm. Operator class Ref. [13] Ref. [14] Proposed (crossover only) (mutation only) (memetic) LLM-Designed Mutation No Yes Yes LLM-Designed Crossover Yes No Yes LLM-Designed Local Search No No Yes In this paper, we propose a ReEvo-designed memetic optimizer [17] for secure port selection in downlink multiuser FASs, which outperforms state-of-the-art LLM-GAs in terms of secure sum-rate. Each candidate port subset is scored by its achievable secure sum rate, computed via a secure weighted minimum mean-square error (WMMSE) beamforming procedure. Under this secrecy-driven fitness, ReEvo successively evolves three complementary operators offline, namely crossover, mutation, and local-search. The learned crossover exploits elite-port statistics and grid topology; the mutation performs feasible one-in-one-out swaps at both local and global scales; and the local-search operator generates four complementary one-swap neighbors per offspring. All three operators are frozen after offline evolution and embedded into a memetic search framework, requiring no LLM queries during online execution. Unlike prior LLM-GAs that design only crossover or mutation operators without security consideration, our method covers all discrete search stages, explicitly accounts for eavesdropper leakage, and performs systematic local refinement, all under the same secrecy-aware fitness. Table I contrasts the LLM-designed operators of [13] and [14] with those of the proposed algorithm. Simulation results demonstrate that our proposed algorithm achieves a higher secure sum-rate than the conventional GA and the state-of-the-art LLM-GAs. I System Model and Problem Formulation We first define the system model, and then formulate joint secure port selection and beamforming Problem. I-A System Model We consider a multiuser downlink fluid antenna system (FAS) in which a base station (BS) serves K single-antenna users in the presence of a passive single-antenna eavesdropper. Let ≜1,…,KK \1,…,K\ denote the user index set. The BS has a rectangular FAS aperture of dimensions λWx×λWyλ W_x×λ W_y, where λ=c/fcλ=c/f_c and Wx,WyW_x,W_y are normalized by the carrier wavelength. A uniform Nx×NyN_x× N_y grid provides Ns=NxNyN_s=N_xN_y candidate ports, of which exactly nsn_s are active. Let (nx,i,ny,i)(n_x,i,n_y,i) denote the two-dimensional grid index of port i, where 1≤nx,i≤Nx1≤ n_x,i≤ N_x, 1≤ny,i≤Ny1≤ n_y,i≤ N_y, and i=ny,i+(nx,i−1)Nyi=n_y,i+(n_x,i-1)N_y. The physical distance between ports i and j is di,j=(nx,i−nx,jNx−1λWx)2+(ny,i−ny,jNy−1λWy)2d_i,j= ( n_x,i-n_x,jN_x-1λ W_x )^2+ ( n_y,i-n_y,jN_y-1λ W_y )^2. Consistent with the channel generator, define Ji,j=j0(2πdi,j/λ)J_i,j=j_0(2π d_i,j/λ), where j0(x)=sin(x)/xj_0(x)= (x)/x and j0(0)=1j_0(0)=1. This isotropic three-dimensional model differs from the cylindrical Bessel correlation in Jakes’ model [18]. The spatial correlation matrix is =[J1,1J1,2⋯J1,NsJ2,1J2,2⋯J2,Ns⋱JNs,1JNs,2⋯JNs,Ns]∈ℝNs×Ns. J= bmatrixJ_1,1&J_1,2&·s&J_1,N_s\\ J_2,1&J_2,2&·s&J_2,N_s\\ & & & \\ J_N_s,1&J_N_s,2&·s&J_N_s,N_s bmatrix ^N_s× N_s. (1) Because J is real and symmetric, write its eigendecomposition as =T J= U U^T, where U is real and orthogonal. Let rkr_k and rer_e denote the BS-to-user and BS-to-eavesdropper distances, respectively. We model the large-scale power gains by βk=β0(rk/r0)−α _k= _0(r_k/r_0)^-α for k∈k and βe=β0(re/r0)−α _e= _0(r_e/r_0)^-α, where β0 _0 is the reference gain at distance r0r_0 and α is the path-loss exponent. The channel vector of user k∈k is kH=βkkH1/2T,k∈, h_k^H= _k\, g_k^H ^1/2 U^T, k , (2) where k∼(,Ns) g_k ( 0, I_N_s) for k∈k . The eavesdropper channel is eH=βeeH1/2T h_e^H= _e\, g_e^H ^1/2 U^T (3) where e∼(,Ns) g_e ( 0, I_N_s). Independent Gaussian vectors are drawn for the users and the eavesdropper, and are mapped through the same correlation matrix; hence, the links share spatial correlation but have independent small-scale fading. Shadowing is omitted. As an upper-bound benchmark, we assume that the BS has perfect instantaneous channel state information (CSI) for every link; eavesdropper CSI may have been acquired while that terminal was previously active. The channels remain quasi-static within each optimization run, so all candidate configurations share the same propagation state. Robust design under imperfect or delayed CSI is outside the present scope. Let i e_i denote the iith column of Ns I_N_s. When nsn_s distinct ports with indices m1,…,mnsm_1,…,m_n_s are activated, their port selection matrix is defined as ns≜[m1,…,mns]∈ℝNs×ns E_n_s [ e_m_1,…, e_m_n_s] ^N_s× n_s. Each column of ns E_n_s selects one physical port, so feasibility requires ns(:,ℓ)∈1,…,Ns,ℓ=1,…,ns. E_n_s(:, )∈\ e_1,…, e_N_s\, =1,…,n_s. (4) and the selected ports must be distinct: ns(:,ℓ)≠ns(:,q),ℓ≠q. E_n_s(:, )≠ E_n_s(:,q), ≠ q. (5) Together, these constraints activate exactly nsn_s distinct ports. Define the effective channel vectors ¯k=nsHk h_k= E_n_s^H h_k and ¯e=nsHe h_e= E_n_s^H h_e. Stacking the user channels gives ¯=[¯1,…,¯K]H∈ℂK×ns H=[ h_1,…, h_K]^H ^K× n_s. The BS jointly designs the port selection matrix ns E_n_s and the beamforming matrix =[1,…,K] W=[ w_1,…, w_K], where k∈ℂns×1 w_k ^n_s× 1 is the beamformer for legitimate user k∈k . Let d=[x1,…,xK]T x_d=[x_1,…,x_K]^T collect the unit-power data symbols, i.e., [|xk|2]=1E[|x_k|^2]=1. The transmitted signal is =nsd=∑k∈nskxk, x= E_n_s W x_d= _k E_n_s w_kx_k, (6) Because the columns of ns E_n_s are orthonormal, the transmit-power constraint becomes ‖ns‖F2=‖F2=∑k∈‖k‖22≤Pmax.\| E_n_s W\|_F^2=\| W\|_F^2= _k \| w_k\|_2^2≤ P_ . (7) The receiver noises satisfy nk∼(0,σk2)n_k (0, _k^2) and ne∼(0,σe2)n_e (0, _e^2). The received signals are yk y_k =kHnskxk+∑j≠kkHnsjxj+nk, = h_k^H E_n_s w_kx_k+ _j≠ k h_k^H E_n_s w_jx_j+n_k, (8a) ye y_e =∑k∈eHnskxk+ne. = _k h_e^H E_n_s w_kx_k+n_e. (8b) Under single-user decoding, the eavesdropper treats all other streams as interference. The resulting SINRs are γk _k =|kHnsk|2∑j∈∖k|kHnsj|2+σk2,k∈, = | h_k^H E_n_s w_k|^2 _j \k\| h_k^H E_n_s w_j|^2+ _k^2, k , (9a) γe,k _e,k =|eHnsk|2∑j∈∖k|eHnsj|2+σe2,k∈. = | h_e^H E_n_s w_k|^2 _j \k\| h_e^H E_n_s w_j|^2+ _e^2, k . (9b) Accordingly, the achievable secrecy rate of user k is Rks=[log2(1+γk)−log2(1+γe,k)]+,k∈,R^s_k= [ _2(1+ _k)- _2(1+ _e,k) ]^+, k , (10) following the standard wiretap-rate construction [19]. I-B Joint Secure Port Selection and Beamforming Problem Mathematically, the joint secure port selection and beamforming problem for the downlink multiuser FAS is formulated as follows: P1: 1: maxns,∑k∈Rks(ns,) max_ E_n_s,\, W _k R^s_k( E_n_s, W) s.t.(4),(5),and(7). .t. eq:port-membership,\ eq:port-distinct,\ and\ eq:power-constraint. Physically, selecting a port changes the sampled channels of every user and of the eavesdropper at the same time. The objective therefore rewards ports that strengthen the desired links while suppressing multiuser interference and information leakage, subject to the total transmit power. Since the port-selection constraints introduce a combinatorial discrete space and the secrecy sum-rate is nonlinear in the selection and beamforming variables, Problem P1 is a nonlinear mixed-integer nonconvex program. I ReEvo-Designed Memetic Algorithm To solve Problem P1, we develop a ReEvo-designed memetic algorithm comprising an offline LLM-driven operator design stage and an online memetic search stage that requires no LLM application programming interface (API) calls. In the offline stage, ReEvo evolves three complementary discrete operators (crossover, mutation, and local search) under a secrecy-driven fitness evaluated via secure WMMSE beamforming. In the online stage, each candidate port subset generated by the frozen operators is scored via secure WMMSE beamforming; the memetic search then evolves toward higher secure sum-rates without any LLM queries. Fig. 1 illustrates the overall architecture and highlights the distinction between our method and prior LLM-GAs that design only a crossover operator [13] or only a mutation operator [14]. Fig. 1: Flowchart comparison of [13] and [14] with the proposed algorithm. I-A Secure WMMSE Beamforming For a fixed ns E_n_s, we use a safeguarded WMMSE-based procedure [20]. Initialize =¯H(¯¯H+10−6)−1 V= H^H( H H^H+10^-6 I)^-1 and (0)=Pmax/‖F W^(0)= P_ V/\| V\|_F; if the solve fails, use =¯H V= H^H. With the scalar estimate x^k=uk∗yk x_k=u_k^*y_k, the user’s minimum mean-square error (MMSE) receiver, mean-square error (MSE), and weight are Tk T_k =∑j∈|¯kHj|2+σk2, = _j | h_k^H w_j|^2+ _k^2, (11a) uk u_k =¯kHkTk,εk=1−|¯kHk|2Tk, = h_k^H w_kT_k, _k=1- | h_k^H w_k|^2T_k, (11b) qk q_k =εk−1. = _k^-1. (11c) When the eavesdropper decodes stream k and treats the remaining streams as interference, its corresponding variables are Te T_e =∑j∈|¯eHj|2+σe2, = _j | h_e^H w_j|^2+ _e^2, (12a) ue,k u_e,k =¯eHkTe,εe,k=1−|¯eHk|2Te, = h_e^H w_kT_e, _e,k=1- | h_e^H w_k|^2T_e, (12b) qe,k q_e,k =εe,k−1. = _e,k^-1. (12c) For an arbitrary receiver u, the MSE is ek(u,)=|u|2Tk−2Reu∗¯kHk+1e_k(u, W)=|u|^2T_k-2Re\u^* h_k^H w_k\+1. The rate identity is ln(1+γk)=maxu∈ℂ,q>0lnq−qek+1 (1+ _k)= _u ,q>0\ q-qe_k+1\, attained at (11). For the eavesdropper, −ln(1+γe,k)=minu∈ℂ,q>0qe,k−lnq−1- (1+ _e,k)= _u ,q>0\qe_e,k- q-1\, attained at (12). Frozen auxiliary variables lower-bound the legitimate rate but upper-bound the negative eavesdropper rate. Thus the following linearization yields a trial model for the unclipped rate difference, not a guaranteed secrecy-rate lower bound. Omitting the common 1/ln21/ 2 factor and constants gives ~=argmax‖F2≤Pmax−tr(H)+2Retr(H), W= _\| W\|_F^2≤ P_ -tr( W^H A W)+2Re\tr( B^H W)\, (13) where A =∑k∈qk|uk|2¯k¯kH, = _k q_k|u_k|^2 h_k h_k^H, (14a) k b_k =qkuk¯k+ce¯e¯eHk(t)−qe,kue,k¯e, =q_ku_k h_k+c_e h_e h_e^H w_k^(t)-q_e,ku_e,k h_e, (14b) ce c_e =∑j∈qe,j|ue,j|2,=[1,…,K]. = _j q_e,j|u_e,j|^2, B=[ b_1,…, b_K]. (14c) Specifically, for the positive quadratic kHek w_k^H C_e w_k, where e=ce¯e¯eH⪰0 C_e=c_e h_e h_e^H 0, convexity gives kHek≥2Re(k(t))Hek−(k(t))Hek(t) w_k^H C_e w_k≥ 2Re\( w_k^(t))^H C_e w_k\-( w_k^(t))^H C_e w_k^(t). This affine minorization produces the ek(t) C_e w_k^(t) term in (14b). The Lagrangian stationarity condition of (13) is (+μ)~=( A+μ I) W= B, and hence, when nonsingular, we have ~=(+μ)−1. W=( A+μ I)^-1 B. (15) Since ⪰0 A 0, the KKT conditions solve (13) globally: μ=0μ=0 for a feasible unconstrained solution, otherwise bisection enforces ‖~‖F2=Pmax\| W\|_F^2=P_ with μ>0μ>0. The implementation adds 10−1010^-10 I if the zero-multiplier linear solve fails. For each trial (η)=(1−η)(t)+η~ W(η)=(1-η) W^(t)+η W, evaluate ∑k∈Rks _k R_k^s using the per-user secrecy rates in (10). A negative per-user difference contributes zero, while that stream still causes interference. The unclipped trial model retains all streams. Start at η=1η=1 and halve it for at most 20 trials; retain the incumbent and stop if none is accepted. The acceptance tolerance is 10−1010^-10; termination also occurs after 30 iterations or improvement below 10−6max(1,|∑k∈Rks|)10^-6 (1,| _k R_k^s|). In exact arithmetic, accepting only nondecreasing steps preserves feasibility and gives 0≤∑k∈Rks≤∑klog2(1+Pmax‖¯k‖22σk2).0≤ _k R_k^s≤ _k _2 (1+ P_ \| h_k\|_2^2 _k^2 ). Thus exact monotone objective values converge if continued indefinitely; this is not a beamformer or stationary-point convergence guarantee. I-B ReEvo-Designed Memetic Port Search We encode a port subset as a binary chromosome ∈0,1Ns s∈\0,1\^N_s satisfying T=ns 1^T s=n_s. Following [15], the LLM acts as a hyper-heuristic. Let =c,m,lQ=\c,m,l\ denote the crossover, mutation, and local-search operator classes, respectively. DeepSeek Reasoner evolves each class separately. For class q, each program χq _q is an individual in population Φq _q. Its meta-fitness is the best secure sum-rate attained when an inner GA-based search uses χq _q on the fixed training channel set: Rsec() R_ sec( s) =∑k∈Rks(), = _k R_k^s( s), (16a) Fq(χq) F_q( _q) =max∈GAq(χq)Rsec(), = _ s _q( _q)R_ sec( s), (16b) Because (16) includes secure WMMSE optimization, programs are selected by the target secrecy objective rather than a surrogate port score. The three operator classes receive feasible binary chromosomes and grid indices; crossover also receives population fitness and ranks. Crossover combines two parents, mutation performs a one-in–one-out swap, and local search generates four neighbors: nearby, long-distance, same-row/column, and crowded-to-sparse relocation. Returned chromosomes are repaired to contain exactly nsn_s active ports; invalid programs are discarded. All fitness evaluations use the same training channels, beamformer initialization, and stopping rule. Algorithm 1 Offline LLM operator design and API-free secure FAS optimization 1: for q∈c,m,lq∈\c,m,l\ in order do 2: Initialize program population Φq _q from seed and LLM code. 3: while fewer than NevalN_ eval programs have been evaluated do 4: Evaluate training fitness FqF_q by secure WMMSE. 5: Reflect on higher/lower-fitness code; generate programs and update Φq _q. 6: end while 7: Freeze the best program χq∗ _q^* by training fitness. 8: end for 9: Initialize P feasible chromosomes; evaluate and cache fitness and beamformers. 10: for g=1,…,Gg=1,…,G do 11: Preserve E elites and select parents for P−EP-E children. 12: Apply χc∗ _c^* and χm∗ _m^*; repair cardinality. 13: Apply χl∗ _l^* to create NlN_l neighbors per child. 14: Score uncached candidates by secure WMMSE. 15: Retain the best P−EP-E candidates with the E elites. 16: end for 17: return Best chromosome and its cached beamformer. Algorithm 1 summarizes the procedure. Crossover is trained with conventional mutation and no local search; mutation is trained with crossover fixed; local search is trained with both fixed. Programs are selected by training fitness and then checked on separate validation channels. During online execution, the three frozen operators generate offspring and neighbors, while caching and elitist replacement control the WMMSE evaluations. IV Simulations Table I summarizes the simulation parameters. The power sweep uses normalized gains βk=βe=1 _k= _e=1 and noise variances σk2=σe2=1 _k^2= _e^2=1. Equivalently, rk=re=r0r_k=r_e=r_0, β0=1 _0=1, and the path-loss exponent cancels. Each realization includes all K user channels and one eavesdropper channel. All methods share test channels, initial populations, and random seeds at each power. Offline ReEvo uses DeepSeek to generate operator code with 1010 programs in the population. Fitness uses 1010 training channels; selected programs are checked on 2020 disjoint validation channels without reranking. Training and validation searches use 2020 and 50 generations at power 2.52.5, respectively. Final testing uses 2020 separate channels and 2020 random seeds; training and validation use 1010 and 2020 channel realizations, respectively. The online optimizer uses frozen code, with no trainable neural-network layers or hidden dimensions and no LLM calls. Fig. 2: Mean secure sum-rate versus total transmit power. (a) 1.0 W (b) 2.0 W (c) 3.0 W (d) 4.0 W (e) 5.0 W Fig. 3: Secure sum-rate convergence for five total transmit power levels. Throughout, the reported rate is the total secrecy rate summed over users and averaged over test channels, never divided by K. The same test channels are reused across all total transmit power levels. The error bars show one sample standard deviation of the 20 per-channel total rates. TABLE I: Simulation parameters. Parameter Setting Grid / aperture 20×2020× 20 / 0.5×0.50.5× 0.5 m2 Carrier frequency 3.43.4 GHz Users / eavesdropper K=10K=10 / 1 Active ports ns=10n_s=10 Distances / path loss rk=re=r0r_k=r_e=r_0; βk=βe=1 _k= _e=1 Noise variance σk2=σe2=1 _k^2= _e^2=1 (normalized) Transmit power Pmax∈1,2,3,4,5P_ ∈\1,2,3,4,5\ W Population / elites P=20P=20 / E=4E=4 Offspring / generations 16 / 100 Mutation probability 0.2 Operator train / validation 10 / 20 disjoint channels Test channels / random seeds 20 paired / 20 seeds LLM / programs DeepSeek / 10-program population Fig. 2 shows that the secure sum-rate of all four methods increases as PmaxP_ grows from 11 to 55 W, with the proposed algorithm remaining the highest at every point. At 1 W, it achieves 11.42311.423 bit/s/Hz, corresponding to gains of 7.6%7.6\%, approximately 6%6\%, and approximately 4%4\% over GA, LLM-GA-crossover [13], and LLM-GA-mutation [14], respectively. At 5 W, it achieves 23.61123.611 bit/s/Hz, yielding gains of 8.2%8.2\%, approximately 5%5\%, and approximately 4%4\% over the same three baselines. The two LLM-GA baselines consistently lie between GA and the proposed algorithm, with visibly overlapping error bars at some operating points. A possible explanation is that elite-aware recombination preserves useful spatial patterns, while local and global exchanges explore the tradeoffs among signal strength, interference, and leakage. This ordering holds at equal generation counts, though the additional local-search evaluations may particularly account for the gains obtained by the proposed algorithm. Note that each operating point plotted in Fig. 2 is the generation-100100 terminal value of the corresponding convergence curve in Fig. 3; that is, Fig. 2 summarizes the final (generation-100100) data of Fig. 3 as a function of transmit power. Fig. 3 shows secure sum-rate convergence over 100100 generations. The proposed algorithm separates from the baselines early and stays ahead in all five power panels, while all curves gradually flatten as the populations approach stable incumbents. The terminal values at generation 100100 correspond to the respective operating-point results summarized in Fig. 2, linking the convergence endpoint to the power-sweep comparison. Local search evaluates additional one-swap neighbors, so these curves do not establish faster convergence in runtime or evaluation count. V Conclusion This paper presented a ReEvo-designed memetic optimizer for joint port selection and secure beamforming in multiuser fluid antenna systems. An LLM evolves dedicated crossover, mutation, and local-search operators offline under a secrecy-driven fitness, and the frozen programs incur no online LLM-query overhead. For each candidate port configuration, the beamformer is optimized by secure WMMSE. 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